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Please note!

    Listed below are questions submitted over the year by users of "From Stargazers to Starships" and the answers given to them. This is just a selection--of the many questions that arrive, only a few are listed. The ones included below 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.

            Note about this web page only. It got corrupted and repaired, but odd letters may still appear uninvited. Just ignore them!

    This project started at a time when downloads used slow phone lines, and therefore the questions were grouped in files of 15-20 each. With any request for a particular question, only the appropriate file needed to be downloaded.

    By now (2009) the list has grown too long to include in every such file, and therefore most access is through this comprehensive listing. Alternatively, an index file listing questions by topic can be linked from here.
  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?

  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

To avoid excessive file length, entries #43 to #438 are not listed here. The full list can be reached at

  1. Second Moon for Earth?
  2. The year 2012 and a distant companion of our Sun
  3. Distance between two points on a sphere
  4. Getting sucked n by Gravity
  5. The work of Nikola Tesla
  6. Firing a cannon straight up
  7. Does one see half the sky--or more, or less?
  8. Why are nights dark?
  9. The origin of the Solar System
  10. Flying to other planets
  11. The heat of the Sun's corona
  12. Crossing our galaxy's equator
  13. Newton's 3rd law--in statics and dynamics
  14. Barycenter of Earth-Moon system
  15. What if Earth rotated in only 10 hours

  16. What Book covers material of "Stargazers"?
  17. Climate Change
  18. A classroom Demonstration
  19. Why doesn't the Solar System Collapse?
  20. A Diamond Core for Jupiter?
  21. Why no "artificial gravity" on the space station?
  22. Precession of the axis of Mars
  23. Does the axis of the Sun precess?
  24. Can a microwave oven produce 900 deg Celsius?
  25. Beaming energy through space
  26. The year 2012
  27. The Earth's Precession Cycle
  28. The empty space inside an atom

  29. Rotation of Galaxies
  30. Sailplane flight
  31. How far to the Pole Star?
  32. Missed Discoveries
  33. Independent study for bright students
  34. Double slit interference experiment in space
  35. Ionizing Radiation and the Origin of Life
  36. On Earth's spin and Moon's appearance
  37. Back to the Geocentric Universe?
  38. Radiation risks from uranium counterweights
  39. The centrifugal force from Earth's rotation
  40. Earth's rotation and human lifespan
  41. Dependence of cosmic redshifts on direction
  42. Difference between Gravity and Magnetism
  43. SciFi world with ahort days and long nights
  44. Celestial Equator and Ecliptic Equator
  45. Cavendish gravity constant G drops out
  46. Teacher seeks material
  47. Solar Sails
  48. Life under stronger gravity
  49. Message from Kansas
  50. Finding true north in an underground mine
  51. Aristarchus
  52. Calculation of Gravity
  53. Message from Michigan
  54. Confused about "Temperature"
  55. "Negative work" and energy
  56. The Coriolis force on a moving air mass
  57. Recent change in sunset?
  58. Space and Dark Matter
  59. Newton's 3rd law
  60. Shift of Earth Axis in 2012?
  61. Ptolemaic Theory of Planet Motion
  62. Electricity from Earth's Rotation?
  63. Change in Earth's gravity after Tsunamis
  64. Science fair expt. on light output of CFLs
  65. Does iron 56Fe have the most stable nucleus?
  66. "Black Light Telescope"
  67. Message from New Jersey

    465.  Rotation of Galaxies

    Dr. Stern,

        I read your
    article on Rotating Galaxies and Dark Matter and have a few questions about the assumptions made in the calculations of mass and the velocity of the starts within galaxies that led to the theory of dark matter.

        My first question is what percentage of black holes and their average size and dispersion throughout a galaxy was used in calculating the mass of the galaxy?

        My second question is whether or not gravitational time dilation was factored into measurement of star velocities at various distances from the galactic center. I am wondering to what degree the time dilation between stars close to the galactic core and those near the edge would have on our perceived measurements of their velocities and if this could account for a significant percentage of the disparity in anticipated velocities. I hope you have a chance to reply, I am very curious about this topic.



    I am not an expert on the subject, so what follows is more personal guess than solid knowledge.

        About the first question--we do not know enough about the distribution of black holes even in our own galaxy, but knowing that mass is really not needed. What is needed is the distribution of mass throughout the galaxy--including that of visible and dim stars, black holes and any invisible "black" matter.

        If most of the matter were in a central black hole (not likely), the velocity of stars in the galaxy would follow Kepler's 3rd law. If the distribution of matter (against distance from the center) followed the distribution of luminosity, the outer dim parts of the galaxy would still follow Kepler's third law. For a long time this was believed to be the case. while those regions were considered too dim to measure their Doppler shifts. We now know those shifts, and the outer parts rotate much faster than expected, suggesting they sense a much stronger gravity than the one inferred from the central luminosity.

        I think star velocities at various distances from the center are fairly accurate. Only when emitted in a very small volume around a black hole does light undergo gravitational red shift. The orbits measured near our galactic center (see section on the black hole in the center of the galaxy) are further away.  

    466.  Sailplane flight

    If you are willing, perhaps you can verify my analysis of a simple physics problem with our model sailplanes. If you do not want to take the time I will understand.  BUT this is an interesting question.

           We are members of the Pikes Peak Soaring Society. See out web site at We fly unpowered sail planes and gain altitude by circling in thermals same as the full size planes. For many years many of us believed that the plane was "unaware" of the ground. That it operated in a "river of air". Recently we have recorded flights with a GPS and have found data that has caused me to believe otherwise.Let me set up a situation, show you my simple analysis, and then ask you if my analysis is correct.

           A steady wind is blowing out of the north at 20m/sec. A sailplane is circling in this air at a constant airspeed of 20m/sec. So going south the plane's ground speed is 40m/sec and going north the planes ground speed is 0 m/sec. Since the plane is traveling at a constant airspeed, the drag energy of the plane is constant.

        So Ep (potential energy) = mass * gravity * height and Ek (kinetic energy) = 1/2 mass * velocity^2 and Em (total energy) = Ep + Ek + Edrag and I'm ignoring other forms such as lift and sink. Since Em must remain a constant as the plane's ground speed changes from 40m/sec to 0 m/sec the Ek=0 and Edrag hasn't changed so the Ep must increase meaning the plane must rise (or descend more slowly depending on Edrag).

           Is this correct thinking? Is the V in 1/2mv^2 the ground speed?? We are having a big disagreement on this point. My thinking is that if Ep is using earth's gravity then Ek must be earth referenced also. Am I missing something.

        I would appreciate your analysis.


    A short answer: an airplane is indeed "unaware of the ground," its airspeed alone determines lift and drag. That blissful unawareness ends of course when it lands or takes off. That is when speed relative to the ground makes a difference: you'd rather have your speed relative to the ground equal to your airspeed MINUS the wind speed, not PLUS. So you take off and land into the wind (and avoid crosswinds).

