Aberration--A shift of direction (or location) from the one predicted by a simple calculation. Abberation of starlight--a small shift in the observed position of stars, due to the Earth's orbital velocity.

Absolute temperature--temperature in degrees centigrade (also known in this case as "degrees Kelvin" K°) measured from the absolute zero of -273.1° C, the temperature at which all atomic and molecular motions are expected to cease.

Acceleration -- Rate at which velocity changes (negative acceleration--slowing down--is also known as deceleration). Acceleration is a vector quantity.

Angle of attack--in the theory of airplane wings, the angle between the wing profile (roughly, measured along its bottom) and the wing's motion relative to the surrounding air.

Anomaly -- in orbital motion, one of the angles which gauges the motion of a planet or satellite around its orbit, increasing by 360^o every revolution. The true anomaly f equals the polar angle f in polar coordinates with origin at the center of the motion (e.g. Sun or Earth). The mean anomaly is a related angle which increases in direct proportion to the time elapsed (the true anomaly does not--the motion is faster near the center). The eccentric anomaly is an auxiliary angle used in relating true anomaly (which is observed) and mean anomaly (which is calculated).

Aphelion -- the point in a planet's orbit furthest from the Sun (Helios is Greek for Sun). See perihelion, apogee.

Apogee -- the point in a satellite's orbit furthest away from Earth (see perigee, aphelion).

Apparent motion -- The observed motion of a heavenly body across the celestial sphere, assuming the Earth is at the sphere's center and is standing still.

Atlas -- An early liquid-fueled rocket, used by US astronauts and still in use for unmanned launches. Because of its lightweight construction it uses no staging, but only drops two of its engines.

Azimuth and elevation -- Two angles which give the direction of a surveyor's telescope (theodolite). Azimuth is the rotation angle of the telescope around a vertical axis, measured (counterclockwise from above) from due north, a direction whose azimuth is zero degrees. Elevation is the angle the telescope is lifted above the horizontal plane.
[In 3-dimensional polar coordinates centered on the instrument, azimuth is f, elevation is 90^o-q; the direction of straight up has elevation 90^o but q = 0].

Ballistic pendulum -- A device often used for measuring the energy of motion of a bullet, adapted by Goddard to measure the thrust of small rockets with various nozzles. For a bullet is is a heavy block of wood or sand-filled box, hanging by a string; the bullet is weighed, then fired into the pendulum, and the distance the pendulum rises allows the bullet's velocity to be deduced.

Angle of attack

Binomial Theorem--A formula first derived by Newton, giving (1+z) ^a, the result of raising 1 + z to an arbitrary power a, as a sequence of form

where the terms A_i (i = 1,2,3...) are given by the formula and where a can be positive, negative, fractional or whole. When the magnitude of z is less than 1, the higher powers get smaller and smaller and the formula can be made as precise as one wishes by including enough of them (for z of small magnitude, 1-2 terms are sufficient), although the result is never exact. For magnitudes of z equal to 1 or more, the formula only holds for values of a which are positive whole numbers. In that case, for any z, the result is exact and the sum of terms with powers of z does not go on arbitrarily but ends with z ^a.

Black body radiation--light or other electromagnetic radiation emitted due to heat by a solid, liquid or dense gas, with no color of its own (hence "black"). Distinguished by a continuous distribution of spectral color, with its peak of emission shifting towards shorter wavelengths as the temperature increases--e.g. infra-red for a warm hand, red for a hot iron bar, yellow for the glowing filament in a lightbulb.

Black hole--an extremely compact object, collapsed by gravity which has overcome electric and nuclear forces. It is believed that stars appreciably larger than the Sun, once they have exhausted all their nuclear fuel, collapse to form black holes: they are "black" because no light escapes their intense gravity. Material attracted to a black hole, though, gains enormous energy and can radiate part of it before being swallowed up. Some astronomers believe that enormously massive black holes exist in the center of our galaxy and of other galaxies.

Bulge of the Earth The extra extension of the Earth's equator, caused by the centrifugal force of the Earth's rotation, which slightly flattens the spherical shape of the Earth. The Earth's bulge causes the planes of satellite orbits inclined to the equator (but not polar) to slowly rotate around the Earth's axis.

Buoyancy--The lifting force acting in a fluid on bodies and regions less dense than their surroundings. The buoyancy of hot air--the force that also lifts hot-air balloons--is the main cause of weather-related flows in the Earth's atmosphere. Also see convection.

Calendar -- A system of marking days of the year, usually devised in a way to give each date a fixed place in the cycle of seasons.

Calorie -- Unit used in measuring the energy of heat or chemical energy. A "small" calorie is the heat needed to warm up one gram of water by 1 degree centigrade and equals about 4.18 joule. A "kilocalorie" or "big calorie" equals 1000 calories and is the unit usually used in describing the energy content of food.

Cartesian coordinates -- A system of uniquely marking the position of a point on a plane [or in 3-dimensional space] -- by 2 [3] numbers (its "cartesian coordinates") giving its distances from 2 [3] mutually perpendicular lines ("cartesian axes"). The distances and the axes to which they are parallel are usually marked (x,y) in a plane and (x,y,z) in space; the "origin" is the point at which the axes intersect.

Celestial coordinates -- see "right ascension and declination."

Celestial pole -- One of the two points in the sky around which the celestial sphere seems to rotate.

Celestial sphere -- An immense sphere surrounding Earth, to which the fixed stars seen at night appear to be attached. Although strictly speaking such a sphere does not exist, it is often used as a convenient tool for mapping the position of stars and other heavenly bodies. In a similar way, although it is clear that the apparent rotation of the celestial sphere is really due to the Earth rotating around its axis, that rotation is often used for convenient description of apparent motions such as the rising and setting of stars.

Center of gravity -- (CG), also known (more precisely) as center of mass. In a distributed mass, an appropriately defined "average location" of its parts. If the mass is a rigid (=undeforming) body subject to the earth's gravity, then if it is supported at the CG, it will stay balanced and not tilt to any side.
 In a system subject only to internal forces, the center of gravity always stays in the same spot; hence the Earth-Moon system rotates around its mutual center of gravity (not around the Earth's center), and a rocket flies forwards when it ejects a high-speed stream of gas backwards.

Centrifugal force -- A force which must be included in the calculation of equilibria between forces in a rotating frame of reference (e.g. rotating carrousel, rotating space station, rotating Earth). In the rotating frame, the forces on a body of mass m are in equilibrium (as evidenced by the body staying at the same place) only if all forces acting on it, plus a "centrifugal force" mv²/R directed away from the center of rotation, add up to zero. See Coriolis force.

Centripetal acceleration -- The acceleration associated with motion around a circle, directed to the center of the circle.

Centripetal force -- The force making a motion is a circle possible, always directed to the center of the circle. To make a (small) object of mass m move with velocity v around a circle of radius R, a centripetal force of magnitude mv²/R must be applied.

Chromosphere--a reddish layer in the Sun´s atmosphere, the transition between the photosphere and the corona

CME--see coronal mass ejection.

Color--a quality of light, depending on its wavelength. Spectral color of an emission of light is its place in the rainbow spectrum. Perceived color (or visual color) is the quality of light emission as conveyed by the human eye, combining the impressions of 3 types of light-sensitive cells which the eye contains. Perceived color can be the response to certain combinations of spectral colors, e.g. brown responds to green and red (or blue, yellow and red).

Comet--a body of dust, frozen water and gases falling sunward from the outer regions of the solar system. Comets become visible when they approach the Sun, as sunlight evaporates their upper layers and creates long tails of dust and ions. Comets are believed to be remnants of the formation of the solar system; some of them (like Halley's comet) are diverted by the attraction of planets into orbits of relatively short periods around the Sun.

Component of vector--When a vector is resolved into a sum of vectors in specified directions, each of those vector is the component of the given vector in the specified direction.

Conic Sections -- The family of curves generated by planes intersecting with a cone. Several cases are distinguished, depending on the angle between the plane and the axis of the cone. Precise definitions exist for each, but in general terms, when the plane is:

--Perpendicular to the axis, the curve is a circle.
--Moderately inclined to the axis, the curve is an ellipse.
--Parallel to one of the straight lines which generate the cone, the curve is a parabola.
--Even more steeply inclined, the curve is a hyperbola.

Conservation of momentum--A fundamental law of motion, equivalent to Newton's laws: in a system of bodies (=objects), the (vector) sum of all momenta cannot change due to any internal interactions.

Constellation -- A named grouping of fixed stars, e.g. Orion or the Big Dipper.

Convection A circulating flow in a fluid, carrying heat away from its source. Convection in the atmosphere carries heat from the sun-warmed ground to higher layers, where it is radiated away into space; the lower levels do not radiate efficiently because of the greenhouse effect. Atmospheric convection is the engine that drives the Earth's weather. Convection is also believed to occur in a certain depth range below the Sun's surface, helping carry away heat from the Sun's core region.

Copernican System -- A theory of planetary motions, proposed by Copernicus, according to which all planets move in circular orbits around the Sun, the ones closer to the Sun moving faster, with the Earth itself a planet orbiting between Venus and Mars.

Coriolis force -- A force which must be included in the calculation of motion in a rotating frame of reference, if the body moves in such a way that its rotation velocity changes. In general, it tends to preserve that part of its velocity. The Coriolis force is responsible for the swirling of hurricanes and large weather systems--for air flowing into a region of low pressure, counterclockwise north of the equator, clockwise south of the equator (reverse directions for air flowing out of a high pressure region). See centrifugal force.

Corona--the outermost layer of the Sun´s atmosphere, visible to the eye during a total solar eclipse; it can also be observed through special filters and best of all, by X-ray cameras aboard satellites. The corona is very hot, up to 1-1.5 million degrees centigrade, and is the source of the solar wind

Coronal hole--an area in the Sun's corona that appears dark when viewed in the far UV or in the long-wavelength end of the x-ray range. Coronal holes seem associated with sources of fast solar wind, probably because their field lines do not curve back to the Sun. Over most of the Sun their shapes are changeable and irregular, but the Sun's polar regions seem to contain "permanent" coronal holes.

Coronal mass ejection (CME)--a huge cloud of hot plasma, occasionally expelled from the Sun. It may accelerate ions and electrons and may travel through interplanetary space as far as the Earth´s orbit and beyond it, often preceded by a shock front. When the shock reaches Earth, a magnetic storm may result.

Crab nebula --a cloud-like nebula observed in the Crab constellation, the remnant of a supernova explosion observed in China in 1054. It contains a very rapidly rotating (and hence, young) pulsar, which is probably the remnant of the supernova. The emissions of radio waves and light from this nebula suggest the presence of high energy particles.

Declination -- See "right ascension and declination"

De Laval nozzle -- A device for efficiently converting the energy of a hot gas to kinetic energy of motion, originally used in some steam turbines and now used in practically all rockets. By constricting the outflow of the gas until it reaches the velocity of sound and then letting it expand again, an extremely fast jet is produced.

Diffraction grating A flat optical surface, transparent or reflecting, ruled with many parallel grooves at precisely spaced distances. The active parts are not the grooves but the flat sections left between them, which act like a large number of precisely spaced slits. The light waves passing those slits resonate with each other in a way which depends on wavelength, causing different wavelengths to be steered in different directions. The overall effect on light containing different wavelengths is like that of a glass prism: the intensity of the light deflected is much smaller than with a prism, but the ability to separate close colors is much better.

Drag--the air resistance encountered by a moving object. Drag is one of the four forces sensed by an airplane, the others being lift, thrust and weight.

Eccentricity -- Number between 0 and 1, gauging the elongation of elliptic orbit. The eccentricity e of the orbital ellipse is one of the "orbital elements" characterizing it.

Ecliptic -- A line around the middle of the celestial sphere, connecting the points occupied by the Sun over the year. The moon and the visible planets also appear to move very close to that line, which cuts the celestial equator at an angle of about 23.5^o . See plane of the ecliptic.

Electromagnetic field (EM field)--the regions of space near electric currents, magnets, broadcasting antennas etc., regions in which electric and magnetic forces may act. Generally the EM field is regarded as a modification of space itself, enabling it to store and transmit energy. See also (below) "electromagnetic wave" and magnetic field.

Electromagnetic wave or "electromagnetic radiation"--a combination of oscillating magnetic and electric fields, spreading in wavelike fashion through space at a speed of about 300 000 km.sec. James Clerk Maxwell's theory in 1864 suggested that light was such a wave, and today we know that such waves include all forms of light--also infra-red and ultra-violet, as well as radio waves, microwaves, x-rays and gamma rays.

Electron--a lightweight particle, carrying a negative electric charge and found in all atoms. Electrons can be energized or even torn from atoms by light and by collisions, and they are responsible for many electric phenomena in solid matter and in plasmas. (About the discovery of the electron in 1897, click here.)

Ellipse -- A closed curve resembling a flattened circle (the shadow of a circle tilted towards the light is an ellipse). May be defined:

1.   As the collection of points whose distances (R1, R2) from two given points (the foci of the ellipse--in singular, focus) add up to the same sum.
   
2.    Or else , in polar coordinates (r,f), as the curve whose points satisfy a relation r = a(1 - e)/(1 + e cosf) where a is the semi-major axis, half the width in the direction through the two foci. One of the foci is then at the origin and e is the eccentricity, a number ranging from 0 (circle) to 1 (parabola).
   
3.    Or else, in cartesian coordinates with the origin halfway between the foci, as the curve of all points (x,y) whose coordinates satisfy (x/a)² + (y/b)² = 1

Energy -- Ability to perform work, i.e. to advance against resistance, for instance lift a body against gravity, or drag it against friction. See also Work.

Epicycle -- A circle around a point which (in the simplest form of Ptolemy's system) moved steadily around the celestial sphere. Greek astronomers proposed that planets moved along epicycles around the Sun or around other points which circled around the sky; later additional corrections were added. The theory of epicycles was the earliest explanation for the irregular apparent motion of the planets--prograde (forward), then retrograde

Equatorial axis -- Among the two mutually perpendicular axes of a telescope, the one that points at the celestial pole. To keep a star in view, the telescope must be rotated around this axis at the same rate as the Earth turns.

Equilibrium (of forces) -- A situation when more than one force acts on a body, but because the sum of forces is zero, no motion results.

Equinox -- the time of the year (around March 21 and September 23) when the position of the Sun in the sky (following the ecliptic) crosses the celestial equator. To a good approximation, the length of the day and night are then equal, and the Sun rises exactly in the east and sets exactly in the west. . Equinox is viewed as the beginning of spring and fall.
   The term is also used for each of the two points on the celestial sphere at which the ecliptic and the celestial equator intersect, i.e. the points occupied by the Sun at equinox.

Explorer 1 -- The first US artificial satellite, launched 31 January 1958 by a 4-stage modified military rocket. Provided the earliest observations of the Earth's radiation belt.