        As for energy-- let me here review the energetics of glider flight. Be very careful! In my book, there is no such thing as "drag energy". There does exist a drag force F and a drag power Pd, the energy gain per second caused by drag; it has a minus sign, because drag causes energy LOSS, not gain

        Suppose you stand on a high tower and drop the glider from there. As it descends, its potential energy Ep decreases and its kinetic energy Ek =1/2mv^2 increases. As v increases, so does the lift on the wings, until that lift fully supports the plane's weight. After that v should stay at a constant Vo--were it to increase, the airplane would rise and stop gaining kinetic energy. If Vo stays constant, Ek also stays constant

        Now the lift force L is proportional to the drag force D--the lift-to-drag depends on the design of the glider and of course on the angle of attack, which the rudder can adjust. That equality determines the glide angle G and ultimately brings the plane to a landing. The rate Pp at which potential energy Ep is lost (P here stands for "power") equals the power lost to drag, while Ek stays put.

        Now look at a similar scenario, but with the plane launched into a rising thermal with vertical speed V. The motion relative to the air is as before, with descent rate Vo sin(G). Viewed from the ground, the glider is given an additional vertical speed V. If V minus the descent rate is positive, the glider rises. If negative, it still descends, but perhaps more slowly. In the first case, the reservoir of potential energy from which the glider draws is increasing: it not only falls, it is also being lifted. The rate of energy loss to drag is the same, assuming the same airspeed.

        Add now a horizontal wind speed Vw , which I guess would make the thermal rise diagonally. It displaces the flight path, but the plane still flies relatively to the air. Only when it lands does the modification of total velocity relative to the ground make a difference.

        See also sections 22c and 22d in "From Stargazers to Starships," and maybe sect. 15. And
    section 8a about Pike's Peak!  

    467.  How far to Pole Star?

    I have no idea whether you are still willing to answer questions but I found a web site from a few years ago with your address so....I'm giving my questions a try.

        Where is the pole star? In other words is it in our galaxy? About how far away is it in light years is it?


    Hello, Jim

        Yes, Polaris is in our galaxy, about 430 light years away. See .

        Polaris has no particular link to Earth, it just happens to be close to the rotation axis of the Earth. That axis slowly rolls around a cone, so in ancient times other stars were close to the "pivot of the sky", and others will replace Polaris in the future. See  

    468.  Missed Discoveries

        I've been looking for examples, especially in physics, where the exclusion of outliers have led to the postponement of a future discovery. My search through the internet and Physhare's archives have left me with very little. I came across some mention of Kepler's decision to consider elliptical orbits rather than circular ones, because of some outlying data. I'm looking for good examples which are understandable to a high school age audience. Any leads?


    Dear Tom

        I do not know exactly what you have in mind, but here are some thoughts:

        ---Galileo (in 1613?) apparently observed Neptune and counted it as a background star in his telescopic drawing.

        ---Gilbert cites (1600) the
    magnetization of an iron rod on a tower in Rimini, not realizing it was probably caused by lightning. (

        ---Carrington observed a "white light" solar flare in 1859 and a magnetic storm a day later. He guessed at the connection, but no further flares like this were seen. When Hale built his spectroheliograph (1890), flares could be seen in the red line of hydrogen, and were suddenly recognized and associated with magnetic storms. ( and linked files)

        ---I vaguely recall that in the 1930s Fermi and his Rome buddies bombarded heavy elements with the newly discovered neutrons and after chemical separation, claimed to have created new heavier elements. Actually, their chemistry separated fission fragments.

        ---Larry Morley in 1962 submitted an article on magnetic evidence for seafloor spreading, and it was rejected--rumor has it, by both "Nature" and the" J. of Geophys. Res." A year and later Matthews and Vine convinced the community.

        There must be more, but I don't remember. Penicillin was discovered around 1930 but was neglected for about 10 years; Avogadro's law dates I think to 1814 but was ignored until Cannizzaro in 1860 brought it up in a conference. Steven Brush at the U. of Maryland may have a list of "premature discoveries".  

    469.  Independent study for bright students

    I teach in a small rural school. I have one section of physics with 20 students. The abilities (math and science) range from low (can almost do basic algebra to calculus). Yesterday I had a student approach me and ask if he could do some sort of independent study due to the fact he "had taken a two week class that covered all mechanics" and he is bored. (I had this student in AP Chemistry last year and do believe that he has learned and absorbed most of the basic physics concepts we will cover. Very intelligent)

        My thoughts are I will not be able to challenge him with what I have to offer in this class, but would like to. I cannot however justify using my whole prep to prepare advanced materials for one student when I have three other preps to get ready for.

        Has anyone had this come up? Does anyone have ideas for an independent study that would challenge him and take minimal time to prepare?     Any other advice?


    Hi, Jeff

        I do not know the level of your students, but for the last 15 years (I'm retired now) I have produced web resources for students and schools just like yours. Just finished the draft version of one on electricity and magnetism--"All Things Electric and Magnetic", home It is quite elementary but ends with Maxwell's equations.

        Other collections are "From Stargazers to Starships"--biggest and most mathematical, tough it stops short of calculus--and two non-math ones on magnetic phenomena inside Earth and in the space around it. Central home page is All stop short of calculus, have timelines, translations and for Stargazers, lesson plans, problems and a math course. All are compact and easy to copy, including 600+ pieces of answered correspondence.

        Project? Let your student choose. Electricity can be a project by itself; in "Stargazers", calculate Copernican and Keplerian theory, flight to Mars, Flight to Venus, Sections S-4 and S-5 followed by overview of early quantum physics, or a course on Nuclear Energy... or whatever.

        If you like it, please tell others, and comments are always welcome. Now that the school year is starting, I may get 20,000 page- uses per day, worldwide, but there can always be more, and it is free.

        Tell your student about the "Hyperphysics" site, too. David P. Stern  

    470.  Double Slit Interference Experiment in Space

    Dear Dr David,
        what were the results of the double slit experiment being carried out in space (on mir or the international space station)?
        (Double slit experiment: Beam light of a well-defined color onto two closely spaced parallel slit: a screen intercepting the light from the two slits further along (other light being screened away) will show a pattern of light and dark strips, which can be explained by interference between two waves spreading from the two slits. If the light is weak, we can still capture the stripes with a photographic time exposure.
        Yet... assuming light consists of "photon particles", one can make the source so dim thatwe can be sure that photons pass through it one by one. If a photon then passes either the left slit or the right slit. How can it then produce a pattern expected from two waves, each starting at a different slit?
        The answer is in the quantum laws: light spreads like a wave and only assumes the photon identity when it passes on its energy)


    Dear Asim
        I am not aware of double slit experiments being carried out in space. Would you expect them to differ?

        A comparable effect exists with radio telescopes. There is an array of about 30 large antennas in Arizona which combine their signals electronically. When they observe a radio galaxy, is each photon observed by one of the telescopes, or is there a radio wave, which consolidates its energy into each photon observed?

    471.  Ionizing Radiation and origin of Life

        I am a Portuguese Biomedical Engineering student and I'm finding it hard to find reliable information on radiation, beginning of life and evolution! What types of ionizing radiation were important in the beginning of life and in what ways? Does ionizing radiation have a big influence on natural evolution? I know it can cause gene mutations, but was/is evolution being hijacked by radiation?


        The questions you ask are very fundamental and perhaps the most honest answer is “no one is sure”. I will try to write below what I know, but keep in mind I am not a biochemist
    1.    The word "radiation" is used both for nuclear radiation (alpha, beta, gamma rays) and electromagnetic radiation (light, radio, microwave, X rays). Nuclear radiation generally destroys chemical bonds and that way can create mutation, and very short wave EM radiation has similar effects (gamma rays are electromagnetic). From what I read, however, the most common effect is to disrupt and kill living cells. Some viruses ands chemical substances also create mutationss, e.g. cancer-causing chemicals or viruses. I doubt ionizing radiation had much to do with the origin of life, but maybe ultra-violet did (enough energy to affect the chemistry, not enough to ionize) .

    2.     Evolution in higher organisms may be related to some such causes—but such evolving life already uses DNA and RNA, and other quite complex chemicals. Viruses, chemicals and energetic photons can affect the copying of RNA and DNA, but we do not know how that complex mechanism started. The most primitive life we see is already quite advanced, and any earlier more primitive life seems extinct. Some scientists are experimenting with processes which might create simpler life, but I know of no success. However, please ask your professor!

    472.  On Earth's spin and Moon's appearance

    Here is Rafael from Brazil, I have two questions.

        (1)     Did that comet which extinguished dinosaurs 65 million years ago accelerated earthspin?
        (2)     How many times bigger would we see the Moon if there was no atmosphere ?

    Sorry if it was already asked before,
    I searched for them but did not find.


    Dear Rafael

       When asteroids or comets collide with Earth--unless they come straight down (vertically), Earth spin is changed--up, down and/or in direction. But the effect in any case is far too small to make any measurable difference. The spin of the Earth is gradually slowed down by tides, a very slow process though a continuous one.

        The atmosphere does not make the Moon seem smaller. What it does is bend rays of light near the horizon. This makes the Moon seem flattened within 1-2 degrees of the horizon, and makes it visible for some minutes before it rises and again after it sets.

    473.  Back to the geocentric universe?

    Is space turning around the earth or is it static?
    If space turns, what is the direction of rotation, is it clockwise or anti-clockwise?
    And at which altitude does the direction of rotation change?

    If the Earth revolves around the sun, and the Earth settles in space on 21 June towards the sun and after 6 months on September 23 the earth will be back facing to the sun then it would not be possible to see the earth on that day because of the large size of the sun which would obstruct the view. This is contrary to reality as space settles orbiting, and the earth remains. This indicates that the Earth is at Standstill. It turns neither around itself nor around the Sun


    Sorry, but the Earth does move, it rotates around its axis and also orbits around the Sun.

        Evidence for the rotation is the fact that it is slightly elliptical, that is, wider at the equator. (So are other rotating big planets, especially Jupiter, whose flattening is evident in telescope pictures). As a result of this deformation, the acceleration of falling objects near the equator is slightly slower, and pendulum clocks there are slower. See

        One evidence for orbital motion is as follows. The Earth-Sun line rotates around the sphere of the sky in one every year (and again in any other year), going around the line of the ecliptic and through the constellations of the zodiac. This alone could mean the Earth orbits the Sun, or the Sun orbits Earth, or both orbit some point in-between.

        However, the motion of other planets (Venus, Mars, Jupiter etc.) also agrees with their rotation around the Sun according to Kepler's third law. That agreement also extends to Earth, regarded as a planet, and is expected from Newton's laws of motion and Newton's law of gravity, which form the foundation of mechanics.

        The motions of artificial spacecraft like "Voyager" also agrees with those laws, which give not only positions in the sky but also the forces that drive them. If the sky rotated and the Earth stood still, the forces required would differ and would be impossibly large. And by the way, whether a rotation is "clockwise" or "counterclockwise" depends on where you are when you view it. If you have a transparent clock and look at it from the back, the hands move counterclockwise.

    474.  Radiation risks from uranium counterweights

    I apologize for any mistakes while speaking. [I am a] hospital cardiologist, a physician but also an officer of the army at the age of 51 who [sought] specialization in aviation medicine and space at the university "La Sapienza" of Rome. My thesis is that November 15 will discuss: "conditions as a result of air crush." I refer to the disease by contamination of depleted uranium used as a "counterweight" to the wings, rudder etc. aircraft.

        But being a doctor and not an aeronautical engineer I have problems, including collection of material, so that I can understand why people use the counterweights as flight dynamics? I hope I can help, even with a simple explanation about it. In awaiting your kind response, I hope, I send cordial greetings.


       I don't know how much radiation is added by depleted uranium in counterweights, nor do I know of the role of counterweights in wings. On the tail rudder the reason may be that the rudder surface is all on one side of the axis, and a counterweight shifts the center of gravity closer to the axis.

        In any case, uranium is not very radioactive, because it has a half-life of billions of years. Nuclear reactor wastes with half-lives of years are much more dangerous. Also, almost all alpha particles emitted are stopped by the air, or by the cover of the counterweights.

        By the way, just for fun, look up on the web "fiestaware"
      (that was tableware with brilliantly colored uranium glaze, popular in the middle-1900s until it was pointed out that they were rather radioactive.)

    475.  The centrifugal force from Earth's rotation

    I'm a Phd student, and I work at the university of Florence. I have visited your website, and it's very interesting and also well done.
        I write this email because I'd like to ask you a couple of things.

        --I work with a centrifuge and I have to calculate the value of all forces in this point on the edge of a rotating disk (this is a view from above). I know that I have to consider the diameter, rounds for minute, and also the gravity. Can you help me to see if my calculation was correct?

        --I have read in some books that in the past the rotation speed of the earth around its axis was greater, and also the length of the day was smaller, like 20 hours a day. So we can think that if the centrifugal force was greater the attraction of gravity perceived was less? As you say in


    Motion of (say) a stone in a circle has a constant acceleration a towards the center, and if the stone has mass m , the force needed to keep it moving in its circle is F = ma. The acceleration a is calculated in

        If no force acts on the stone, it will stay in the same position. However, in a rotating system where EVERYTHING is rotating, to keep the stone fixed in the same place, we must supply a "centripetal" force F = ma towards the center, to keep it rotating. From the point of view of the rotating system (rotating room, Earth etc.), unless we provide such a force it will fly off in s straight line, in the direction of rotation, like mud from a motorcycle wheel.

        It is as if the rotation added an extra "centrifugal" force OUTWARD, which needs to be balanced to keep the stone from changing its position. If the stone rotates at velocity v and radius R, that force is m(v^2)/R.

        That is for a stone staying in the same position on a turning table. If instead of a stone you had a moving object, say a mouse, an additional "Coriolis force" is also needed, to make it follow the path it intended to take and not be pushed to the side (See section 24b).

        The rotation of the Earth is indeed slowing down, but only very slowly—over billions of years. The reason is that the gravity of our Moon (and of the Sun) raises tides in the oceans, waves which ideally should advance around the Earth. Continents, islands and shallow seas are in the way of such waves and change the pattern of tides, also reducing their energy. Energy in nature must be conserved, and here it is provided by reducing the rotation of the Earth (and the motion of the Moon).

        If you looked at you would see that effective gravity at the equator is indeed smaller, by something like 1%. This was first discovered when pendulum clocks which worked accurately in Paris were found to run slower at the equator, but were accurate again after they were taken back to Paris. Note also that the centrifugal force moves the "up" direction given by a weight hanging on a string, to make a slight angle with the direction to the center of the Earth.

    476.  Earth's rotation and human lifespan

        Please could you enlighten me. For some time I have often wondered that if the earth sped up considerably would we get older quicker? What effect does the earths speed have on our time? If the earth speeds up does time speed up? And in effect we get older quicker?