Field The region in which a particular type of force can be observed; depending on the force, one can thus speak of a gravity field, magnetic field, electric field (or when the two are linked by fast oscillations, electromagnetic field) and nuclear field. The laws of physics suggest that fields represent more than a possibility of force being observed, but that they can also transmit energy and momentum, e.g. a light wave is a phenomenon completely defined by fields. For that reason a field is often viewed as a space which was modified by the sources of the force which the field represents.

Firmament -- The celestial sphere and the collection of stars whose position is fixed on it.

First point in Aries -- Another name for the position on the celestial sphere of the vernal equinox. It is called so because in ancient time that point was in Aries, a constellation of the zodiac. It is currently moving from Pisces to Aquarius.

Flare (Solar flare)--a rapid outburst on the Sun, usually in the vicinity of active sunspots. A sudden brightening (only rarely seen without special filters, isolating the red light of hydrogen) may be followed by the signatures of particle acceleration to high energies--x-rays, radio noise and often, a bit later, the arrival of high-energy ions from the Sun. Flares appear to be associated with rapid energy releases high above the photosphere, apparently from the magnetic fields of sunspots. Their link to coronal mass ejections, which may also be powered by magnetic energy, is still unclear.

Fly-by maneuver (or swing-by maneuver) -- The encounter between a moving spacecraft and a moving planet or moon, affecting the spacecraft's motion like an elastic collision (in which no energy is lost to heat). Depending on the details of the encounter, the spacecraft can gain or lose appreciable amounts of energy, and appreciable changes in the direction of its motion can result.
   Fly-by maneuvers with the Moon have been used to reach the L1 Lagrangian point; fly-by maneuvers with the planets have played an essential role in space missions exploring the solar system.

Force -- In mechanics, the cause of motion. It is a vector quantity, in the direction of the acceleration it causes.

Frequency (Often denoted by n, the Greek letter letter nu.) --the number of back-and-forth cycles per second, in a wave or wave-like process. Expressed this way, the frequency is said to be given in units of Hertz (Hz), named after the scientist who first produced and observed radio waves in the lab. Alternating current in homes in the US goes through 60 cycles each second, hence its frequency is 60 Hz; in Europe it is 50 cycles and 50 Hz.

g -- The symbol used for the acceleration due to gravity. At the Earth's surface it averages 9.81 meters/second², directed towards the Earth's center. In common talk, "g forces" are stresses due to acceleration, e.g. on astronauts or payloads. In the same vein, "zero g" is the condition when no acceleration is sensed, because gravity is already fully employed supplying the centripetal force which holds the object in its orbit (or alternatively from the rotating frame of reference, because gravity is fully balanced by the centrifugal force).

Gamma rays--electromagnetic waves of the highest frequencies known, originally discovered as an emission of radioactive substances. See also radioactivity.

Geodesy -- The study of the shape of the Earth, e.g. its deviations from an exact sphere.

Gnomon -- The part of a sundial which casts the shadow, usually a rod or fin pointed at the celestial pole.

Greenhouse effect The surface of the Earth is, on the average, in a state of equilibrium between heating and cooling: that is, on the average, the rate at which sunlight heats it equals the rate at which it loses heat.

If no atmosphere existed, all that loss would take place by infra-red radiation from the surface. The Earth's atmosphere, however, absorbs infra-red, which heats it up and slows down the escape of heat. The same process occurs in glass-covered greenhouses, whose panes let sunlight in but absorb the infra-red emitted back, keeping their interior warm even in winter. For that reason, the process is known as the "greenhouse effect."

Some gases which constitute only a small portion of the atmosphere--water vapor, CO₂ (carbon dioxide) and CH₄ (methane)--are major contributors to the greenhouse effect. Burning coal and oil in the last century has markedly increased the CO₂ content of the atmosphere, which is why some scientists credit the warming trend experienced in the last decades of the 20th century to an increased "greenhouse effect."

Gregorian calendar -- Introduced in 1582 by Pope Gregory the 13th, this calendar modifies the Julian calendar for greater precision, decreeing that century years such as 1900 are not leap years, except if the number of centuries is divisible by 4 (e.g. 2000).

High Energy Particles--charged atomic particles moving rapidly, often at a significant fraction of the speed of light. They can penetrate matter, ionize the material which they traverse and emit energetic photons (e.g. of x-rays). See also solar energetic particles.

Ice ages -- Times in the geological past when great glaciers extended far into Europe, Asia and America.

Inertia -- The property of matter to resists accleration or deceleration, i.e. any motion which is not in a straight line and with constant velocity

Inertial force A force which must be added to the equations of motion when Newton's laws are used in a rotating or otherwise accelerating frame of reference. Some call it a "fictional force" because when the same motion is solved in the frame of the "outside world&," these forces do not appear.

Infra-red radiation (or infra-red light). The region of the electromagnetic spectrum adjacent to that of visible light, but with longer wavelengths (0.65-10 micrometers, typical). Infra-red radiation is emitted by hot objects and by excited molecules. See also greenhouse effect.

Ion--usually, an atom from which one or more electrons have been torn off, leaving a positively charged particle. "Negative ions" are atoms which have acquired one or more extra electrons, and clusters of atoms can also become ions.

Ionization--the process by which a neutral atom, or a cluster of such atoms, becomes an ion. This may occur, for instance, by absorbtion of light ("photoionization") or by a collision with a fast particle ("impact ionization"). Also, certain molecules (such as table salt or sodium chloride, NaCl) are formed by natural ions (like Na+ and Cl-) held together by their electric attraction, and they may fall apart when dissolved in water (which weakens the attraction), enabling the solution to conduct electricity.

Iteration--The repetition of a process of calculation again and again, each time improving the accuracy of the result. For an example of iteration (with "Kepler's Equation") see here

Jet Propulsion Lab -- An outgrowth of the Guggenheim Aeronautical Laboratory of Caltech, in Pasadena (near Los Angeles, California). JPL was the center of US rocket development in World War II and was founded by Theodore Von Karman and Frank Malina. Today it is the focus of NASA's exploration of the planets and of distant space.

Joule -- (pronounced like "jewel"). Unit of energy: the ability to overcome one Newton along 1 meter (assuming g = 10 meter/sec², it is also the energy required to lift 1 kg by 0.1 meters). Named for James Prescott Joule, one of the first to measure the "rate of exchange" between mechanical energy and heat.

Julian Calendar -- Introduced in 46 BC by the Roman ruler Julius Ceasar, this calendar assumes a year of 365.25 days, and uses a cycle in which 3 "ordinary" years of 365 days are followed by a "leap year" with 366 days. Leap years are the years whose number is divisible by 4.

Kepler's laws --
Three laws of planetary motion, published by Johannes Kepler using accurate observations by Tycho Brahe and shown by Isaac Newton to be a direct result of his theory of gravitation and his laws of motion:

1. Planets move in ellipses, with the Sun at one focus.
   
2. The line connecting the planets to the Sun sweeps equal areas in equal times.
   
3. The square of a planet's orbital period is proportional to the cube of its mean distance from the Sun.

Comments:
  1st law: This corrected the simpler model of Copernicus, which assumed circles. More accurately, the focus is at the center of gravity of the Sun and orbiting body (discounting other planets) and non-periodic motions along parabolas or hyperbolas are also possible.
  2nd law: The second law expresses the way a planet speeds up when approaching the Sun and the way it slows down when drawing away.
  3rd law: The third law gives the exact relation by which planets move faster on orbits which are closer to the Sun, e.g. Venus moves faster than Earth (see retrograde motion). For a more precise formulation, "mean distance" should be replaced by semimajor axis.

Kilowatt-hour -- (KWH). The amount of energy supplied by one kilowatt (1000 watt) for 1 hour (3600 seconds), equal to 3 600 000 joule. Electric bills are usually figured by the number of KWHs consumed.

Kinetic energy -- Energy stored in the motion of a mechanical system--e.g. by a rolling car, or a turning flywheel.

Lagrangian points -- In a system of two large bodies (Sun-Earth or Earth-Moon), these are the points where a small third body will keep a fixed position relative to the other two. Named for French astronomer Louis Lagrange (1736-1813) who first studied them and who showed there existed 5 such points. In the Sun-Earth system only two are important, both on the Earth-Sun line--the L1 point 236 Earth radii sunward of Earth, and the L2 point at a similar distance on the night side. The L1 point is a good "early warning" outpost intercepting shocks and particles emitted by the Sun and its vicinity has been occupied by several spacecraft. Altogether five Lagrangian points exist in the Earth-Sun or Earth-Moon system.

Latitude and longitude -- Two angles which specify a location on Earth. If a line is drawn from the Earth's center to the given location, then latitude is the angle between that line and its projection on the plane of the Earth's equator (latitude also equals 90^o- q, where the "co-latitude" q is the angle between the line and the axis of the Earth).

  To define longitude, imagine a large number of planes ("meridional planes") all of which contain the axis of the Earth. Assuming the equator is a circle, divide it into 360 degrees and fractions of degrees: then each meridional plane can be labeled by the angle at its intersection of the equator, and the longitude of a point is the angle f marking the meridional plane on which it sits. Longitude is similar to the angle f of 3-dimensional polar coordinates or to right ascension, but is measured from a zero longitude chosen as the longitude of the Greenwich observatory near London, Great Britain.

Law of areas -- Another name for Kepler's 2nd law.

Lift--the lifting force on a flying object (in particular, a wing or an aircraft), due to its motion relative to the surrounding air. Lift is one of the four forces sensed by an airplane, the others being drag, thrust and weight.

Liquid fueled rockets -- Rockets in which a liquid fuel (kerosene, liquid hydrogen) is combined in a combustion chamber with a liquid oxidizer (usually liquid oxygen, also fuming nitric acid or hydrogen peroxide). Very efficient and controllable, such rockets are generally used in spaceflight. Unlike solid fueled rockets, they can be shut off by remote command, simply by closing off their fuel line.

Magnetic field--a region in which magnetic forces can be observed. See "electromagnetic field," a more general field also including electric forces.

Magnetic field lines--lines in space, used for visually representing magnetic fields. At any point in space, the local field line points in the direction of the magnetic force which an isolated magnetic pole at that point would experience. In a plasma, magnetic field lines also guide the motion of ions and electrons, and direct the flow of some electric currents.

Magnetic storm--A large-scale disturbance of the magnetosphere, often initiated by the arrival of an plasma cloud originating at the Sun.
   A magnetic storm is marked by the injection of an appreciable number of ions from the tail regions of the magnetosphere into ]the near-Earth magnetosphere, a process accompanied by increased auroral displays. The injected particles cause a world-wide drop in the equatorial magnetic field, taking perhaps 12 hours to reach its greatest intensity, followed by a more gradual recovery.

Magnetosphere -- The outermost environment of Earth, dominated by the Earth's magnetic field. The magnetosphere is the site of the radiation belt and many intricate phenomena. See solar wind.

Mass -- The mass of a body can be loosely defined as the amount of matter it contains. That is expressed in two ways:

1. inertial mass, the resistance of the matter to acceleration or deceleration, as given by the factor m in Newton's 2nd law F = ma
   
2. gravitational mass, the force exerted on the matter by gravity ("weight"), given near the surface of Earth by F = mg.

Metonic Calendar -- Named for the Athenian astronomer Meton, it is based on the moon, counting each cycle of the phases of the Moon as one month. Days are kept approximately in step with the seasons by including 7 leap years of 13 months in each cycle of 19 years. Used by the Chinese and the Jews.

Microwaves Electromagnetic waves longer than infra-red but shorter than radio, with typical wavelength 0.1-10 centimeters.

Milankovich theory -- Theory by which ice ages were caused by slow changes of the motion of the Earth in space, including the coupling between the 26 000 year cycle of the precession of the equinoxes and the annual variation of the Earth-Sun distance.

Momentum (plural: momenta). The momentum of a moving object is the product (result of multiplication) of its mass and velocity; like velocity, momentum is a vector. The law of conservation of momentum states that when two or more objects interact--a cannon fires a shell, a rocket shoots out a fast jet of hot gas, a bowling ball scatters a group of pins--the total vector sum of their momenta is unchanged. That, too, is an equivalent formulation of Newton's laws.

Muslim Calendar -- Based on a year of 12 months, each corresponding to one cycle of the Moon, but without the Metonic correction. Its months migrate through the seasons.

Neutron A particle found in the nuclei of atoms, similar to a proton but with no electric charge. Among light nuclei (helium, carbon, nitrogen), the ones that are most stable contain equal numbers of protons and neutrons. In heavier elements, the most stable ones have majority of neutrons, growing with mass. Varieties of nuclei also exist ("isotopes") which have other ratios between their numbers of protons and neutrons, but when the departure from the "most stable ratio" becomes large, neutrons can convert to protons + electrons (or vice versa), producing one form of radioactivity.

Neutron star A star (approximately sun-sized or larger), a remnant of a supernova explosion, in which gravity has caused all matter to collapse to a giant nucleus, composed only of neutrons. The collapse is also expected to greatly amplify any magnetic field present in the pre-collapse star, as well as speed up enormously any rate of rotation. It is believed that pulsars, pulsating radio sources with very precise pulsation periods, are neutron stars of radius about 10 km and rotation period about 1 second. Their magnetic axis spins and beams radio waves, in a way similar to the way a lighthouse beams its light. We detect pulsars when the Earth is in one of the directions swept by the beams.

Newton -- Unit of force, the force which, when applied to one kilogram mass, causes an acceleration of 1 meter/sec².

Newton's laws of motion -- Three laws which form the foundation of classical mechanics, i.e. of the theory of ordinary motions (not motions on an atomic scale, covered by quantum mechanics, and not at velocities close to that of light, covered by relativity). The laws introduce the concepts of force and mass and state (in modern terms)

1. In the absence of forces, an object ("body") at rest stays at rest, and an object moving in a straight line with constant velocity persists in doing so.

2. A (small) body subject to a force accelerates; the acceleration is in the direction of the force and proportional to its magnitude, and inversely proportional to the mass of the body: F = ma.

3. Forces are produced in pairs, in opposite directions and equal magnitudes.

Newton's laws (2) and (3) in Mach's formulation reduce to:" When two small bodies act on each other, they accelerate in opposite directions and the ratio of their accelerations is always the same."

Nuclear forces The short-range forces acting on protons and neutrons in atomic nuclei. Two types actually exist, the "strong force" which holds nuclei together, and the "weak force" which determines the ratio between the numbers of protons and neutrons.

Nuclear fusion The process of releasing energy by combining hydrogen atoms to form helium, or more generally, to combine light nuclei into heavier ones. Nuclear fusion appears to be the source of the energy of the Sun and of stars.

Nucleus (atomic; plural: nuclei). The small concentration of protons and neutrons, positively charged, at the center of atoms. The nuclei of atoms are positively charged and contain by far most of their mass (all but about 0.05% or less).

Orbit -- The path of a body in space, generally under the influence of gravity.