    Hello, Joe
        The motion of the Earth through space has nothing to do with personal aging. We get old because the various chemical "factories" in our body wear out. Cells can replicate just so many times before they die of old age (look under "telomeres", also read the fascinating book "The Immortal Life of Henrietta Lacks") and the motion of Earth does not affect this. In any case, motion in a straight line at constant speed has no physical effect; the rotation of the Earth around its axis changes perceived gravity, but by less than 1%, which probably is too small for any visible effect (except the accuracy of pendulum clocks, maybe).


    Hey David,
        Thank you so much for your reply. As you probably understand I am unfortunately not quite as talented as yourself when it comes to matters such as this. But what you have explained has certainly got me to understand my original question. And it lead me to wonder where I got the idea that the earth speeding up in its rotation would result in age increasing. Which in turn reminded me of the superman films that were made many moons ago where he flew around the earth in the opposite direction which would then in turn turn back time. And so you see where I got this thought from. Hope that made you smile.

    477.  Dependence of cosmic redshift on direction

    Dear D Stern,
        Sir, as an authority who I can believe and respect, please help explain a troublesome mystery to me? what really causes the cosmological redshift, and is there a local intrinsic component? is it really from the big-bang and a constant of Hubble's Law, or is there an intrinsic component that you can speculate describe causing it ? Ejection jets of plasma filaments Arp discovered in many quasars gravitational lensed, have mysterious time dilation and extreme redshifts, yet are connected nearby to spiral galaxies by luminous filaments and are younger then their parent galaxy. Please help me write a story about cosmology for my science website for my readers to learn the truth. sincerely,


    Dear Pat
        It just so happened that today's newspaper (11-18-2010) contained the obituary of Allen Sandage, the man who spent much of his life continuing Hubble's work, in particular, measuring and understanding the "Hubble constant" of the expansion velocity. (A copy is attached.)
        In all this, Sandage and other astronomers never found a satisfactory alternative to the expanding universe. Arp for a while created some doubt, but today's cosmologists have no doubt that the red shifts of distant galaxies mark an expansion dating from the "big bang." The red shift turned out larger than Sandage's estimate, and the expansion of the universe seems to be slowly speeding up, not clear why (look up "dark energy").
        Galaxies near to us are said to have their own motion, added to the general expansion. At cosmological distances there is really no way of measuring any sideways motion.
        On all this, I highly recommend to you "Lonely Hearts of the Cosmos" by Dennis Overby. Although nearly 20 years old and although recent advances are not covered, it gives a pretty good historical account of modern cosmology.


    Hello Mr Stern,
        Thank you for answering. I'm working on a story, and need expertise. Please inform if Lerner is correct stating that our galaxy is part of the local supercluster aligned with "the dipolar CMB [Cosmic Microwave Background] axis"? If we're expanding along this supercluster axis and are aligned with the CMB dipole, then should redshifts vary the most when we look parallel along the axis, and the least in the perpendicular direction? Penrose claims "concentric circular patterns" from past eons, before the big-bang happened. If there have been many big-bangs in the infinite past, why can't they do away with believing and searching for dark matter?
        Thank you

                Further Reply

    Dear Pat
        Better ask someone more familiar with the subject. I have no idea who Lerner is, nor do I understand "times before the big bang" since time supposedly started at the BB (there is no "infinite past" we know of). Nor do I know about the CMB dipole (supposedly quite small), or about the true distribution of galaxy redshifts—we have sampled only a small part of distant galaxies.

        You should ask someone who has worked with the Wilkinson Microwave Anisotropy probe. See  

    478.  Difference between Gravity and Magnetism

    Frankly, I'm no scientist, but I have enough ancient history, physics, and astronomical influence to understand what could/might/can happen if the Earths field fluctuated.

          I thought about it very simply, what keeps us on the ground...Gravity(duh). Then, what 'creates' or causes Gravity?...The earth's magnetic field(basically). Now, what would happen to gravity as the Earth's magnetic field weakened/Strengthened? I would expect us to have a bit of a ''lightness'' to things, if not catastrophy (the great lakes draining into the gulf, mountains falling to the sea, Mass earthquakes, Doomsday etc etc). I would also expect the moon to vary in its orbit, I don't know how, but if the moon revolves around Earth's magnetic field, then it could either leave earth's orbit, or crash into it (depending on Gravity's increase/decrease).

        There is an infinite number of things that can happen if the Poles swap, I'm sure, but what if it proves more terrible than we imagine? A weaker magnetic field would also mean a lack/loss of atmosphere, right? How does someone prepare for that kind of thing, and if this is old news to you, what do you think of it?
        Please reply, and thanks for reading if you did


    Gravity and magnetism are two different types of force. Gravity originates in mass and ALWAYS attracts. Magnetism originates from electric currents (or particle spin, sometimes) and always creates two OPPOSITE magnetic poles with opposite forces, or else more complicated forces which cannot be described by magnetic poles. Any object which is not magnetized (like you or me) is not attracted or repelled by it.

        The Moon, for instance, has some very weak magnetism (in spots), maybe from meteorites or ancient lavas, but has enough gravity to let astronauts walk over its surface.

        A reversal of magnetic polarity is possible (and has happened many times in the geological past), because the electric currents in the Earth's core, which create it, are constantly shifting. See "The Great Magnet, the Earth" which I wrote. They shift all the time, so magnetic charts need to be corrected every 10-20 years. But it has nothing to do with gravity, and the atmosphere does not change either.

    479.  SciFi world with short days and long nights

    I'm working on a Fantasy novel.
            Since a few weeks I think about an unique night and day cycle for the imaginary world that I'm creating, and I don't seem to succeed. I desperately need the help of an astronomer, and you seem to be my savior. You see, I want for my world an "inversed" cycle, meaning that the nights are way longer than the days. I thought about 7 hours of day and 12 hours of night, but I want it to be plausible. I'd be dishonored to insult any scientific reader by my ignorance.
            So, I'm humbly asking you if such a cycle could be possible, and if not; would you be as kind as proposing me a similar one (always with the long nights) ?
        Thank you very much for your time, Mr Stern.


    Stars and planets exist in many forms, but not every prescription can be filled. I'll try to come close.

        Planets which (like Earth) rotate around their axis independently of their orbit always have a steady rotation period, which means, half day, half night (although the proportions may go up and down throughout the orbit). Astronomers however look now at dimmer, red stars, M-type Dwarfs, where a planet orbiting in less than a week gets just enough heat to maintain liquid water.

        It would be a weird world, with a bigger-looking "Sun" (bigger because it is closer, actually it is maybe half the diameter of our Sun), rather red. That's OK for plants, which absorb red, the green is the color they reflect as unwanted.

        Many astronomers are searching for such planets; the Kepler mission is doing so right now. David Charboneaux in Arizona expects their rotation to be tidally locked, one side always facing their Sun. Hard to imagine life on such a planets, except in the narrow twilight zone between night and day, and water will be either ice (on the night side) or vapor. But maybe it is locked into a different resonance, say three rotations for two orbits, like Mercury. This gives unequal nights and days, though not like the ones you propose. It would be a weird place anyway

        Happy new year!

    480.  Celestial Equator and Ecliptic Equator

    Can you explain the differences in the position of the celestial plane and the ecliptic plane for he three positions of the earth? I am having a hard time explaining this to my students in a way they will understand. Thank you!
        [From middle school teacher]


    Use a beach ball to represent the Earth, and stick a length of masking tape around the equator (a table lamp at the edge of the room could be the Sun). A human standing on the equator is carried around the equator in about 24 hours by the rotation of the Earth around its axis. (The flat surface defined by the strip is the "celestial equator" [not "celestial plane"].)