Orbital elements -- Variables which characterize the motion of an orbiting body. For a planet or satellite in an elliptic orbit, 6 orbital elements exist: the semi-major axis gives its size, eccentricity its shape and mean anomaly its position along the orbit, at the given time. The three other elements are three angles which give the orientation in space of its orbital plane, e.g. that plane's inclination (to the plane of the Earth's equator or the ecliptic,depending on choice of coordinates).

Orbital period -- The length of time required for a body to complete one full (closed) orbit.

Particle--in general, a charged component of an atom, that is, an ion or electron.

Perigee -- the point of a satellite's orbit closest to Earth (see perihelion, apogee).

Perihelion -- The point in a planet's orbit when it is closest to the Sun (Helios is Greek for Sun). See aphelion, perigee

Photon --colloquially, a "particle of light." Although light spreads as an electromagnetic wave, it can be created or absorbed only in discrete amounts of energy, known as photons. The energy of a photon is greater the shorter the wavelength--smallest for radio waves, increasingly larger for microwaves, infra-red radiation, visible light and ultra-violet light. It is largest for x-rays and gamma rays.

Photosphere--The layer of the Sun from which all visible light reaches us. The Sun is too hot to have a solid surface and the photosphere consists of a plasma at about 5500 degrees centigrade.

Plane of the ecliptic -- (also called "the ecliptic" for short) The orbital plane of the Earth around the Sun. The line of the ecliptic on the celestial sphere is formed by the intersection of the plane of the ecliptic with that sphere. The reason the major planets and Moon appear in the sky close to the ecliptic is that the solar system is flat, and its orbital planes are very close to each other. We observe their motion (very nearly) edge-on.

Planets -- Celestial bodies such as the Earth which orbit the Sun (and by extension, similar orbiters around distant stars). Counting from the Sun outwards, planets visible to the eye are Mercury, Venus, (Earth), Mars, Jupiter and Saturn. The telescope also sees the more distant Uranus, Neptune and Pluto, as well as smaller asteroids (most of them inside the Jupiter orbit) and Kuiper objects (in the outer solar system). See also retrograde motion

Plasma --a gas containing free ions and electrons, and therefore capable of conducting electric currents. A "partially ionized plasma" such as the Earth's ionosphere is one that also contains neutral atoms.

Polar Coordinates -- An alternative system of marking a point on a plane by its radial distance (r) from an "origin" and a polar angle (f). Polar coordinates in 3-dimensional space use (r) and two polar angles (q,f) giving the direction from the origin to the point.
  When 3-dimensional polar coordinates overlap a cartesian (x,y,z) system, q is the angle between the line to the origin and the z-axis, while f is the angle (counter-clockwise when viewed from +z) between the projection of that line onto the (x,y) plane and the x-axis. Concerning (q,f), see also latitude and longitude, declination and right ascension, azimuth and elevation.

Polaris (Pole Star, North Star) -- A fairly bright star, the last star in the tail (or handle) of the constellation of the Little Dipper (Ursa Minor). Currently located within a fraction of a degree from the celestial north pole, the point around which the celestial sphere appears to rotate. In the northern hemisphere, the direction towards Polaris is very nearly due north.

Potential energy -- Energy stored in the set-up of a mechanical system--e.g. by a weight able to descend (in the presence of gravity), or by a compressed spring.

Power -- The rate at which energy is supplied. See watt.

Precession -- A modern term, derived from the precession of the equinoxes and meaning a motion around a cone of the rotation axis of a spinning body.

Precession of the Equinoxes -- A slow motion of the axis of the Earth around a cone, one cycle in about 26000 years. As a result, the celestial pole moves around a circle in the sky, and in ancient times, for instance, was quite far from Polaris. Discovered by Hipparchus around 130 BC as a slow shift of the vernal equinox around the ecliptic (i.e. around the zodiac).

Prominence A cloud of cooler plasma extending high above the Sun"s visible surface, rising above the photosphere into the corona.

Propeller pitch--the angle at which the propeller blade (or part of it) "bites" into the air, its angle of attack.

Proton --an ion of hydrogen and one of the fundamental building blocks from which atomic nuclei are made.

Ptolemy's System -- The explanation given by ancient Greek astronomers to the motion of planets around the sky, described in a book by the Greek Ptolemy, around 150 AD. It regarded Earth as the center of the universe and assumed the motion of planets was a superposition of circular motions (see epicycles).

Pulsar. See neutron star

Pythagoras, theorem of -- A proved assertion in geometry, that in a right-angled triangle which has sides of length (a, b, c), if c is the long side facing the right angle, then a² + b² = c²

Radiation --a term used for phenomena that spread radially, especially of two:

• In the narrow sense, some type of electromagnetic wave: radio, microwave, light (infra-red, visible or ultra-violet), x-rays or gamma rays are all types of electromagnetic radiation.
  
• Colloquially, an abbreviation of "ionizing radiation" meaning any spreading emission which can penetrate matter and ionize its atoms. That includes x-rays and gamma rays, but also high-energy ions and electrons emitted by radioactive substances, accelerated by laboratory devices or encountered in space (e.g. the "radiation belt" and "cosmic rays," also known as the "cosmic radiation").

Radioactivity --Instability of some atomic nuclei, causing them to change spontaneously to a lower energy level or to modify the number of protons and neutrons they contain. The 3 "classical" types of radioactive emissions are (1) alpha particles, nuclei of helium (2) beta-rays, fast electrons and (3) gamma-rays, high-energy photons.

Radio waves--Electromagnetic waves of relatively low frequency.

Reaction force -- The added force implied by the lack of motion (equilibrium) when an applied force exists (e.g. gravity).

Re-entry (atmospheric re-entry) -- The return of a spacecraft from orbit to Earth, in which the kinetic energy of the orbital motion is converted into heat. Since that heat is sufficient to melt the spacecraft, if the spacecraft is to land intact, the heat must be safely dissipated. Heat-resistant shields of various types are used, and the reentry is at a shallow angle, to stretch out the process.

Retrograde motion -- Temporary reversal of the apparent motion of a planet along the ecliptic. Caused because (by Kepler's 3rd law) a planet moves faster the closer it is to the Sun, so that (for instance) Jupiter appears to move backward when the faster-moving Earth overtakes it.

Right angle -- The angle formed when two straight lines intersect and the 4 angles at their crossing are all equal. When measured in degrees it equals 90^o.

Right ascension and declination -- Two angles marking the position of a star on the celestial sphere. Imagine a line from the observer to the star, and draw its projection (like a shadow) onto the celestial equator. Declination d is the angle between the line and its projection (d = 90^o - q, where q is the angle to the direction to the celestial pole); it is negative south of the equator. RA is the angle between the projection and the direction to the vernal equinox or first point in Aries.

Rocket -- A device shooting out a fast jet of gas, in order to produce a force in the opposite direction. See center of gravity, also Newton's laws of motion in Mach's formulation.

Rotation axis of the Earth -- The imaginary line around which the Earth turns. Its inclination of about 23.5^o to the ecliptic is the reason for the seasons of the year.

Saturn V -- The biggest rocket built to date, weighing 2700 tons fully loaded. It was used to launch NASA's Moon mission and the Skylab space station.

Second law of thermodynamics -- A fundamental law of energy exchange, one of whose formulations is "no process is possible whose only net effect is the flow of heat from a cold body to a hot one." A consequence of this is that in any system only part of the heat energy can be converted to other forms; the rest of the heat flows to lower temperature.

Semimajor axis -- a property of an ellipse, equal to half its greatest width, as measured along the line connecting its two foci. The semi-major axis of an orbital ellipse is one of the "orbital elements" characterizing it, and is directly related to the energy of the motion.

Shock--A sudden transition at the front of fast flow of plasma or gas, when that flow moves too fast for the undisturbed gas to move out of its way. Also occurs when a steady fast flow hits a magnetic or solid obstacle.

Solar activity A general term for those processes and changes on the Sun that rise and fall with the sunspot cycle, e.g. flares.

Solar cycle (or sunspot cycle)--an irregular cycle, averaging about 11 years in length, during which the number of sunspots (and of their associated outbursts) rises and then drops again. Like the sunspots, the cycle is probably magnetic in nature, and the polar magnetic field of the Sun also reverses each solar cycle.

Solar energetic particles--high energy particles occasionally emitted from active areas on the Sun, associated with solar flares and coronal mass ejections. The Earth's magnetic field keeps them out of regions close to Earth (except for the polar caps) but they can pose a hazard to space travelers far from Earth.

Solar wind -- A fast outflow of hot gas in all directions from the upper atmosphere of the Sun ("solar corona"), which is too hot to allow the Sun's gravity to hold on to its gas. Its composition matches that of the Sun's atmosphere (mostly hydrogen) and its typical velocity is 400 km/sec, covering the distance from Sun to Earth in 4-5 days. The solar wind confines the Earth's magnetic field inside a cavity known as the magnetosphere and supplies energy to phenomena in the magnetosphere such as polar aurora ("northern lights") and magnetic storms.

Solid fueled rockets -- Rockets which burn a solid mixture of fuel and oxidizer, and have no separation between combustion chamber and fuel reservoir. Gunpowder is such a mixture and was the earliest rocket fuel. They are somewhat less efficient than the best liquid fuel rockets, but are preferred for military use because they need no lengthy preparation and are easily stored in ready-to-fly condition. They are also used in auxiliary rockets that help heavily loaded liquid-fuel rockets (Space Shuttle, Delta) lift off and go through the first stage of their flight.

Solstice -- The time of the year when the Sun's position is the sky is most distant from the celestial equator. To a good approximation, north of the equator the day (around June 21) and the night (around December 21) are at their longest at the summer and winter solstices, and that is when those seasons are assumed to begin (the dates themselves, however, are known as midsummer day and midwinter day, respectively). Summer north of the equator coincides with winter south of it (and vice versa), and solstice names are also interchanged there.

Spectral line A narrow range of spectral color, emitted (or absorbed) by a specific atom (or molecule).The energy of its photon corresponds to the difference between two energy levels of the atom, and such photons are emitted when the atom "falls" from the higher level to the lower one.

Spectrum In the original meaning, the spread of colors seen in the rainbow, covering all pure colors the eye can see. Spectrum of a substance, e.g. of an atomic element, is the collection of spectral lines emitted by it.

Sputnik ("satellite") -- The first artificial Earth satellite, orbited by the Soviet Union on October 7, 1957, using Korolev's R-7 rocket.

Staging of a rocket -- The placing of smaller rockets on top of larger ones, increasing the lifting ability of the combined set-up.

Stellar evolution (stellar=of a star). The different phases in the lifetime of a star, from its formation out of gas and dust, to the time after its nuclear fuel is exhausted. Based on observations of stars at various stages of their evolution, astronomers have developed a general theory of stellar evolution, by which the Sun is a typical "main sequance" star, in the middle of its evolutionary lifespan

Sundial -- A device for telling time of day by the shadow which sunlight produces on the instrument. See gnomon.

Sunspot--An intensely magnetic area on the Sun's visible face. For unclear reasons, it is slightly cooler than the surrounding photosphere (perhaps because the magnetic field somehow interferes with the outflow of solar heat in that region) and therefore appears a bit darker. Sunspots tend to be associated with violent solar outbursts of various kinds.

Supernova (More accurately, type II supernova.) When a star burns up all its fuel, it collapses and the released gravitational energy blows off its top layers, creating a supernova explosion. What remains of the star depends on its mass. Low-mass stars crush their atoms and become white dwarfs, about as big as Earth. High mass stars collapse into black holes whose gravity prevents any light from escaping. Stars with masses between those extremes collapse into neutron stars, consisting of extreme dense nuclear matter held together by gravity and nuclear force, with a radius of the order of 10 km.

Sweepback--the angle by which the wing of an airplane is swept back, measured from the direction perpendicular to the fuselage.

Synchronous orbit -- The circular orbit above the equator at a distance of 6.6 Earth radii, in which a spacecraft has an orbital period of 24 hours. Such satellites stay above the same spot on Earth and are therefore ideally suited for transmitting communications and broadcasts.

Thrust--the force acting on a rocket or an airplane, produced by the action of its motor and pulling it forward. In an airplane, thrust is one of the four forces sensed by an airplane, the others being lift, drag and weight

Ultraviolet (UV)--electromagnetic radiation resembling visible light, but of shorter wavelength. UV cannot be seen by the eye, and much of it is absorbed by ozone, a variant of oxygen, at altitudes of 30-40 km. Satellite telescopes, however, can and do view stars and the Sun in UV, and even in the extreme UV (EUV), the range between UV and X-rays.

Unit vector A vector of unit length. Vectors have both magnitude and direction, but in some calculations it is convenient to separate the two. Denoting vector by an underline, a vector V can be represented by two factors multiplying each other, a unit vector V_u giving just the direction, and a magnitude V, i.e., the vector is V=V_uV.

V2 -- Abbreviation of "Vergeltungwaffe 2" (vengeance weapon 2), a 12-ton German rocket carrying a 1-ton explosive charge, used in World War II, starting in 1944. The V2 had a range of around 200 miles, used a liquid-fuel rocket and was the first large military rocket.Click here for a calculated example involving the acceleration of the V2.

Vector -- A quantity having both magnitude and direction, e.g. displacement, velocity, acceleration and force. Vectors are added when, for instance, one moves in a frame that itself is moving too (e.g. swims across a flowing river). Vectors are added like arrows, end to end, and the sum (for two) is the vector from the tail of the first vector to the tip of the second.

Vector resolution--The representation of a given vector as the sum of vectors in given directions. See componenet

Velocity -- Rate of position change, a vector quantity.

Vernal equinox -- The spring equinox. The term is also used for the point occupied by the Sun at that time, one of the two intersections on the celestial spher, between the ecliptic and the celestial equator. Also known as first point in Aries.

Watt -- Unit of power, the rate at which energy is supplied. One watt is the power which supplies 1 joule per second, 1 kilowatt = 1000 watts. A grown human climbing stairs (e.g.) supplies about 100 watt; 1 horsepower = 736 watt. Named for James Watt, inventor of the modern steam engine.

Wave A disturbance spreading in space, obeying a certain "wave equation." Sound waves, ocean waves and electromagnetic waves are some of the examples; other, more complicated types of waves can spread in plasmas.

Wavelength (Often denoted by l, the Greek letter letter lambda.) The distance between two crests of a propagating wave of a single frequency n . If v is the velocity at which the wave advances, v=ln.

Wave number A term used for the inverse of the wavelength, i.e. for 1/l

Weight -- The force exerted on mass by gravity.

Weightlessness (or "zero g") the condition when no force (such as weight) is sensed. Occurs in orbit or free fall, when gravity already produces its full acceleration and can produce no further effect.

Work -- The overcoming of a resisting force over a distance. The work performed when a force F overcome an equal resisting force along a distance x in the same direction equals Fx, i.e. F times x.
    If the force is not in the direction of the motion, only the vector component of F in that direction enters the calculation.
    Energy can be defined as the ability to perform work.

X-1 -- A rocket-powered research airplane, the first to fly faster than sound, on 14 October 1947.

X-rays--electromagnetic waves of short wavelength, capable of penetrating some thickness of matter. Medical x-rays are produced by letting a stream of fast electrons come to a sudden stop at a metal plate; it is believed that X-rays emitted by the Sun or stars also come from fast electrons.

Zodiac -- Twelve constellations dividing the ecliptic into approximately equal parts. Each month the Sun is in a different constellation of the zodiac.

Below is a list of questions submitted by users of "From Stargazers to Starships" and the answers given to them. This is just a selection--of the many questions that arrive, the ones included are either of the sort that keeps coming up again and again, or else the answers make a special point, often going into details which might interest many users.

1. About asteroids hitting Earth.
2. The swirling of water in a draining tub.
3. Dispensing water at zero-g.
4. Robert Goddard and World War II.
5. Asymmetry of the Moon's orbit.
6. Measuring distance from the Sun.
7. Who owns the Moon?
8. Acceleration of a rocket.
9. Rebounding ping pong balls (re. #35)
10. Rebounding ping pong balls and gravity-assist
11. Why don't we feel the Sun's gravity pull?
12. How hot are red, white and blue (etc.) stars?
13. How does the solar wind move?
14. The shape of the orbit of Mars
15. What if the Earth's axis were tilted 90° to the ecliptic?

    StarFAQ2.htm

16. Mars and Venus
17. Where is the boundary between summer and winter?
18. The Ozone Hole
19. What keeps the Sun from blowing up?
20. Those glorious Southern Skies!
21. Should we fear big solar outbursts?
22. Planetary line-up and the sunspot cycle
23. What are comet tails made of?
24. If light speed sets the limit, why fly into space?
25. Does precession mis-align ancient monuments?
26. Why does the Earth rotate? Why is it a sphere?
27. What's so hard about reaching the Sun?

28. Where does space begin?
29. Gravity at the Earth's Center
30. Radiation hazard in space (3 queries)
31. "Danger, falling satellites"?
32. The Lagrangian L3 point
33. Distance to the Horizon on an Asteroid
34. Overtaking Planets
35. Falling Towards the Sun
36. The Polar Bear
37. Are the Sun's Rays Parallel?
38. More thrust in reverse than going forward?
39. The varying distance between Earth and Sun
40. Mission to Mars
41. Kepler's calculation
42. The Appearance (Phase) of the Moon

If you have a relevant question of your own, you can send it to u5dps@lepvax.gsfc.nasa.gov.
Before you do, though, please read the instructions

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1. About asteroids hitting Earth

   A friend asked if I could find anything on an asteroid heading for earth & a laser that supposedly is in space that will eliminate the asteroid before it hits earth. Is there any such thing, or is he reading too many sci-fi books?

           Reply

   About asteroids heading for Earth: the best account I know is a section "The Shoemaker Comets" in the book "First Light" by Richard Preston. As for lasers capable of destroying one, they are (at least right now) pure sci-fi.

   The above book makes an interesting point: it would be very hard to spot an asteroid heading for Earth. Astreroids are usually detected in photographs of the sky (via a telescope) by the fact they move across the line of sight, leaving a streak rather than a spot. If they move across the line of sight, they are not going to hit Earth; if they are heading straight for Earth, they leave no streak and attract no notice.

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2. The swirling of water in a draining tub

   I am a grandmother, soon to be 55 years old, who often gets into heated arguments in her maillists! My question, to avoid the argument by having facts, is: The direction of draining water in the tub, sink and toilet is said to be the opposite in Australia. Someone said the Coriolis Effect governs this, and it is a myth. Someone said the CE has nothing to do with it, and it is a myth. Then again someone said it is NOT a myth. I am on the fence with this one, as I cannot argue something I do not have one idea about!! Can you help me? Thanks in advance!

           Reply

   Your first respondent was right: the Coriolis effect governs it, and it is a myth. The Coriolis effect can govern the swirling of fluid flows, and where it does, the swirling is opposite in opposite hemispheres. However, it is only appreciable on a very large scale. Hurricanes obey it: tornadoes, which are much smallers, do not, and neither do kitchen sinks, which are much smaller still.

   For details and explanations, look up on the world-wide web here.

   .
   

3. Dispensing water at zero-g.

   I am a student currently studying for a degree in engineering. As part of this degree we have been given the task of designing a water heater and dispenser for use in zero gravity. It has been suggested to use a bladder in a pressurized container heated using microwave or Radio Frequency technology. The heater must heat approximately 100 ml to 80 degrees celsius, and the entire system can use no more than 12 volts. How would you suggest a layout for this type of system might look? Any information that you could provide would be most appreciated.

           Reply

   Our research group is concerned with plasmas and magnetic fields in the rarefied medium between here and the Sun. We have no expertise at all in zero-g and space-station hardware.

   This does not stop me from speculating about your request, of course. The key word is "dispensing": what do you mean by that? You cannot just have a tap and let out the hot water--it will form globs that drift away in zero-g and ultimately contaminate your circuitry or mess up your living quarters.

   So you need three elements--a container where the water is heated, a tank from which the water is obtained and a container for the hot tea or whatever you want to make with the water.

   The first and third may well be plastic bladders, whose volume can adjust. The reservoir would have an outer bladder with water only and and inner bladder filled with air, and as the astronaut with a squeeze-bulb pumps air into the inner bladder, water is squeezed out.

   The heating vessel--you could use RF heating, but I suspect it will be somewhat heavy, will need stepping up the voltage from 12 volt and also will have to be shielded from radiating. In an environment where every superfluous gram costs a great deal, wouldn't a simple resistive heating element--with a thermostat, of course--be simpler? It could be in a cylindrical container with a spring loaded piston which is initially at the bottom. When refilling it from the reservoir the water enters from below and pushes the piston up, against a ratchet, and when the astronaut wants a drink, he or she releases the ratchet and the spring loaded piston pushes the water out, into the third container. The trick is to never mix any air with the water--once they are together, they are hard to separate.

   This opinion comes to you with no warranty by NASA or anyone. Have fun! Now, let me go back to serious work...

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4. Robert Goddard and World War II.

   I just came upon your website "Stargazers to Starships". Great site! I am researching a school project on Goddard and found the information here useful. I have a few questions, perhaps you can help me.
   1. When the U.S. was spending money on the a-bomb during WWII, do you think this prevented the government from providing Goddard with money to research rockets for the military?
   2. The German's developed the V-2 rocket, and Goddard believed they copied his design. I read that Germany sent spies to observe Goddard. Did Goddard know he was being watched?

           Reply

   To answer your questions:
   
   1. During WW-II, the government also spent money on rockets. The A-bomb project did not cut into this. Goddard was part of that effort, but the biggest rocketry effort was probably at Caltech, with Theodore Von Karman and Frank Malina. See the section in "Stargazers" on the evolution of the rocket.

      Part of the problem was that Goddard preferred to work alone, while the Caltech people brought in bright students and had much better engineering support.

   2. I never heard about the Germans spying on Goddard, and it seems very unlikely. They too had much better engineering support and took Goddard's ideas--DeLaval nozzle, liquid fuel, using the fuel to cool the engine, steering vanes in the exhaust etc.--and developed them beyond what Goddard himself was able to do.

      A similar thing happened in WW-I. The Wright brothers invented the airplane in 1903, but the Europeans took their work and expanded it greatly, so that the German, British French and even Russian airplanes in that war were far superior to the ones America produced. After America entered the war, its pilots all flew British and French machines.

   .
   

5. Asymmetry of the Moon's orbit.

   Subj: Moon's perigee/apogee

   I have just read your article in "Stargazers", but what I am trying to dertermine is the observed variations in the time between events of perigee and apogee. For example it may be 14 days from perigee to apogee and say 12 days from apogee to perigee. Then at a further time the periods can be reversed. I am seeking an explanation of this dynamic variation.

           Reply

   I looked up the ephemeris tables of the Moon, and you are right: counting only the times between minimum and maximum distance from Earth, those distances ARE variable, more than one would expect for, say, an Earth satellite in a long elliptical orbit.

   All I can give you now is a guess. The motion of the Moon is really a 3-body process, influenced by the Sun as well, with further perturbations perhaps due to Jupiter etc. The orbit is close to a circle, which means that a pull of a few 1000 km this way or that can shift the time of largest and smallest distance by a great amount, in contrast to what it would do to a high-eccentricity orbit.

   The literature comments "The orbit of the Moon is complicated" and I think your question illustrates that complexity. If you look at page D-46 of the US Astronomical Almanac, for instance, you will see that even the "low precision formulae" for lunar motion are alarmingly long, and better approximations (found for instance in "Astronomical Algorithms" by Jean Meeus) are even longer.

   So the bottom line (as they say) is that Kepler's laws still hold, but actual motions may be complicated by additional factors.

   .
   

6. Measuring distance from the Sun.

   I hope this isn't too dumb a question, but when a planet's distance from the sun is given, should that be assumed to be from the center of the sun to the center of the planet, or is it a measure of the surface of the sun to the surface of the planet?

   -- and if it's surface to surface, then what is considered the 'surface' of a gas giant?

           Reply

   Your question isn't dumb, and it has a simple answer: from the center of the Sun. A spherical mass--Sun, Earth, red giant or whatever-- pulls objects outside it with the same force as it would, if all its mass were concentrated in its middle. As far as gravity is concerned, the position of the surface makes no difference.

   By the way--the Earth does not orbit the center of the Sun. If the solar system contained only it and the Sun, the two would orbit their common center of gravity. Of course, the Sun being much more massive, that point is very close to the center of the Sun.

   With more planets, the system orbits around the common center of gravity, which I suspect is close to the center of gravity of its heavyweights--Sun, Jupiter and Saturn. Viewed from some other solar system, far away, this would make the Sun's position wobble a bit, in response to the motions of the planets. In recent years, astronomers have observed such subtle wobbles in the motions of quite a few nearby stars, and concluded that like the Sun, they had planets, too--big planets, like Jupiter. It is still too hard to detect the effects of lightweights such as Earth, but progress is being made.

   Keep up your interest!

   .
   

7. Who owns the Moon?

   Dear Gentlemen,

   If you be so kind as to reply, please tell me, is it true that the Moon has a formal proprietor and who is this man?

   Thank you in advance for your kindness.

           Reply

   I do not know who told you differently, but the moon belongs to all of us together, even you, even I. When Neil Armstrong stepped onto the moon he said "We came in peace in the name of all of mankind" and that still holds true.

   .
   

8. Acceleration of a Rocket

   I've looked your site and have taken some information but I need more for my project. In my project I want to search on the G force on the rockets at launch.

           Reply

   I really do not know. The g-forces on a rocket vary with the design. Manned rockets stay under about 5g, unmanned scientific satellites may be launched at up to 10-12g, small sounding rockets with strongly built instruments sometimes reach 30g, and missiles can also accelerate very rapidly. The greatest acceleration is usually not at launch but just before burn-out, because the thrust of the motor changes little (or not at all), while the mass goes down as fuel is burned.

   .
   

9. Rebounding Ping-Pong Balls (re. section #35)

   Can you send or suggest any more references to support the 20 miles ping pong ball in and the 60 miles back out? I am having trouble with my colleagues who say it should be 40 miles back.

           Reply

   I hope you have a nice bet riding on this matter, because in that case you win. The correct velocity is indeed 60 mph. The way I gave it in "Stargazers" was meant to make it intuitively easy, but a rigorous calculation gives the same result.

   In what follows we agree that velocities from right to left are positive, from left to right are negative.

• A ball of mass M₁ moving with velocity -V₁, against...
• A paddle of mass M₂, moving with velocity V₂

• A ball of mass M₁ moving at velocity +W₁
• A paddle of mass M₂ moving with velocity W₂

Conservation of momentum:

M₂V₂ - M₁V₁   =   M₂W₂ + M₁W₁         (1)

Conservation of energy (we assume the encounter is perfectly elastic-- approximate for the ping-pong ball, very well observed by gravity- assist maneuvers of spacecraft around planets):

M₂V₂²/2 + M₁V₁²/2   =   M₂W₂²/2 + M₁W₁²/2

multiply by 2:

M₂V₂² + M₁V₁²   =   M₂W₂² + M₁W₁²         (2)

In both numbered equations we collect all M₂ terms on the left and all M₁ terms on the right:

M₂(V₂ - W₂)   =   M₁(W₁ + V₁)         (3)

M₂[V₂² - W₂²]   =   M₁[W₁² - V₁²]         (4)

By a well known factoring identity, for any two numbers A and B

M₂(V₂ - W₂)(V₂ + W₂)   =   M₁(W₁ - V₁)(W₁ + V₁)         (5)

If we divide equals by equals, what remains is still a valid equality. So let the left side of (5) be divided by the left of (3), the the right side of (5) by the right of (3):

V₂ + W₂   =   W₁ - V₁         (6)

Add V₁ to both sides

V₁ + V₂ + W₂   =   W₁

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10. Rebounding ping-pong balls and gravity assist

    Hello!

    I've enjoyed browsing your fine web site, From Stargazers to Starships, and I figured I would take a moment to let you know that. I was particularly intrigued by the chapter "Project HARP and the Martlet. " There is one possible error I found in the site. In Sections 35 and 35a, on planetary swing-bys and the so-called "slingshot effect, " you state that the maximum velocity increase is imparted to a spacecraft when it approaches a planet head-on, or retrograde to its orbit. My reading indicates that the opposite is true. My sources are the following web sites:

    JPL's Basics of Space Flight
    http://www.jpl.nasa.gov/basics/bsf4-1.htm#gravity

    Scientific American
    http://www.sciam.com/askexpert/astronomy/astronomy10.html

    I expect the discrepancy stems from the fact that the model used in From Stargazers to Starships is based on the ping-pong paddle example. The key difference is that the force exerted by a ping-pong paddle on a ball is repulsive, whereas gravity is attractive. Thus the numbers are the same but the sign is reversed.

    By the way, I did find the analogy to the Pelton turbine very interesting. Thank you again for a very informative web site!

            Reply

    I believe that the ping-pong analogy is still valid, because it can be reduced to simple arguments of the conservation of momentum and energy, which should hold equally in a planetary-assist maneuver. Some other correspondent questioned this result, and as a result, you can find that calculation in item #9 of the question-and-answer section of "Stargazers," linked at the end of the home page [the item preceding this one].

    What seems to confuse the issue is the following. A spacecraft would get its biggest boost if it approached head-on, made a hairpin turn around the rear of the moving planet and returned along a path 180 degrees from its first approach (that would be the ping-pong analogy). Viewing the encounter from far north, if we put the moving planet at the center of a clock dial with the Sun’s direction at 12 o'clock, we would see the planet moving towards 3 o'clock, so our satellite has to approach from that direction and return to it again.