        In one year the Earth is carried in a big near-circle around the Sun. The flat surface of that near-circle is the "plane of the ecliptic". We sit in the middle of the circle (neglect the size of the Earth, much smaller) and see the Sun somewhere around the circle, depending on the date. During the year it seems to make a full circuit

        The plane of the ecliptic and the celestial equator are NOT the same. If they were, the rotation axis and the direction perpendicular to the orbit would have been the same. Actually they make an angle of about 23.5 degrees. (Use a pencil on top of the ball to visualize the northern part of the rotation axis, which always points in the same direction--towards the pole star, more or less.

        In December, the pencil points AWAY from the Sun. The north pole is in the shadow (polar night), the position of the Sun at noon is north of the equator and the Sun in Pennsylvania is above the horizon less than half a day.  Sunrise is later than average, sunset earlier.

        In June, the pencil points TOWARDS from the Sun. The north pole is in sunlight all day long (though the Sun is never far from the horizon, so it's still cold), the position of the Sun at noon is south of the equator and the Sun in Pennsylvania is above the horizon more than half a day. Sunrise is earlier than average, sunset later.

        Halfway between at equinox (March or September) the Sun is right above the masking tape, and daylight lasts about 12 hours. (If you lived in Argentina, December would have long days and summer, June short days and winter.) For more, see and adjacent sections

    481.  Cavendish gravity constant G drops out

    Dear sir,
        I am in seventh grade, and I'm reading the distance to Lagrange point L1. I can understand up to this part, but I don't get how you find the ratio of the masses of Earth and Sun: Please help.
    GM/(r-R)3 - Gm/R2(r-R) = GM/r3

    Please help.


    Dear Sreejato, it's been so long since I looked into these sections, I do not even remember where everything is derived! However, from the equation early in sect #34a
    GM/(r3) = (2 pi /T)2
    if we know the mean orbital distance r of Earth and its period T (1 year in seconds), we can derive GM, where G is the gravitation constant measured by Cavendish, and M the mass of the Sun.

        Also, an apple falling from a tree (or any other object on the Earth's surface) falls at an acceleration g and behaves as if all the mass m of the Earth was concentrated at its central point. So if we know the Earth's radius, represented as RE, and remember that the acceleration from gravity at the surface of the Earth is g Gm/(RE)2 = g

        we can divide the first equation above by the second. The result only involves (Gm/GM), in which the value of G does not have to be known.

    482.  Teacher seeks material

      My name is Sona, I am from the southern part of India and this is my 7th year in US. I teach Math & Physics for high school. I am planning to teach AP Physics next academic year. My major subject is Math and I am also teaching Physics. I might need your help & suggestions to get ready for next year. Thanks.


    Hello, Sona
        I am not a teacher, just a retired NASA physicist, turning 80 later this year, and have written web courses on physics and astronomy at the HS level for both schools and the public; see which you may find useful, also the start of a course on electricity at I hope these and others can work for you. The site on physics, astronomy and space (home page also contains a set of 46 lesson plans.
        For a possible outline of a science curriculum see .

    483. Solar Sails

    Hello Mr. Stern.
        I happened upon your page and found it very interesting. I would like to ask a question or two myself. First: I once read an article in a science magazine that claimed it would be possible to use the solar wind for propelling a starship. The authors claimed a device much like a sail could catch the solar wind and move the ship away from the sun .They went on to claim that very high velocities could be achieved close to half the speed of light. Do you agree or is it not possible?

        Also I once read a publication about possible spaceflight and one problem to moving at high speed the authors addressed was that space wasn't totally empty but had particles moving through it. A collision with a ship moving at a large fraction of the speed of light would be fatal to the crew. They had no solution except to limit the speed of the ship to prevent damage from such collisions. But I wonder if a strong magnetic field or multiple fields could deflect such particles. I once read a book for laypeople on science and it claimed that even neutrons though they have no charge have a magnetic property called spin.
        So could a strong magnetic field provide protection?


    Dear Robert
        It is possible to propel a spacecraft by SUNLIGHT, reflected from a stretched thin "solar sail." See . Sunlight pressure is very gentle, so any practical payload requires a huge but very light sail; for this, new technology is needed. In any case, velocities attained would be far below the speed of light c (unless the Sun's light is somehow beamed-see sci. fi. book mentioned on the web page), because as the payload accelerates, its distance increases and the Sun seems dimmer.

        The solar wind won't work. Its particles are very sparse, and they move at perhaps 0.14% of the speed of light.

        We do not know enough about distant space. Dust hitting a fast spacecraft may perhaps punch pinholes (and if the velocity is a good fraction of c, go right through), but I am not sure how much to expect. A magnetic field will not deter neutral matter. Neutrons and atoms have spin, but a magnetic field will just shift their rotation axis, not move it in space. See discussion of Nuclear Magnetic Resonance near the end of

    484.  Life under stronger gravity

        I have a relatively simple question to ask, I just cannot find the answer anywhere an I would greatly appreciate your help.

    the fuels we use here on earth such as kerosene or petrol be able to lift it's own weight on a planet with a greatly increased gravitational force? And if not do you think that if we had evolved on a planet with a heightened gravitational force the way fuel is formed would be different making the energy output greater?


    Dear George
        How is one to know? Kerosene and other hydrocarbons would be the same anywhere, and so would oxygen and hydrogen which are a little more "thrustworthy". The way they formed can only be guessed, but if it involves "cooking" carbon-containing plant residue with water (and overcooking leads to natural gas), then it seems to require plant life. You won't easily find more concentrated fuels.

        I don't know if life could evolve in a much larger gravity (or if it did, evolve from single cells to larger organisms), but it is fun to speculate. Look up "Mission of Gravity" by Hal Clement  

    485.  Message from Kansas

    Dr.Stern, thanks so much for sharing your knowledge at this most excellent web site. God bless you!
              [Many similar messages were received in the past 15 years but not posted]

    486.  Finding true north in an underground mine

        Just for a point of interest is that we do make use of the rotation of the earth underground in mines.

        One of the methods that we ( in South Africa) as Mine Surveyors, use to determine the direction underground (at 4km+ below surface) is by means of a gravitational Gyro with two degrees of freedom. The gyro wheel is started, or released, with its axis in a horizontal position.

        The two forces that operate on any given particle of the gyro wheel at any given time is the direction of the spin and the gravitation force. The gyro wheel (spinning at + - 20 000 rev/min) and axis try to maintain its direction in space.

        The resultant force try to force the 'particle' so that the axis will point in a true north direction but with the continued acting of the force resulting from the spinning of the planet it results in the axis of the spinning gyro wheel to oscilate around true north. The gyroscope is mounted on a theodolite and with the neccessary observation the direction of true north is obtained and thus also the direction of any line in the underground excavation. The resultant accuracy so required is of such a nature that the direction that obtained from the gyro-base so established is of a high standard even over distance of a km or more.


    Thank you, Hennie
        Your instrument seems to be similar to a gyrocompass, as used aboard airplanes and ships. As I understand the operation (I may be wrong!) one could start on the Earth's surface, pointing the axis towards the celestial pole (the southern one, in South Africa), and then spin up the flywheel. The axis would continue to point to the pole even when taken underground, and its horizontal projection ("vertical shadow") would point south.