    When the Voyager and Pioneer spacecraft approached Jupiter and Saturn, however, they were coming from the Earth, which is roughly in the same direction as the Sun; in any case, their initial orbital velocity, which was essentially that of the Earth, which moves in the same direction as other planets', did not allow a head-on approach. Instead, they entered around 12 o'clock on the dial. They still rounded the night side and exited around 3 o'clock, which gave them an apprecible boost, though perhaps not the biggest one possible.

    I have some old issues of "Science" on these events and in the one of the Pioneer 10 fly by, for instance (page 304, 25 January 1974), the satellite enters at 1 o'clock and leaves a bit after 3 o'clock. For the Voyager 1 fly-by of Saturn (p. 160, April 10, 1981), entrance is around 11:30 and exit around 4:30 on the same dial.

    You are right, of course, in that the force on the ping-pong ball is repulsive while the planet's gravity attracts the spacecraft. However, the strongest attraction occurs when the spacecraft is at its closest approach, on the night side, and its direction then is along the velocity of the planet, the same direction as the force exerted in the ping-pong analogy.

    With all this, I am grateful for your message. It again shows that at least some users go into the details of "Stargazers". Quite a few errors were caught only thanks to people like yourself who checked out such details.

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11. Why don't we feel the Sun's gravity pull?

    Dear Dr. Stern:

    I have asked several teachers and many other people the following question but have not received any respectable answer:

    The Earth is 93 million miles from the sun. Other planets, and even much denser planets I might add, are much further yet from the sun. The obviously strong gravitational attraction of the sun holds all of these planets in orbits around the sun. If gravity could be simply defined as a force that attracts matter, and the sun's gravitational pull is sufficient to hold the Earth in orbit, what keeps it from pulling me off the Earth? In fact, the gravitational pull of the sun is so weak at this distance that It can't even produce enough pull to raise a hair on my head. So how can it hold the Earth and several even denser planets (even further out) in orbit?

    So--if the gravitational force of the sun is powerful enough to hold the Earth in orbit, then how could the Earth's gravitational force be powerful enough to hold me down, counter-acting the gravitational force of the sun? Please unconfuse me!

            Reply

    Dear student

        Two effects are at work, each of which would be quite sufficient:

    (1) The force of gravity goes down with distance squared. For example, since the Moon is about 60 times further from the center of the Earth that you or anyone who is standing on the surface, the pull of the Earth on each pound or kilogram of the Moon is 60 x 60 = 3600 times weaker than the pull on the same mass on the surface.

    So: the Sun is indeed more massive, but also much more distant. As a result, its pull on each kilogram or pound at the Earth's distance is only about 0.06% of the Earth's pull near the surface.

    (2) Being on the orbiting Earth, your body already responds to the Sun's gravity, by sharing the Earth's velocity of 30 km/s around the Sun. Therefore there is nothing left over from the Sun's pull to make you move any more.

    In a similar way, an astronaut in orbit feels weightless, because the Earth's gravity is already fully employed in keeping up the orbital motion. The astronaut is not beyond the reach of Earth's gravity: if it were so, the spacecraft would fly away never to return, rather than stay in orbit. It is just that--like a stone in free fall--gravity is already doing to the astronaut all it can. It also does so on the spaceship the astronaut rides in, leaving no extra force pulling the astronaut down to the floor, or in any direction.

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12. How hot are red, white and blue (etc.) stars?

    Hi, My name is Donny and I have a question that I cannot seem to find an answer to.... How hot, exactly, is a blue star, a red star, a white star, and other color of star?

            Reply

    Your question has an answer, but you have also to learn a bit about what color is. Look at the following web site

    http://www.phy6.org/stargaze/Sun4spec.htm

    The stars for which statements about temperature are made are glowing dense bodies of gas, so for them the "black body spectrum" is relevant. In that spectrum, the curve of intensity against wavelength (color) typically rises to a peak and then drops.

    The total area under the curve tells how bright the light is: the hotter the emitter, the higher the curve and the brighter the light. You know this from experience: a flashlight with a weak battery glows weakly in orange, a flashlight with a good battery glows bright yellow, and if you connect a 3-volt battery to a 1.5 volt lightbulb, you get a very bright, very white flash, and then darkness, because you have heated the wire inside the lightbulb so much that it melted, and you have just lost your lightbulb.

    And in that sequence, you also see the color move along the rainbow: orange with a little heating (a feeble red when the battery is almost dead) yellow under normal operation, white when it's too hot. The color you see is where the peak is--and if it is blue, you see white, because all other colors are also emitted, and white light is what the eye then sees.

    Stars are like that too. We can say the Sun's photosphere radiates pretty much like a black body at 5780 degrees absolute or about 5500 degrees centigrade, by the way its colors are distributed. The color tells how hot it is, and I think "blue" here means white-blue; such a star would be at about 10,000 degrees.

    David

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13. How does the solar wind move?

    I am confused about the solar wind and don't want to mislead my students. On a web site about magnetic storms I read the following:
    
    "This storm affects the earth when it is on the western half of the sun, not when it is dead center. This is because the solar wind follows a curved path between the sun and the earth not a straight-line path."
    
    Is the solar wind influenced by the magnetic field of the sun so it has a curved path to the earth? Or is this too much of a simplification? What really happens?

            Reply

    Physics and astronomy get complicated at times. Will the interplanetary magnetic field curve the path of the solar wind? Without peeking at the observations, one can only say "it depends," and what it depends on is the ratio between the density of particle energy (density n times average of 0.5 mv^2) and the magnetic field energy density (B^2/2 mu-zero). This ratio is often called "beta" in plasma physics, and it's an important quantity in experiments aimed at confining a plasma for nuclear fusion. If beta is much less than 1, the magnetic field is the dominant factor and particles meekly follow its field lines, making containment easy. Practical fusion however requires a greater beta, and if beta exceeds 1, the plasma starts pushing the magnetic field around. The way it does so is by subtly segregating its charges, to create a charge density and hence an electric field, and electric fields can allow a plasma to move whichever way it wants.

    Suppose the magnetic field is constant and equals B₀ in the z direction, and the plasma is moving along the x axis. Then an electric field E₀= -vB₀ in the y direction will allow it to do so, canceling the magnetic force on any electric charge q, equal to qvB₀ along -y. (It also works out with spiraling particles).

    The same happens with the solar wind, where beta may be 5 or more. As a result, the solar wind moves radially out, though it gets buffetted a bit, and it's not clear by what.

    Now what about the MAGNETIC field? There is a rule (for plasmas with high beta, satisfying the "MHD condition"), that "particles that initially share a field line, continue doing so indefinitely" (there exist some extra "fine print" conditions, but we ignore them here).

        What follows below is the original answer sent to the questioner. Later this was converted to a graphical excercise, Section S-6a   Interplanetary Magnetic Field Lines, linked to section S-6. You can either link there or continue below (or both), as you choose.

    Take a sheet of paper, put on it a small circle--that is the Sun viewed from far north of it, or rather, it is a circle in the corona, some level above the Sun, where the solar wind begins. On this scale, let's say the solar wind moves one inch (1") per day (or if you wish, 2 cm). Draw from the center 6 or 7 radial rays 13.3 degrees apart. Mark as "P" the point where the first ray--the one furthest clockwise--cuts the circle. We look at 6 ions located at P, and therefore presumably on the same field line--let's number them 1, 2...6. We have advance information that 1 will be released into the solar wind today, 2, tomorrow, 3 the day after, and so on. Mark P with 1--that is where ion no. 1 is today.

    Next day, P is on the second ray. Point 1 has moved 1" outward, radially, and Point 2 is at the base of the new ray, ready to go. Next day: Point 1 is now 2" out on the first ray, point 2 is 1" out on the 2nd, point 3 at the base of the 3rd, ready to move. And so on.

    Five days later, 1 is 5" out on the first ray, 2 is 4" out on the 2nd 3 is 3" out on the 3rd, etc., and 6 is at the base of the 6th ray. However, all these points started on the same field line, so they are still strung out along one line. CONNECT THE DOTS marking the outermost ions on the 6th day and you have a spiral line of the interplanetary field: if the ions started on the same line, they must still be on one.

    The solar wind in all this has moved radially. But now and then the sun releases bursts of high energy particles, say from flares. The energy of these particles may be high enough to endanger astronauts in interplanetary space--but their density is very low, so their beta is also low. THEY therefore are guided by the magnetic field lines (rather than deforming them to their own flow), and therefore they move spirally.

    The solar wind takes about 5 days to cover 1 AU. Therefore, if the Earth is to receive particles guided by an interplanetary field line when it is on the first ray, the emission has to be at the base of ray 6--that is, near the western limb. The high-energy particles take only an hour or so to arrive, depending on their energy of course.

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14. The shape of the orbit of Mars

    Dear NASA,

    I have read your articles about stargazers and I believed this is one of the most interesting subjects in astronomy. Here is a question which came up when I was reading 'Planetary evolution', could you please help, thanks. Mars moves in an elliptical orbit around the Sun, what is the relative distance of the Sun to this ellipse? Would it be at one end of the major axis of the ellipse?

            Reply

    The eccentricity of the Mars orbit is 0.09337, the semi-major axis of the orbit is A = 1.524 AU (1 AU is the mean Sun-Earth distance, about 150,000,000 km; AU stands for astronomical unit) and distances of perigee (closest approach) and apogee (most distant) are B = 1.381 AU and C = 1.666 AU (letters are just notation for here).

    These are the numbers. What do they mean? I remember seeing long ago a German physics text from the 1920s drawing the orbit of Mars. One side of the line was a circle, one side was the orbit, and the varying thickness of the line showed the difference between the two. It was hard to see that difference!

    Let us calculate the length and width of the ellipse. The length (through the two foci--the line on which the Sun is located) is 2A = B + C = 3.048 or 3.047 AU. The displacement of the center from either focus is D = (C-B)/2 = 0.1425 AU and the width is 2G where

    G² = A² - D²                 G = 1.51732 AU         2G = 3.035 AU I do not think you or I would be able to distinguish an oval with dimensions (3.048, 3.035) from a true circle! The position of the Sun at one focus is however notably asymmetrical, about 10% of the distance from the center to the edge.

    David

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15. What if the Earth's axis were tilted 90° to the ecliptic?

    I was recently looking at the webpage "Seasons of the Year" and I read about what would happen if the earth's axis were perpendicular to the ecliptic. I was just wondering if you could give me some insight on what would happen if the ecliptic was inclined at a 90-degree angle with respect to the celestial equator? Would this mean that earth's orbit would travel along this "new ecliptic" while the north and south poles are travelling along this "new ecliptic"?

            Reply

    The hypothetical case you describe does in fact exist: for some unknown reason, the spin axis of the planet Uranus is almost exactly in the ecliptic.

    That means that at some time one pole (let me call it the north pole, even though that "north" direction is almost perpendicular to the northward direction from Earth) points at the Sun. Then the northern hemisphere is in constant light and the other one in constant darkness. Half an orbit later--42 years or so--the roles are reversed. And halfway between those times, the planetary rotation axis is perpendicular to the Sun's direction, making day and night alternate in a way similar to what the Earth experiences at equinox.

    I leave it as an excercise to you to figure out whether Uranus ever receives sunlight the way Earth does at solstice.

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16. Mars and Venus

    This is a query on Mars. The ferric oxide on the Martian surface contains a lot of oxygen and if heated sufficiently would yield free oxygen. Does the presence of this substance on Mars indicate that at one time there must have been a lot of atmospheric or dissolved (in water?) oxygen available on Mars?

    These are my questions about Venus:

    1.     Why is it that Venus is depicted by Magellan photos as being Red/Orange in colour? If these are radar images how is the "..actual colour of sunlight that reaches the Venusian surface through the thick cloud layer .. " derived? The Magellan images of the surface of Venus are quite bright. Would it really be that bright under such heavy cloud cover?

    2.     What generates the high velocity (up to 400 km/hr) winds which move from east to west in Venus's upper atmosphere, given that the surface of Venus rotates at a leisurely 6.5 km/hr?

    3.     What conditions did astronomers expect to find on the surface of Venus before the first probes landed? Thank you for your effort in advance.

1. Oxygen is not a rare element, Mars, the Moon, etc. have a lot of oxygen, always combined with other elements into stony stuff. The element that is really important to life is hydrogen. The recent signs that the Moon may have hidden water were exciting not because it is hard to find oxygen on the Moon (it must be separated, of course) but because hydrogen is rare. I am not sure about hydrogen on Mars. Jupiter and other cold big planets of course have plenty, and so do their moons, which may be more accessible. Still, they are pretty far away.

2. The colors of radar maps on Venus are probably false colors. The color and intensity of sunlight on the surface should be known, because the Russian landers took photos. However, I don't know it.

3. What drives winds on Venus is not the rotation but the same cause for winds as on Earth--the heat of the Sun. Venus is closer to the Sun, so maybe its atmosphere is more agitated. See the sections in "Stargazers" on sunlight and on the way it creates the Earth's weather

   What one observes, in any case, is the wind at the top of the clouds, which might be analogous to the jetstream above Earth, not a good measure of winds at the surface.

4. I don't know--you must find out by yourself. I know Venus was expected to be "as hot as hell"--but the features of the surface could not be guessed.

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17. Where is the boundary between summer and winter?

    This may seem like a silly question but is there a line on the earth where on one side is summer and the other winter? Sort of in the same way that you can go back and forth between two days at the International Date Line.

            Reply

    Yes, there exists such a line and it is called the equator, but the boundary between summer and winter is not as sharp as the one of (say) the international date line.

    Right now it is fall here, but spring in Chile and Argentina, and 2-3 months from now it will be mid-winter here and mid-summer in those countries. At our latitudes, these seasons are well defined. However, a broad belt centered on the equator does not have well-defined summer or winter. The Sun's heat fluctuates somewhat as its noontime passage moves north and south. On the equator, for instance, it passes right overhead around the 21st of March or September, 23.5 degrees off to the north on June 21 and the same amount south of "overhead" (zenith) on December 21.

    These small changes do not make much of a change in solar heating. The big difference is made by local climate patterns, e.g. seasonal rains like the monsoon. These countries do not have summer and winter the way we do: for instance, when my daughter visited Darwin, Australia, some years ago, she was told that loacally the year had only two seasons, "the wet" and "the dry. "

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18. The Ozone Hole

    I am a auto mechanic and I have one simple question for you. Scientists say there are 2 holes in the atmosphere, ironically they are around the north and south pole, and they blame these holes on chlorine monoxide or refrigerants i.e. fluorocarbons (CFC) escaping into the ozone. Wouldn't the more likely cause of the holes be the magnetic lines of flux? One more quick question: could there be a way of tapping into that magnetic field as an energy source?