            In practice, however, it is hard to set it pointing precisely at an exact point in the sky. One then compromises by lining it up on the ground precisely in the horizontal north-south direction. At a latitude of (say) 35 degrees, it then points to some point on the celestial sphere 35 degrees away from the celestial pole.

            After the gyroscope is taken underground, if its axis were free to shift to any direction in space, it would precess
    around a cone with opening angle 35 degrees (like the axis of the spinning top illustrated in the section on precession), with the cone's axis pointing at the celestial pole. If however the hardware limits it to point only in horizontal directions, it will swing back and forth every 24 hours, tracing the projection or "vertical shadow" of a line rolling around the above cone. The pattern is symmetric, and its center (like the direction exactly halfway between the greatest excursions to one side and the other) is true north. Gravity is only needed to define the horizontal surface.

    487.  Aristarchus             (cc from a discussion)

    David P.Stern claims Aristarchus knew the Moon was 60 Earth radii away from the Earth. His proof is based on the computation of the size of Earth's shadow and time needed for the Moon's center to cross it. The latter parameter he estimates as 3 hours.

            Further, the Earth's shadow is assumed to be cylindrical (obviously, because the Sun is supposed to be in infinity) and the path of the Moon's center is supposed to be equal to 2 Earth radii but then David P. Stern says the shadow is rather conical since the Sun is not a point but a disc and therefore the path is less than 2 radii by 25%. Which means Aristarchus never arrived at the claimed result of 60 radii.

            I am wondering whether David P. Stern took into account a more known result by Aristarchus: that the sun only by 20 times is farther from the Earth than the Moon. This might restore the size of the shadow back to 2 radii.

            But my main point is that I have never heard this result (60 Earth radii, or even as an approximate) was claimed for Aristarchus. Or was it?


    Dear Ari
            Very interesting! When I first wrote about ancient Greek estimates of the Moon's distance, I cited one by Hipparcos, based on a partial eclipse of the SUN, described on one of my web pages. That calculation came from Pannekoek's "History of Astronomy" (which I own) and it was of special interest since the total solar eclipse of 1999 followed almost the same path. You can find all this discussed in In connection with this, I called up Prof. Owen Gingerich, and told him what I had done. He said Aristarchus had already estimated that distance many years earlier and explained how. I found that credible--the method is simpler!--and wrote it up. As I noted in the next web page after the above (which describes the estimate of the Sun's distance), that agreed with what William Gilbert in 1600 claimed.
            The fact the shadow is a cone can be ignored in a crude estimate of the Moon's distance. It is important in answering the question, would a spacecraft at the Lagrangian L2 point be in the Earth's full shadow or not. Will it? [almost]

    488.  Calculation of Gravity

          If a planet has mass two times and radius three times greater than those of earth, then a 10 kg mass on its surface would weigh how much??

          Sir this is the question. Please email the solution to me at the earliest.
    A curious mind,


    Dear Adithya
            If this is a problem given to you in science class, please tell the teacher you had this help.

    If G is the Cavendish constant of gravity, M the mass of Earth, R its radius and g the acceleration due to gravity at the surface of Earth, then
    g = GM/R2
    If g' is the acceleration of gravity on the surface of the planet
    g' = G (2M)/(3R2) = (2/9) GM/R2 = (2/9)g
    You should be able to derive how many newtons this causes to a 10 kg mass,

    489.  Message from Michigan

              Thank you for taking the time to answer my phone call today. I have been building small sections of your Stargazer site into the physics curriculum of several of the schools that are a part of the Henry Ford Learning Institute. The work you have put together is very comprehensive and will be a tremendous help to students as they continue to work toward a more complete understanding of the physics in the world around them. Please know that in all cases where we have referenced your work, full citation credit has been given. Thanks again for your time today and your years of hard work on the Stargazer project!!


    Hello, Mike
              You are welcome to it all! Are you also using the lesson plans of "Stargazers"? And... encourage the kids to browse the questions-and-answers part!
              The most recent collection is "All Things Electric and Magnetic." It extends to a level usually not included in high school, but the first 11 or so sections (except for most of E4) are fairly basic, and contain an introduction to electricity in the home.
              By the way, math teachers may also find useful material in the "Math Refresher" part of "Stargazers."

    490.  Confused about "Temperature"

    Greenhouse gases are to blame for global warming. The scientific facts are all meteorologist only recognize two temperature readings, the actual temperature, which is generated by the sun, and the heat index, or the ambient temperature, which is purportedly generated by greenhouse gases, due to the absorption of solar UV radiation.
          Greenhouse gases trap IR solar radiation preventing it from escaping back into space, thereby raising the heat index. Or the ambient temperature?? It's the actual temperature that has risen over the decades, not the heat index. The ambient temperature only gets as much as 15 deg (F) above the actual temperature. The higher the actual temperature the higher the heat index.

          Does the greenhouse gas theory represent a third temperature reading? What temperature reading does greenhouse gases represent??   Greenhouse gases only radiate IR radiation due to the absorption of UV solar radiation. Only the sun can generate heat. Unless there's a third temperature reading that all meteorologists around the world are not aware of? What temperature reading does global warming represent?


    You must have got your definition of temperature from some strange source. At any point inside matter (e.g. earth, air, rock, rubber, brick) there is only one temperature, measurable by suitable instruments (temperature is associated with matter: in empty space the concept is not useful). It is usually measured in degrees Kelvin, and is proportional to the local energy content per unit mass.

          The atmosphere has only one significant energy input, sunlight. Any energy received from the Sun at the Earth's surface must be returned to space, else the temperature of Earth will rise to where the ocean boils and the hills melt. However, the only way to remove energy (other than reflect it before it is absorbed) is radiate it to space, from the top of the atmosphere.

          Most heat of the Earth is radiated away from the surface as infra-red radiation (IR). The wavelength depends on temperature: the smith's hot iron radiates cherry-red light, the hotter filament of a flashlight radiates up yellow (both also radiate IR). The earth is only hot enough to emit IR (and less intensely, but from a huge area).

          The atmosphere is largely opaque to IR, due to molecular gases such as water vapor and carbon dioxide which absorb and scatter it; the more of them are present, the shorter the path IR travels before being re-absorbed. The various processes involved in transporting the surface heat to the top of the atmosphere--conduction, convection and global flows--are what drives our weather and climate, and determines the temperature on the ground.
          For more read

          Please stop writing to me on this matter.


    Greenhouse gases concentrations is said to affect the heat index, or ambient temperature. The average global heat index, or solar IR radiation only get as high as zero to 15 deg (F) above the actual temperature, or solar UV radiation. ??

          Name me a period in time, where the heat index, or the solar IR radiation was higher than the actual temperature, or the solar UV radiation? Global warming is represented by the heat index, or solar IR

          Am I making yourself clear,or am I speaking in another language?

          By the way the internet has many reports of false peer-reviews, and you should know this, look at the evidence! Please respond honestly.      

                Second reply                        (actually, 3rd)

    I really would like to end this discussion. Please study the web site and others related to it. Unless you do (or learn about its material from other sources), you will not get real understanding

          The heat index (see wikipedia) was devised as index to the amount of discomfort we humans feel from heat and humidity (see section on "Convection and Humidity" on the site). Humidity adds discomfort to heat. One possible reason--when we inhale dry air and then exhale, our interior is somewhat cooled by evaporation (the air we exhale is humid). With humid air, we can't load as much humidity into what we exhale, since it already comes with some water vapor. Humidity also adds to the energy content of air, but I do not know if the definition of the heat index is based on that added energy.

          The actual temperature gives the local heat-energy content of warm air (assumed to be dry). Solar UV radiation is something completely different, and solar IR is not the heat index. The greenhouse effect is related to IR emitted from the warm ground, not the Sun.

          Please make sure you understand these matters before making any claims!

    491.  "Negative work" and Energy

    Respected Sir
          Recently my physics teacher gave me a definition of positive work as "the work done when force and displacement are in the same direction." But he also said that when we throw an object down the work done is negative. However I couldn't understand that part. When we throw an object down the force applied and displacement of the body are downwards i.e. in the same direction. But my teacher said that by convention any thing that goes down is negative. My opinion was that it depends upon your frame of reference and relativity.

          I hope you can help me out on this misconception.
    A curious mind


    Dear Adithya
          You should discuss this with your teacher; these things are much more easily handled using the concept of energy. In simple mechanics, that means potential energy or kinetic energy, whose sum is conserved.

          Whether you throw a stone up or down, in both cases your arm muscles do work overcoming inertia. The work increases the stone's kinetic energy.
          If gravity is also present and the stone flies freely though space, its gravitational potential energy will also change, but that is a separate process.

          The potential energy increases if you throw the stone up, so that it slows down and its kinetic energy is reduced.
          The potential energy decreases if you throw the stone down (or just let go of it), so that it speeds up and its kinetic energy grows.

    If the stone is thrown up, it performs work against gravity, at the expense of its kinetic energy.
    If the stone is thrown down, gravity performs work on the stone, increasing its kinetic energy.

          This may perhaps be viewed as "negative work against gravity."

    492.  The Coriolis force on a moving air mass

    Dear Dr. Stern,
          I have just 'discovered' you and have been very pleased to have you explain some subjects for me in a manner that I can easily follow.

          For a long time I have been interested in the coriolis effect and have been in contact with various people about some of my thoughts on it. I have found that there is a lot of wooly thinking on the subject and there are some other people who probably understand the subject but cannot explain it to me in language I can understand.

          I would be very grateful if you would comment on my theories for me.

          Briefly, talking about coriolis effect on the surface of the earth, I maintain that there is no coriolis effect on a body moving East or West. And I also maintain that the mass of a body has no bearing on the amount of coriolis effect shown by it. To illustrate my theory...           [rest omitted]


    Dear Mike
          A Coriolis force is associated not just with the rotating Earth, but with any rotating frame of reference, like (for instance) that of a rotating amusement-park ride. Like the centrifugal force, it is not an independent force, but only enters if we describe the motion in terms of distances and velocities in the local frame of reference.  For atmospheric motions, that of course is the most convenient frame: wind velocity, for instance, is always measured relative to the ground, ignoring the fact the ground itself is rotating.

          I do not know how much physics you have under your belt.  It is always best to have a formula for the Coriolis effect, and here it is, copied from an old text. Let A be the vector describing the Earth's rotation, directed along the axis of that rotation (often denoted by a small Greek omega), in radians per second which for the Earth is a rather small number. Let V' be the velocity relative to the ground (hence the apostrophe) of some object with mass m. Then the Coriolis force on the object is 2m[AxV'] where "x" denotes vector multiplication. The vector W resulting from such is perpendicular to both A and V' in the right-handed direction, proportional to their magnitudes and to the sine of the angle between them.
      ("Right handed" distinguishes, which of the two perpendicular directions is chosen. Stretching fingers of the RIGHT hand if A is thumb and V' is index, then W is in the general direction of the middle finger)
    So if wind blows purely east or west, there is still a Coriolis force, but it does not divert the flow, just opposes or aids it by a small amount, also modifies the effective gravity. An especially simple example is provided by "jet planes above the equator" in

          The Coriolis force is proportional to the mass of the object.  You probably meant the Coriolis acceleration, which is not.


    Dr. Stern, I only have high school physics and math. So I have to keep things simple. I am beginning to think that what I understood as coriolis is, in fact something else. Firstly I understand coriolis to be an effect and not a force. Would you be good enough to comment on three examples .

          First, the classic example of a ball propelled from the center of a rotating disc (eg a playground merry go round). If we have a frictonless surface and ignore gravity then, to an observer on the ground, the ball will hold a straight line until it reaches the edge of the disc because of Newton's first law. However, to an observer on the disc, the ball will describe a curved path. That is what I understand as coriolis effect and it is independent of the mass of the ball.

          Second, if a bullet was fired due South from the North Pole and, say, the Statue of Liberty happened to be in the line of fire when the bullet was fired, by the time the bullet reached the Statue's latitude, the Statue would have moved East. And to an observer on the statue, the bullet would have appeared to curve to the West and would pass somewhere to the West. One has to ignore friction and assume that the bullet went into low orbit. As I understand it, the curve seen by the observer on the statue is coriolis and is quite independent of the mass of the bullet.

          A third example would be when an observer at the North Pole watched a satellite in a low earth polar orbit. As that satellite approached from the South, it would appear to move to the West as the observer turned with the earth. I understand this to be coriolis effect. And the effect would be the same regardless of the mass of the satellite.

          Am I missing something?

                Reply to Response

    Dear Mike
          Your suspicion is well founded--none of your examples is an instance of the Coriolis effect. Rather, they describe the effect of mapping a KNOWN motion into another frame of reference, in which it may have a different shape. Take the motion of planets around the Sun: we know they all are closed, nearly circular ellipses, all moving in the same sense, namely counter-clockwise when viewed from somewhere between us and the north star.

          However, when a planet outside the orbit of the Earth is viewed FROM Earth, its motion now and then seems to reverse. That happens because the orbital motion of Earth is faster than that of the planet, and whenever Earth overtakes it, the planet seems to move backwards ("retrograde motion"--see That is relative motion, but not the Coriolis effect, and does not depend on mass.

          The Coriolis effect arises when one applies Newton's laws-- F=ma and all that. The motion is NOT known, one only knows the forces which cause it, and tries to predict it. If our frame of reference is at rest, or moves in a straight line at a constant velocity (cabin of an airliner, say), as long as there is no added acceleration one just applies F=ma to derive, say, how coffee flows from a spout to a cup. Suppose however the frame of reference is accelerating, e.g. the airliner makes a turn (motion in a curved line involves acceleration--see Then, if one tries to calculate the motion relative to reference points INSIDE the cabin, one must supplement Newton's equations with added "inertial forces."

          One such force is the familiar centrifugal force, always present. But if in addition the object whose motion is sought is already moving (say, a ping-pong ball in play inside the cabin), you also need add the Coriolis force. All these forces are proportional to mass, ensuring that the trajectory modification of a big mass is the same as that of a small one.

          My advice: if you want to understand Nature, look up first of all that is known, as described in texts and on web sites like mine. Otherwise you spend too much energy on dead ends, and get frustrated in the process. Following a regular course you will still find plenty of challenge.  

    493.  Recent change in sunset?

    Recently I have been doing some research online and I have noticed a trend of people from all over the world noticing that the sunset position in the sky has changed? They say that the earth's axis has changed and even the inuits are saying this too! People have posted pictures and videos and it's starting to scare me. They are also saying that the moon's [position] has been doing the same and has been weird lately. Is this possible? Is there any truth to it? Has the sunset changed? Or the earth's axis?