            Reply

    There do indeed exist two "holes" in the Earth's magnetic field, around the MAGNETIC poles, whose magnetic field lines go very far from Earth and afford an easy connection to the solar wind and to interplanetary plasma phenomena. On those lines we do observe "polar rain", a drizzle of fairly energetic electrons (more energy than those of the ionosphere, less than those of the usual polar aurora) which seem to come from the Sun. Also, when solar activity floods interplanetary space with energetic ions and electrons, that is where they are most likely to come down to Earth.

    However, the creation and destruction of the ozone layer does not involve the magnetic field. Instead, its factors are chemistry and sunlight, and the "ozone hole" is around the geographic pole, not the magnetic one.

    The ozone layer is maintained as an equilibrium between creation of ozone by ultra-violet sunlight, and its destruction by various natural processes (this is not my field, and I do not know details). During polar winter, the polar cap is dark and ozone is not created, just destroyed (a bit further from the pole, with just a few hours of sunlight and the sun shining at a shallow angle, ozone creation is also reduced). The observation of an "ozone hole" in recent years suggest accelerated destruction, as predicted by Rowland and Molina to come from chlorine in man-made substances.

    As for tapping electric currents from space, I don't think it will work, because (1) they are very spread-out, by our standards--how can you tap a current sheet 100-1000 miles wide?; and (2) between us and them lies the atmosphere, a very effective electric insulator--as is well known to power companies, which string their high-voltage cables through air without worrying about the power leaking away.

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19. What keeps the Sun from blowing up?

    Dear NASA, I have a question abour the sun. We all know that the sun is powered by thermonuclear fusion reactions,so why doesn't it explode like an H-bomb?

            Reply

    What keeps the Sun from blowing up? Gravity.

    The Sun is not exactly like an H-bomb--the bomb has fuel that is easier to "burn, " while to Sun "burns" ordinary hydrogen--but there does exist a similarity. Why does a hydrogen bomb explode? Because an enormous amount of energy is released in a short instant and inside a small volume, heating the material to extreme temperature. The material expands forcibly, creating a powerful shock, and that is the explosion.

    The Sun releases much more energy every second in its central regions, but those materials are under great pressure, from the weight of all the matter piled up on top of them--the thick outer layers of the Sun, pulled down by a gravity much stronger than anything on Earth. That pressure confines the extremely hot gas in the Sun's core. The heat gradually works its way to the surface, but the Sun does not blow up.

    If somehow it could yield to the pressure and expand, the central core would cool down and the nuclear energy release would drop. Then the pressure would decrease again and gravity would reassert itself. Some stars do in fact oscillate, but we should be grateful that the Sun does not belong to that class.

    See more in http://www.phy6.org/stargaze/Sun7enrg.htm

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20. Those glorious Southern Skies!

    Not long ago I visited Chile for the first time and observed the night sky there. At that latitude, the centre of the Milky Way passes overhead, where it makes a grand show...

    Why is there such a difference between Southern and Northern Hemisphere? Is it because of the 23 1/2 degree tilt?

            Reply

    Why such a difference between the southern and northern hemisphere? Because from the point of view of the Earth, all stars are so distant that they appear as if they were attached to a tremendously large sphere, with us in the middle.

    At night, standing on the ground, you only see HALF the sphere. If you stood at the NORTH pole, half the sphere would be all you ever saw, appearing to spin around the point right overhead, the zenith. Standing at the SOUTH pole, you would see the other half, spinning around the point overhead, which is on the OPPOSITE end of the sphere from the overhead point at the north pole.

    If you lived on the equator, the two poles of the sky would be on opposite sides of the horizon, and as the sphere of the heavens rotated around them, you would in principle see ALL the stars, sooner or later. In practice, those close to the poles will be near the horizon and not easy to see.

    Maryland, where I live, is somewhere between the north pole and the equator, so the stars near the north pole are easily seen, and we get to see some stars of the southern hemisphere as well, though not those near the southern pole of the heavens (like the Southern Cross and Alpha Centauri), and many southern stars are only seen here near the horizon.

    Similarly, from Chile you won't see the Pole Star, the Big Dipper or Cassiopeia, but the bright stars near the southern pole more than make up for them, and yes, the brightest part of the Milky way is there, too. North of the equator, the best view of the Milky Way is in mid-summer.

    The 23 1/2 degree tilt has to do with the way the Sun, Moon and planets appear to move--not with the apparent motion of the distant stars.

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21. Should we fear big solar outbursts?

    I have a question pertaining to your studies in the upcoming year, particularly surrounding the forecast Solar Maximum.

    I have heard about the upcoming Solar Maximum starting soon (CNN.com article, Nov. 11, 1999). I have also heard (unofficially), that there could be a very large solar storm near the end of April.

    Finally, it is relatively commonly known that there is going to be an unusual alignment of the planets in our solar system at the beginning of May, 2000. Has there been an in-depth study to determine effects of the combination of these phenomena, and the potential impacts on both our solar system, and our planet?

    The real question; could this combination of phenomena:

    1.) Promote a solar flare, or SME, significantly larger than previously experienced in recorded history?

    ---I have heard of Super flares emitting from G Class Stars, and the theory describes large planets in a close orbit (Jan. 8th Article, Sun-like stars said to emit super flares, CNN). Now, I don't expect this size of phenomena to happen here, but with the unusual planetary alignment, I do believe that this could create larger effects than normal, like a significant Solar-Magnetic Ejection, especially with the excitation of the Solar Phenomena. I'm just curious as to how much larger.

    2.) Disrupt the crust of our planet, creating a significant amount of tectonic activity, and if so, by how much?

    ---Now, I know our planets are very far apart, but if the magnetic attractions are larger than normal, and these magnetic attractions promote significant SME activity, this could promote some strange tectonic happenstance, especially with the fragility of our planet and its crust.

    3.) Potentially disrupt our magnetic field severely with the combination of solar magnetic and gravitational forces?

    ---I am aware of changes in our earth's history of the magnetic poles, could this happen here with the combination of a large SME and gravitational forces?

    No calculations, or in-depth study has occurred, but I have a hunch this should be looked at more closely, and by qualified people.

            Reply

    Your message made me once more appreciate the amount of misleading and loose information circulating on the web. I have spent a great deal of time and thought on creating a web site describing what is known about the magnetic field of the Earth and the Sun's effects on it, and for a real understanding, you better look there:
    http://www.phy6.org/Education/Intro.html

    To answer your questions in brief: The solar maximum is already here [December 1999]. It is not an abrupt event you can date, but the crest of a wave whose width is at least several years. From what I have heard, the current peak is lower than expected.

    No one can predict a large solar storm months ahead of time--the best we can say is that they are more frequent near the peak of the sunspot cycle. Some big ones cause little disturbance near Earth--depends on factors like the precise orientation of the interplanetary magnetic field. Planetary alignments have no effect whatsoever. [See also next item.]

    The large planets you read about are unlike anything in the solar system --usually Jupiter-size or bigger, and very close to the star (this has to do with the method of detection--it's hard to detect long-period planets).

    No solar eruption has ever been found to affect the solid Earth. Their energy is too small, and almost all of it is dissipated outside the breathable atmosphere. No earthquakes follow CMEs.

    I have no control over CNN. But if you seek to understand nature, look up my site and sources linked or cited there.

    Happy new century

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22. Planetary line-up and the sunspot cycle

    Enjoyed browsing through some of your efforts on the Web. I am hoping you could help settle some of my thoughts before I make a fool of myself.

    In your experience, has anyone tried to correlate lineups of the sun, earth and major planets' magnetospheres with the sunspot cycles? My spare-time effort found some correlation between lineups and cycles in a number of years. My wonderment centers around the possibility that some forces of the planets when lined up, possibly relating to their magnetospheres, impact the suns magnetosphere causing a solar max. I've also considered the possibility that related magnetosphere effects could be the cause of previous polar reversals on the earth. Additionally, ringing of our magnetosphere might impact charged tectonic plates...but that is again another direction. Only if you have time, please comment.

            Reply

    There exists a tempting closeness between the length of the solar cycle and the orbital period of Jupiter, but I don't think the two are related. I cannot imagine any mechanism coupling the two-- especially since the Sun rotates in about 27 days, so the relative period of Jupiter going around the Sun is of that order. Furthermore, the solar wind moves with supersonic speed, which means that solar disturbances can (and do) travel downstream with it, but disturbances from a planetary magnetosphere (whatever they might be) don't easily propagate sunward.

    Above and beyond all these, there is always the question of energy-- the currency in which the price of any physical process must be paid. The energy required in the solar cycle is much bigger than anything planetary magnetospheres can supply.

    So what causes the cycle? The Sun rotates unevenly, slower near the poles, faster near the equator, probably because of the way gas flows in it (Jupiter also has such a difference). In a magnetized hot gas, this difference deforms and amplifies the magnetic field, and there exist some general theories of the sunspot cycle based on this, although many details remain unclear. The general idea is that as the magnetic field gets amplified, it forms concentrated "ropes" which push out the hot gas, and when they reach a certain strength, enough gas is displaced that the ropes are light enough to float to the surface, where they are seen as sunspots.

    Again, the magnetosphere is a relatively weak influence on the Earth's internal magnetism--even a big magnetic storm only reduces the surface equatorial field by 1%. Furthermore, the time scale differs--reversals happen on time scales of 0.5-1 million years, while magnetic storms have a 1-day scale or faster.

    What seems to be involved are the currents which circulate in the Earth's core, presumably driven by flows there, which (like flows on the Sun) get their energy from heat. The magnetic field is fairly complicated--the 2-pole structure we see (north-south) is dominant, but not by as much as it seems, because more complicated modes get filtered away faster by distance. Right now the 2-pole field is declining at about 5-7% per century, but the late Ed Benton has shown that the more complex parts are gaining energy, and the total sum is fairly constant. Maybe, when a reversal occurs, for a while the 2-pole part gets small and the total field is rather complex (4, 8 poles..), and when the simple pattern re-emerges, it is reversed.

    Anyway--keep studying, keep up your sense of wonderment

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23. What are comet tails made of?

    Are comet tails the reult of melting and evaporation of ices from the comet core or are they dust collected by the comet as it moves in its orbit?

            Reply

    Comet tails contain both evaporated ices and dust, as explained in the section "Comet Tails and the Solar Probe" near the end of the file http://www.phy6.org/Saberr.htm

    The dust however is not collected by the comet in its orbit, but is part of its make up, probably dating back to the beginning of the solar system. Comets may have two tails, and sometimes these are well separated, as in the recent Comet Hale Bopp: they differ in color, composition, and direction, and are pushed away from the Sun by different forces.

    Dust tails are pushed by light pressure, and their colors are those of sunlight, scattered by them the way clouds on Earth also scatter sunlight. The other tails contain plasma--free electrons and ions, that is, atoms from which sunlight has removed one or more electrons, leaving a positive charge. They glow in the colors characteristic of their material (a bit like the way streetlights produce the characteristic glow of sodium), and are pushed back by the solar wind. As explained on the above web page, the velocity of the solar wind is not too many times larger than that of the comet, and that causes them to point not straight away from the Sun but at a small angle to that direction.

    See also htpp://www.phy6.org/Education/wsolwind.html

    David

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24. If light speed sets the limit, why fly into space?

    Dear sir

    I have a question as to space travel. What is the point in exploring space? Is it just for achievment purposes or in the future will man discover LIGHTSPEED? Because otherwise, the whole thing seem rather pointless. It is rather like asking a garden snail to tour America in it`s own lifetime. Can you put any light on this question?.

            Reply

    From all we know, achieving lightspeed or anything close to it is well beyond today's technology, and I suspect, tomorrow's as well. The purpose of exploring space is different--to expand humanity's reach, and to understand the universe in which we live. Ancient humans may have been content to see the sun, moon and stars rise and set without caring what they were, or how distant. We have come a long way from then--to electricity, cars, airplanes and the internet--essentially, because humans want to understand more. Most Americans would probably feel rather stale if no progress happened over their lifetimes--just different teams making it to the superbowl, different wars being fought overseas. I for one felt excited by the landing on the moon, by the first pictures from Jupiter and Neptune, and of the sun in X-rays (quite different from the bland disk we see). I also feel excited by evidence of distant planets and giant black holes at the center of galaxies. No, I don't think we'll get there in my lifetime or in the next 1000 years--but humanity has a longer timetable, much longer than that of any individual.

25. Does precession mis-align ancient monuments?

    Dear Mr Stern,

    I live in Ireland. There is an ancient monument at Newgrange in this country which was constructed some 5000 years ago. The particular alignment of the monument to the sun allows an inner chamber to be lit by the sunrise at the winter solstice. The construction of such a building so long ago with such accuracy seems almost incredible to me.

    I have a query however. Is the tomb doomed to a long darkness in the future due to precession?

            Reply

    

    
    Look at the above figure, taken from the web page http://www.phy6.org.stargaze/Sseason.htm about the seasons of the year, in section #3 of ""Stargazers." It shows the relation between the Sun and the Earth with its tilted rotation axis, throughout the year (north is up). That relation is what varies the length of the day and the apparent motion of the Sun across the sky, from season to season.

    Imagine you were able to rotate this arrangement by some angle--by 10°, 30°, 90° or whatever--around an axis perpendicular to the plane of the ecliptic. You rotate just the Earth and its orbit (and perhaps the Sun), while the rest of the universe stays as it is.

    The relation between the Sun and the Earth then remains exactly as before--the only difference is that you are looking at it from a different direction. Seasons and the apparent motion of the Sun across the sky are still the same as they were.

    What our imaginary rotation has done is exactly the same as what the precession of the equinoxes does to the Earth's axis. So if an ancient monument is lined up to point at the Sun during solstice, it will continue doing so. Our calendar is also adjusted, so it would also remain the same day of the year.

    On the other hand, an ancient monument aimed at a certain passage of a star would no longer fulfil its function, because now the axis of the Earth points towards a different part of the celestial sphere.

    David

26. Why does the Earth rotate? Why is it a sphere?

    Hi,

    I have been unable to get answers to the following questions concerning the earth, can you help?

    Why does the earth rotate - what are the forces causing the rotation?
    Why did it start rotating in the first place?
    Why are planets round?

    Any help to get these answers is most appreciated

            Reply

    Hi, Mike

    You have asked some very fundamental questions. Why does the Earth rotate? Because whatever it arose from--probably a cloud of gas and dust--was rotating to begin with.

    The thing to keep in mind that even a very slow rotation of a cloud of objects gets greatly speeded up as it condenses at the center. The reason is a basic law (a consequence of Newton's laws of motion) by which a quantity known as ANGULAR MOMENTUM (or rotational momentum) is conserved. The angular momentum can be defined as the average radial distance, TIMES the average velocity of motion, TIMES the mass.

    The mass does not change when matter collects near the axis of rotation, so we neglect the last part. Then, if the material collectes in the middle, where its average radius of rotation is 10, 100 or 1000 times smaller, the average velocity of its particles increases by the same factor.

    You see this happen every day. When water drains from a filled bathroom sink, even if the water in the sink is rotating so slowly that you do not notice, by the time it reaches the drain it is spinning rapidly enough to form a funnel. (It does not spin in the opposite direction in Australia: the effect on which this claim is based is far too weak to have much effect. See "Stargazers," section 24). You also see this in hurricanes and tornadoes.

    And you see it happen when a large object in space collapses. In 1054 a star "went supernova" in the constellation of the Crab, a process in which the top layers blow off and the core collapses to a tiny "neutron star," perhaps 15 km across and as massive as the Sun. The collapsed core of the Crab Nebula apparently rotates 30 times a second, because that is the frequency at which it blinks in x-rays and radio (and I believe in its light, too).

    In the solar system all planets orbit in the same direction and nearly in the same plane, and they and the Sun rotate in the same direction too (= counterclockwise, viewed from north). This suggests that they all condensed from the same cloud.

    Now that other question: why are planets round? Because of their gravity. On the surface of the Earth, solid material--say, rock cliffs --can easily stand the pull of gravity without deforming. But go just a few hundred kilometers inside the Earth, and you find everything under enormous pressure, from the weight of the layers heaped up on top. Under such pressure (and helped by the heat down there!), even solid rock deforms like putty.

    If the Earth were all fluid, gravity would pull it into a symmetric sphere--the same way as it shapes the oceans. The Earth is not fluid, but as mentioned above, it makes no great difference. Actually, a ROTATING fluid Earth would be deformed by the centrifugal force, with the equator bulging out slightly. Gravity is weakened there, by the centrifugal force and by the greater distance from the center. That was observed in Newton's time, and Newton explained it by essentially using a fluid analogy.

    Jupiter is much bigger than Earth and rotates much faster: its equator bulges out so much that pictures taken through a telescope suggest a definite ellipticity.

    Voyager 2 and other space probes have by now cruised through most of the solar system and have imaged its planets and their moons. The rule seems to be that objects with a radius above 150 km are spherical; smaller ones do not have a strong-enough gravity and may be potato-shaped, e.g. the moons of Mars.

    Sincerely

    David

    .
    

27. What's so hard about reaching the Sun?

    Hi there. hope you don't mind a question.

    In http://www-istp.gsfc.nasa.gov/stargaze/Sorbit.htm (at the end) you state:

    "The hardest object to reach would be the Sun itself. Our imaginary spacecraft, freed from the Earth, would be moving like the Earth around the Sun at about 30 km/sec. The only way for it to reach the Sun is to somehow kill that velocity--for instance, by a rocket imparting 30 km/s in the opposite direction; if that were done, the spacecraft would be pulled in by the Sun. The people who propose sending nuclear waste by rocket into the Sun do not seem to know much about orbits! "

    It would occur to me that the challenge of getting to the sun would consist mostly of getting out of Earth's gravitational influence. Ignoring that step (or starting from a point in earth's solar orbit which is NOT on the earth's surface), I would think that just about any deceleration would allow you to reach the Sun. While a deceleration of 30 km/sec would allow an object to "fall like a stone" into the Sun, an orbital velocity of, say, 29.5km/sec, instead of 30 km/sec, would result in a very slow, long, death spiral, but still one which still eventually results in a solar plunge (making the assumption of no external interference, such as another orbiting body didn't snag you along the way or provide a velocity boost).

    What am I missing? Or am I?

    Jim

    P.S. No, I'm not a "nuclear waste into the sun" kinda guy. A perfect place for disposing the stuff, but not worth the risk of putting the waste on top of all that explosive energy and lighting the fuse.

            Reply

    Hello, Jim

    No, I am afraid it won't work. All orbits in the Sun's gravity field are ellipses, or other conic sections: there are no spirals. If you place an object in Earth's orbit around the Sun but free of the Earth's own pull, and cut its velocity from 30 km to, say, 5 km. velocity, it would certainly fall sunward, but it would gain velocity doing so and would whip around the Sun in an extended ellipse. That ellipse would have its apogee (highest point) in the Earth's orbit.

    If you cut down its velocity to near zero, it would again fall sunwards. It is still moving in an ellipse--a very long and skinny one--and if the Sun were just point-size, it would still miss and return to apogee in the Earth's orbit. However, the Sun does has an appreciable size, so that when when the ellipse is sufficiently narrow, the object hits the Sun, and then it never comes back.

    Until recent decades comets were never seen to hit the Sun, because even a slight sideways velocity makes them miss. Since then, because of observations from space (which are able to see small comets close to the Sun) some such comets were observed. Still, it is not a common thing.

    Sincerely

    David

    .
    

      Where does space begin?

    I have a question about how far up do you have to go to get out of the earth's atmosphere to be in space. I would like this answer in the form of miles. I would gratly appreciate any information on this.

    Thank you.

    Reply

    The ocean has a well-defined top surface, where water ends and the atmosphere begins. The atmosphere doesn't: it gets more and more rarefied, and where space begins is open to interpretation.

    Near the ground the atmospheric density drops to 1/2 every 5 kilometers (8 kilometers = 5 miles, very nearly), so at 10 km where jets fly, density is down to 1/4. This continues more or less up to 100 km (the halving distance varies a bit, with temperature), where collisions between molecules become relatively rare. Higher up the oxygen and nitrogen each decrease at its own rate.

    The space shuttle flies at 300-400 kilometers, but even there enough air remains to seriously limit orbital lifetime. Also, enough of that air is ionized--electrons ripped off molecules by the Sun's extreme ultra violet, leaving behind positive "ions"--to reflect radio signals. Satellites orbit at 600-1000 km and up, and that, too, is where the first signs of the radiation belt can be observed, particularly off the Atlantic coast of Brazil, where the magnetic field is relatively weak.

    Somewhere between here and there, you enter "space. "

    .
    

      Gravity at the Earth's Center

    (Two questions with the same answer)

    (1) My students had a couple of questions that I thought were interesting. I told them I'd ask ya'll.

    1. What would you weigh is you were at the exact center of the earth?
       
    2. What would you weigh is you were 3 meters from the center of the earth?

    Please include supporting evidence for your answers

    (2)

    I am confused about Newton's discussion of the force on a particle within a sphere in the Principia. In one place, he says that the force would be zero, since the attraction of all the particles in the sphere would cancel each other out.

    Just a little further on, he says that the force would be directly proportional to the particle's distance from the center of the sphere.

    Can you clarify these two seemingly conflicting statements?

    Thank you for any light that you can shed.

    Reply

        Dear Teacher (and this also answers the student of Newton):

        Yours is an old question, first tackled by Newton, as the "Hollow Earth Paradox." If the Earth where a hollow sphere (inner and outer surfaces spherical) and someone dug a hole that reached the hollow interior, and then stepped into it--what would that person experience?

        Newton's answer--there would be no gravity inside the hollow. Any object thrown into it--say, a stone--would continue in a straight line with constant velocity (ignoring air resistance).

        Newton's argument was roughly as follows. Take an object at a point in space anywhere in the cavity and draw from it a double cone (like a teepee, extending to both sides). Each side of it will cut part of the sphere, and the gravity of the two parts will tend to pull the object in opposite directions (make a drawing and you will see).

        Newton showed that the pulls of both part cancel each other: one part may be closer, but then it will also be smaller. Since all directions can be covered by a collection of such cones, the total force is zero. Today we get this result much more quickly by the theory of the potential, but that takes three-dimensional calculus, which Newton did not have.

        Now: Imagine you are somehow in the middle of the solid Earth--by some magic, not crushed by the rocks, suffocated or incinerated. In your mind you can divide all matter on earth into two parts: a smaller sphere containing everything that is CLOSER than you to the Earth's center, and a hollow sphere containing everything that is MORE DISTANT.

        By Newton, the hollow sphere exerts no pull, while the interior sphere, like the Earth, pulls as if all its mass were concentrated in the middle (that's another thing easily shown from potential theory). If you are halfway to the center, and the density everywhere is the same (actually, matter gets compressed towards the middle) then only 1/8 of the Earth mass is pulling you, but at half the distance, the pull is 4 times stronger ("inverse squares law"), so the final result is 1/2 of the gravity on the surface. At 1/N times the radius, the pull of gravity is just 1/N the pull at the surface.

        As you get deeper and deeper, the inside sphere gets smaller and its pull is weaker, so gravity too weakens. At the center, it is zero. At 3 meters from the center, it is the pull of a 3-meter sphere of rock, experienced on its surface--the pull of a tiny asteroid.

        Please note--that is just the pull of gravity on YOU. The rocks above you are also all pulled down, all the way to the surface of the Earth, and their weight is likely to crush you before you get very far. There may perhaps exist a cave a mile deep, but if so, none is much deeper, because there is too much weight piled on top.

    .
    

    (a)   Radiation hazard in space--1

        I am working at the University of Arkansas School of Architecture along with members of the Habitability team at NASA for the manned Mars mission. It has been explained to me that radiation will be a big issue in the design of a Mars habitat. I was wondering how feasible it would be to use nuclear power to produce a eletromagnetic field around the habitat to reduce or deflect the radiation. Is it possible to create a magnetic field strong enough to provide radiation protection? And if so, how much energy would it require?

    Reply

    Dear Jim     I have not calculated the field needed, but it is probably very strong, too expensive to set up, too much mass and energy are needed, and a strong magnetic field would affect instruments.

        The cheap and simple way is to build a shelter--especially since the dangerous events are the ones of solar outbursts, which are rare and last a day at most. You can calculate the shielding, but 20-50 cm rock should do a pretty good job (remember gravity is weaker, too, they will weigh less than on Earth).

        Have you read Ben Bova's "Mars"? It's fanciful science fiction, but his physics seems OK. The Mars astronauts are hit by a solar outburst halfway to Mars and wait it out, huddled in a special shielded area of their spaceship.

(c)   Radiation hazard in space--3

(Excerpt from question)

    The other night, I was watching a program about the Apollo missions and how they might be a hoax staged by NASA. Many interesting points were raised and by apparently learned men. The point concerning me most was a claim that the craft used to travel to the moon, and the LEM that took them to its surface, would not have provided enough protection from the high levels of radiation in the VanAllen Belt and cosmic radiation traveling through the solar system. The man postulated it would take roughly three feet of lead to shield against such radiation. Can you tell me what material protection the crew members of the Apollo missions had or what measures were taken to protect them?

Excerpt from reply

Dear John

    That program on TV created a flurry of inquiries--I think yours is 5th. ... The cosmic radiation in space might indeed take 3 feet of lead to reduce it significantly--which is about as much protection as the atmosphere gives us.

(By the way, a widespread misconception of the public is that lead makes a better shield than other materials. It does for x-rays, which is why dentists and doctors use lead aprons, etc. However, for high- energy particles of space, all substances are more or less equivalent, for the same amount of grams per square cm.)

Keep in mind, though , cosmic radiation is a very weak source--it carries about as much energy as starlight. So the number of rads one gets from it is not high.

.


  "Danger, falling satellites"?

Hi

I am a writer, so my knowledge is always far behind the "truths" I write. But I was reading your article "Orbits", on the web, while researching a story I am writing, and liked the voice of your writing. So I thought I might ask you some questions. I hope you have the time.

I have searched extensively (without much luck) for information on the issues of reentry. I understand a layman's idea of how you get something into orbit and get it to stay there. I have also read about the demise of the Compton Observatory. Yet when I read about reentry, the issues of angle and speed are not clear.

If for instance a craft were out there going at 17500 mph and I just slowed it down to 60 mph--what would happen? Or if I just stopped it? Would it come crashing down like a lump and burn up along the way. Why does the shuttle enter the atmosphere at such speed and not just pop in with a large parachute? Perhaps it could use rockets to slow the gravity pull while it descends to an altitude where a parachute or simple gliding could be initiated without all that heat.

My problem in my story is that I need for a smallish satellite or vehicle (whatever) to be able to be descending into the atmosphere from orbit (in or out of control), fairly slowly (>400mph or thereabouts-- preferably, much less) between 60000 feet and the ground. Do I have a prayer - other than a Hollywood solution?

Reply

Re-entry from space is discussed in the middle of "Spaceflight" at http://www.phy6.org/stargaze/Spaccrft.htm

You wrote:

"If for instance a craft were out there going at 17500 mph and I just slowed it down to 60 mph--what would happen? Or if I just stopped it?"

You can't do so, no more than you can with your car: if it is going at 60 mph you cannot just slow it down to 10 mph, or to a stop, unless you apply the brakes. If you do that, the brake pads rub against the drums or disks and convert the energy of the car into heat.

The speed of an orbiting object is enormous, and it too must be dissi- pated as heat: re-entering at a shallow angle lengthens the time spent in re-entry, so the heat is generated more gradually and can be radiated away without the spacecraft getting too hot. A small satellite can survive it, if suitably protected or if lucky enough: in the 1960s, USAF airplanes retrieved film packages from spy satellites, ejected in well-protected (but relatively small) capsules. When such satellites reach the denser atmosphere, they slow down--perhaps to 150 mph or less. The film capsules would then deploy a parachute, and as they floated down, a twin-boom transport airplane, with rear door open, would trail a line with a hook, snag them and pull them in. If they were to hit the ground (in principle--actually, rerieval was usually above water) they would of course get banged up somewhat, but their instruments etc. could perhaps survive.

Further message (shortened)

My story (a screenplay) which is more a people story than a James Bond, envolves a collision between a malfunctioning runaway satellite and a Boeing 767.

Reply (shortened)

A film capsule of (say) 10 or 20 kg would be less likely to demolish a 747 in full flight. Still, I would not like to be aboard that plane! It is not the 150 mph (or whatever) of the capsule, but the 600 mph of the airplane, which makes the collision so dangerous. If it hit the main body of the airplane, or a wing, results could be grim. If it hit a jet engine, it would probably demolish it. The satellite itself or the capsule would have a parachute deploy to slow it to much less than 150 mph.

The nearest thing I can recall is an airliner flying over Damascus, Syria, during one of the tense periods between Syria and Israel. The Syrians fired a missile at it, and by some miracle it stuck in a wing and did not explode. The airplane landed safely, but it was a close call.

.


  The Lagrangian L3 point

Hello

I went through the site at: http://www.phy6.org/Education/wlagran.html and was just wondering if there is any information on L3? As I read the article I may have missed its mention. If not could you tell me if there is any information you could point me towards?

Thanks Very Kindly

Reply

Dear Bill

The Lagrangian point L3 is not mentioned because it is only of theoretical interest and has no practical application. If only Earth and Sun existed, L3 would be on the Earth-Sun line, but on the opposite side of the Sun. At that distance, a satellite at exactly 1 AU (Astronomical Unit = Sun-Earth distance) would experience a bit more gravity than the Earth, being pulled not just by the Sun but also by the Earth. Its orbital period would therefore be a tiny bit less than a year. L3 is at a slightly larger distance, where the greater distance from the Sun reduces the Sun's pull just enough to make the satellite's orbital period exactly one year, so that it would keep a fixed position relative to the Earth.

Practically, the feeble pull of the Earth at this distance is negligible compared to other effects, such as the attraction of Jupiter. Besides, it would be hard to communicate to such a spacecraft, since it would be permanently behind the Sun!

Look also at "From Stargazers to Starships", home page at http://www.phy6.org/stargaze/Sintro.htm. Sections 34 there calculate the Lagrangian points.

.


Distance to the Horizon on an Asteroid

Hi,

The reason I stumbled across your page is that I work on astronomical, science fiction and fantasy art and illustration and was looking for a formula that would allow me to calculate the distance to the horizon of any body once one knows the radius of that body. I've been working up a piece illustrating a scene taking place on Ceres and it would be nice to have the horizon more or less where it ought to be.

Any suggestions where I might find such a tool?

Reply

For the distance to the horizon, look up the formula in "From Stargazers to Starships", sect. 8a (where it is derived). It depends on your elevation, of course. All you need is replace the radius R of Earth by that of Ceres, assumed to be spherical.

There is a great story by Arthur Clarke, "Hide and Seek," in which a man in a spacesuit successfully evades a spaceship on a moon of Mars, where the horizon is quite close. Have you read it?

.


Overtaking Planets

Hi - I am looking for the way of calculating orbits of two planets passing each other.

For example:

• Planet A - orbits every 30 years
• Planet B - orbits every 12 years

The two passed each other in 1982. What would be the calculation for determining when the two will pass each other again, in layman terms?

Trying to answer this for a grade school student - trying to assist.

Reply

Hi, Mike

Your example does not sound too practical--it's like asking when does Jupiter overtake Neptune, even at the closest approach they are still very far apart. So let me reformulate

• Earth orbits the Sun in 1 year, the frequency is 1 rev/year.
• Mars orbits the Sun in 1.88 years, same direction
          Its frequency is 1/1.88 = 0.532 rev/year

At some time (say, today) Earth passes closest to Mars. When will it happen again?

Draw the two orbits, one inside the other. Then assume you put the whole set-up on a turntable, rotating with a frequency -1, that is that is, 1 revolution per year but in the opposite sense. Forces in the rotating frame would be quite different, but we ignore that--the motions alone are what counts here.

Frequencies add up, rotation periods don't. The orbital frequency of Earth in the rotating frame is 1 - 1 = 0 revolutions/year, that is, it does not move. That of Mars is 0.532 - 1 = -0.468 rev per hear, in the opposite direction, which make sense--the Earth moves faster, Mars viewed from it moves backwards. Its period T' will be, in the frame where the Earth sits still

T' = 1/0.468 = 2.083 years.

That's you answer. You can use 12 and 30 years, if you wish, the same way.

.


Falling Towards the Sun

In doing research on a recently retired Pelton Wheel, I found your article on the Pelton Wheel and its implications for NASA's Solar Probe. Not being a physicist, I want to verify that I'm interpreting one section of the article correctly:

"...the most economical way of achieving that mission...may well be sending the spacecraft towards Jupiter....It would then make a tight loop around the planet, overtaking it in such a way that practically all its orbital velocity around the Sun is lost, and then fall toward the Sun. "

"Falling toward the sun"...I'm having difficulty visualizing this. Is it similar to the slingshot effect used to get Apollo 13 home? Would that be a grossly incorrect description? If so, could you offer a short, simple lay person description? I'm writing for a power industry internal newsletter and cannot get overly technical.

Reply

Dear Leslie

"A little knowledge is a dangerous thing. " I would guess that you reached my Pelton wheel site using a search engine, and did not note it was unit #35a--the last unit, in fact--of a big educational site about spaceflight, astronomy and physics. You can reach the home page from the "back to index" button on the bottom, and after you do that, go to the preceding unit #35 where gravity-assist orbital maneuvers are discussed. Even though the spacecraft and moving planet (or moving moon) never touch, the result is similar to an elastic collision. Just as Sammy Sosa's home runs are a combined product of the speed imparted by the pitcher and that of the bat, so it was for Voyager 2 and Jupiter, for instance.

It works both ways: head-on collisions gain energy, overtaking ones give it up. Usually in space we want an extra boost, but in a turbine we want the water to lose as much as possible, because by the conservation of energy, what is lost from the water jet is gained by the water wheel. To hit the Sun with a spacecraft, it's not enough to escape the Earth's gravity: do that and you are still circling the Sun, like the Earth, with the same velocity, 30 km/sec. To give up as much is just as hard as gaining an equal amount--which is more than what is needed to escape the solar system altogether.

I am not sure change of velocity was a consideration with Apollo 13, as much as hitting the Earth edge on, so that the spacecraft would be braked by the high atmosphere. Hit any lower and it would hit the Earth (and burn up before doing so), hit any higher and you miss the Earth, go out to space, and long before you are back for another try you have run out of oxygen.

.


The Polar Bear

Could you please assist me with an estimation of the energy absorbed from the sun at the arctic (polar) regions? I would also like to know, if possible, the amount of energy (in Joules or calories) that a polar bear needs for a day. Thanks in anticipation.

Reply

The polar bear is unaware
Of cold that cuts me through
Why not? He has a coat of fur!
I wish I had one too!                         Hilaire Belloc


Your request is one of the strangest I have ever received--do my correspondents feel that NASA knows everything? What is this information intended for?

About the polar bear: I will make a wild guess, 60,000 calories/day. But I really do not know. However a book exists which probably contains the answer, "The Fats of Life" by Caroline Pond. I saw its review in the "New Scientist" supplement of 6 May 1999, the review talks about the bear's metabolism but does not count calories.

The amount of sunlight at the pole depends on season. At the pole, in midwinter it is of course zero, in midsummer (clear sky) I would guess about 0.3-0.4 Kw/sec sq. meter, of which I suspect most is reflected by the ice.

.


Are the Sun's Rays Parallel?

David--thanks for your article. Can you tell me: Are the suns rays parallel ?

Reply

Dear Mary

What a question! Some are, most are not--but the answer depends on what you plan to do with the information.

The Sun covers about half a degree of the sky. So rays that come from opposite edges of the Sun have directions which differ by half a degree and are not parallel.

Rays which reach your left and right eye from a distant star, on the other hand, are very close to parallel--they may meet somewhere at the star, at the same point (and then they converge) or separated points (and then they probably diverge), but the eye and even the the telescope cannot resolve such details.

Rays from the same point on the Sun are pretty much like those from a star. But again, "same point" is hard to pin down--even sunspots may be thousands of kilometers wide.

Response

Thanks yet again. The question echoed what I remember being taught at school. Dont ask in which discipline. I can remember only the statement.

The reason I needed confirmation or refutation is simple. My hubbie has been observing the shadow cast by the sun on our south facing balcony railing at a specific time of day. One of his statements showed that he felt the sun's rays radiate ! I disagreed both with his conclusions and his statement.

You're a star for answering so clearly and quickly and leaving both of us room to be right. Is psychology your second area of specialization ?

.


More thrust in reverse than going forward?

(shortened) Sir,

I was struck by the visual similarity between a Pelton bucket and the split "clamshell" type of thrust reverser on jet aircraft. By an impulse analysis I estimate that the rearward thrust is about 157% of the forward. Is this about right?

REPLY

Dear Fred

I did not understand all you wrote, but please remember the zeroth law of thermodynamics, "there ain't such a thing as a free lunch. "

I don't believe a clamshell thrust reverser can generate more thrust forwards than backwards! There is a fine question of energy, which goes as the square of the velocity--but thrust is momentum transferred, and shooting a mass m with velocity v forward or backwards gives momentum + mv or - mv. In a Pelton wheel, the buckets move relative to the jet, but in a jet-engine clamshell they don't--so they can deflect, but not add any energy.

.


The varying distance between Earth and Sun

Hi

Sorry to be taking up your time, you are without a doubt very busy with answering many questions, but I am a 7th grader in View Ridge doing a report on "distance from the earth to the sun at 1 day from all 12 months." After searching for 3 hours I could not find this data and I thought maybe you could direct me on how and where to find this data or maybe you could send the data to me if it is easily accessible to you. Well thanks for your time and reading this message.

Reply

Hi, Ben

I am not at all sure what your teacher is asking, or why--or what you are supposed to learn from it all. The mean distance of Earth from the Sun is the astronomical unit (AU), equal according to my handbook to 149,599,000 kilometers.

From the nautical almanac; the Sun's distance on day N of the year in AU is

R = 1.00014 - 0.01671 cos g - 0.000 14 cos 2g where in degrees g = 357.528 + 0.9856003 N

A formula exists for finding N based on the way astronomers count days, but I suspect counting from January 1 is OK, because then R is smallest around January 3, which is indeed well known. Being in 7th grade, do you know what a cosine is? If not, look up in the mathematical section of "Stargazers".

.


Mission to Mars

I am a professor in a large university and teach interdisciplinary general education courses. After reading this month's Scientific American [March 2000], I have been thinking about alternative scenarios for Mars missions.

The question is:

Suppose the total mass of the mission payload is M_p, and the total mass of the launch vehicle plus propellant is M_t. How does M_t scale with respect to M_p? If

M_t = K(M_p)^a what is the exponent a? It doesn't seem obvious that it should be 1.

REPLY

Dear Richard_t I suspect that a=1 after all. If you want to send twice the payload, you need a rocket twice as large. There exist no economies of scale.

There does exist a certain flexibility in K, however. You do have to escape the Earth's gravity, at least to a circular parking orbit, and this sets a lower limit to K--it depends on your fuel, and the staging of the rocket, but it is going to be around 20 or more, usually more.

To fly from there to Mars, all sorts of tricks can be employed--ion engines, solar sails, etc.--and the duration of the trip is also a variable. Finally, the spaceship is to stop at Mars, not fly past it, and that requires either extra thrust or some delicate aerobraking. I think the article goes into all this, but the bottom line is--it isn't easy, and would take both ingenuity and luck to be pulled off successfully.

.


Kepler's calculation

    I've been searching for a book that would show me how to re-enact what Kepler did, with Brahe's data. That is, I want to use my 4 inch telescope and my accurate clock to record data that I can use to show that the data fits an ellipse. Where can I find instructions on how to collect the data and where can I find the equations Kepler used to show that the data fit?

    I found your web page course "From Stargazers to Starships" and thought you might know what I am looking for specifically.

Thank you for any suggestions.

Dan

REPLY

Dear Dan

    Tycho Brahe had no telescope, you know, but he built some very accurate quadrants--instruments resembling giant protractors, with sights to line up with stars. With these he tracked the positions of stars very accurately, taking into account factors such as refraction of light in the atmosphere. Kepler's laws were essentially based on the observations of Mars alone. A 4-inch telescope can be aimed much more accurately (the eye has a resolution around a minute of arc, at most), but this does not help much in precise tracking, unless you can determine with equal precision the direction in which it is pointing. That probably needs a strong foundation and accurate and strong mounting.

    That, however, need not be not your problem. You can always "fake your data" and take positions of Mars from the ephemeris table of the astronomical (or nautical?) almanac. Amateur astronomers in your area will have it, also university libraries--you might even find it on the web, I have not looked.

The question is, however, what then? To check the position of Mars in the sky, you need track both Earth and Mars. I don't know if motion of the Earth in a circle around the Sun (the idea of Copernicus) is good enough, but you can try it for a start. In fact, try the same for Mars, too, using the proper orbital period for each: you will get retrograde motion, though positions will not agree exactly.

    To check the uneven motion of Mars is harder. You must draw its ellipse (not accurately--only the calculation needs to be accurate) and mark on it a large number of points, say 36. Using the equation of the ellipse (and you will also need the eccentricity of that ellipse-something Kepler had to find out the hard way), calculate for each point its distance from the Sun (a computer will help). Also calculate the area covered by each 10-degree pie slice, approximating each slice by a triangle, and then from the law of areas you get the time needed to cover that angle, in some arbitrary units. Those units can be found by noting that all the times must add up to one orbital period. Of course, you must also know in which direction apogee is, the greatest distance from the Sun.

    If you now mark 72 positions of the Earth on its orbital circle over 2 years (about one Mars year), each will have its date. For the same date, you can estimate the position of Mars from your 36 points, each of which also has a date, and get the direction to Mars. Oh well--you may need 3-dimensional geometry, because the positions in the Almanac are probably not in ecliptic coordinates (Mars and Earth both move near the plane of the ecliptic) but in declination and right ascension. You can see it will be a big job.

    I do not know how Kepler's calculated all this (it took him years). The position of Mars in the sky (as you can see above) involves BOTH Kepler's first and second laws. My GUESS (just a guess, I may be wrong) is that he assumed the Earth moved in a circle, and that Mars moved in a circle too (he knew the periods of both from long-term observations). He then assumed (like Copernicus) that both moved at constant rates around those circles, and found (as you might--see above) that the positions did not fit. He then MAY have assumed that the position of the Sun was some distance from the center of the circle of Mars, and found in that case that the law of areas could explain most irregularities. FINALLY, he had to give some logical reason for the displacement of the Sun from the center of the orbit, and the most elegant idea he could find was that the orbit was an ellipse and the Sun was at one focus.

    I vaguely recall that the book "The Sleepwalkers" by Arthur Koestler describes those years in Kepler's life, and maybe you will find some clues there. Be warned, though--that is a work of literature by a writer not familiar with math. Maybe you can then write me what you found.

.


The Appearance (Phase) of the Moon

    What did the moon look like in Richmond, VA from February 28 to March 8, 2001? For example: full moon, crescent, etc.

REPLY

Dear questioner

    First of all--the moon looks pretty much the same from anywhere on Earth, at least its light-shadow phase-Richmond or Los Angeles, there is no big difference. The direction in which the light-dark division points may differ, because while the moon seen from Australia and here is pretty much the same, the "up" direction in which our heads point is not.

    To find the phases of the moon, you might consult an almanac. Or else, you might look up the Jewish date, using a web site such as

http://www.rtlsoft.com/hebrew/calendar/today.html.

    The Jewish calendar (actually taken from ancient Babylon) has every month beginning with the new moon--the time the moon passes the sun in its trip around the sky (and is not seen). A day or so later it is a very thin crescent setting just after the sun does. In the days that follow that crescent gets wider and wider, and the Moon sets about an hour later every night.

    About a week after new moon you get a half moon, after that it is "gibbous" and in mid month, around the 14th on the Jewish calendar, you get a full moon rising just when the sun sets. To see the moon during the last week of the Jewish month you must be up pretty late, and you will see a half moon or crescent moon in the east lit up from below, from where the sun will rise some hours later.

    On the Jewish Calendar, February 28 is Adar 5, giving a crescent Moon; March 8 is Adar 13, with the moon nearly full. The month of Adar has 29 days.
            Hoping this answers all your questions

Dr. David P. Stern
Goddard Space Flight Center