    Dear Haidi
         The sunset position changes with the seasons. Right now (2 December) it is moving northwards, reaching its most northerly position on about the 21st and then going back southward. The shift in winter makes nights longer and days shorter. If you are a Moslem, you would already know that the Ramadan fast is longer in summer and shorter in winter.

          The axis of rotation moves around a large cone, as has been known for thousands of years ( ), other motions are periodic and tiny small, too small to be notices by eye or for anything we (or even the inuit) would note.


    Thank you! I had thought that it was northerly leading up the summer solstice, and southerly now. I am a Muslim, and Ramadan this year was during August and so it was verrry long. So, pretty much, the earth's axis hasn't changed and the sun is in its right place? Let's say the earth's axis did change, what effects would that have on our planet? Would it make big changes?

                Reply to Response

    The axis of rotation of the Earth makes an angle of about 23.5 degrees to the direction perpendicular to the plane of the Earth's orbit ["plane of the ecliptic"] around the sun. That angle produces the seasons of the year. If the angle were close to zero, there would be no seasons,  If it were large (say 60 degrees or more) the month-long polar night in winter and polar day in summer would reach countries were most people live. Actual observed and predicted changes in that angle are negligible. See

    494.  Space and Dark Matter

    Greetings Dr. Stern,
          I am hoping you are well, and this e-mail will find its way to you. I read just now a short article at a NASA website regarding supermassive black holes. It was last updated in 2004, so I presume there are facts not presented by "The Black Hole at the Center of our Galaxy." Embedded within was a link to "
    The Doppler Effect S-4A-3 Rotating Galaxies and Dark Matter."

    I have a question after reading that discussion:
          Is it possible that Space, itself, is that "Dark Matter?"

          I believe I understood what I was reading about Dark Matter, but I can't be sure of that, entirely. My question above might reflect a lack of knowledge or understanding, but I hope not.


    Dear Jim
          What you imply is that space like matter pulls itself together by gravitation. It does not seem to do so, on the contrary, it seems to push itself apart, as the expansion of the universe which actually seems to be speeding up (see "dark energy").

          It is possible, however, that what is attributed to dark mass is actually a modification in the laws of mechanics (Modified Newtonian Dynamics of MOND). This area is outside my league, but it has been proposed


    Thank you. Dr. Stern,

          But what I was thinking is that Space is more like a solution within which matter resides, like a bunch of flies in a jar of honey so to speak. Yes, it is expanding, pushing itself apart as it were, but if Space is like a solution, then could that explain what you said here?:
            "What was remarkable was that the near-constancy of V extended even to the far edges of the galaxy, where very little light was emitted. If brightness was an indication of mass, then most of the mass was huddled near the galactic center, and velocities in these outer regions were expected to decrease in accordance to Kepler's law. But they did not."
          I've always held a fascination for the concept of "space." I think it isn't just emptiness, I think it is "something" that has "presence." So, I'm wondering if it isn't that there is not enough gravity in the universe as it seems, it is possible that there is a property within space itself that acts to cause the near constancy of V to extend to the far edges of galaxies?
          Or am I just lacking sufficient understanding of the subject, and merely spouting gibberish?
          Sorry, but I am a never ending source of questions (you have no idea!) and I just want to know as much as I can understand about this incredible place we call the universe. Thanks for any help.

                Reply to Response

    Dear Jim
          Your quote talks about the rotation of galaxies, which are very much smaller than the universe. To misquote a famous American, the universe contains billions and billions of galaxies.

          As for the universe, without the framework of observations, laws and the mathematics behind them, will just lead you to frustration. You cannot predict (or even explain) without them. Learn first about that framework and avoid chasing frustrating shadows.  

    495.  Newton's 3rd law

    Dear dr Stern,
          please have a look at I am sure the figure you will find there is not by you. The text discusses correctly the role of action and reaction. but at the same time it displays as action and reaction the force of gravity and the reaction of the floor. The first is of gravitational nature and the second of electromagnetic nature, and both are applied to the same object.


    Dear Joseph
          The figure was drawn by me (a professionally drawn figure would have looked much better!). The example of the mass resting on a floor is brought up because it is often mentioned by teachers, but it does NOT have to do with Newton's third law. As you noted, it has to do with the equilibrium of a single object, while Newton's law concerns two or more objects.

          Students get confused, especially since the equilibrium can also be described as "action equals reaction." Newton's law only becomes important when objects accelerate.

          If you think of a different and better wording, please tell me!  

    496.  Shift of Earth Axis in 2012

    Dear Dr David,
          I recently became interested in the possibility that the earth would align with the universe in some way in 2012 and there will be a large polar shift that will effect the world as we know it...
          That being said, if the poles do shift and quickly:
    1. what can we expect from the world we live in during the time of change and the following months and years. (THE DAY AFTER TOMORROW?!!)
    2. if you live in America where would the safest place to be/live when this process begins?
    I really enjoyed reading the questions and responses on your site and look forward to reply. I understand you are busy and hope you have not received this question so often as to find it "stupid". I am planning a trip to see Chaco Canyon, New Mexico in December and hope that will be a good spot
    thanks in advance for your time and consideration.
    Very curious ....Kim


    A similar question has arisen before (, also see To change the earth's rotation axis relative to the stars would take an enormous force anchored in some other object, and might tear the Earth apart (for a short while). A less demanding scenario would have the crust of the earth slide around the interior, so that the rotation pole would move (say) to Chaco Canyon, or Sedona, Arizona, but even that would involve enormous forces.
          Astronomy knows no mechanism even for that process for such changes. My advice is, do not worry--buy your Christmas tree for 2012, enjoy the holiday and raise a glass for New Year 2013 a week afterwards.
          By the way, I recently watched the film "2012" on TV, but quit halfway after I found the action too confusing. IMHO it rates 1.5 stars at the most..

    497.  Ptolemaic Theory of Planet Motion

    I am a student in the International Baccalaureate Program in Pensacola, Florida. Currently, I am writing a research paper on Nicolaus Copernicus and his heliocentric theory, and how it compares to Ptolemy's model of the universe in a mathematical sense. I read your article on Copernicus' heliocentric theory (url:, and it was very helpful and informative. However, there was a link towards the bottom of the page that was broken. It was supposed to provide more information on Ptolemy.
          I am sending this email to ask you if you could either provide me with a new link to the webpage, or with the information that was on that page. Specifically, if it is not too much to ask, the mathematical equations that were used by astronomers in the Ptolemaic era along with explanations of those equations.


         Links sometimes disappear, and I will certainly remove this one. I no longer remember anything about its contents--this web page originated about 15 years ago (though the calculation which you read was added only in 2010).
          Personally I am not an expert on Ptolemaic theory--you might look up writings by Owen Gingerich, perhaps. For a short summary of that theory, see .

    498.  Electricity from the Earth's Rotation?

    Dear Dr,
          If Electricity passed around a magnet makes it rotate and a rotating magnet generates electricity, does earth a natural magnet rotating generate electricity? If so can man-kind get any benefit out of it?
          Also... if earth is a rotating magnet, what type of electricity is making it rotate?
          I have very low knowledge of science, but I have these type of questions arousing now and then. Answers to these question can make science more interesting to me ... Can you Dr.?


    You will find discussion of rotation and magnetic fields in "The Great Magnet, the Earth", home page
           especially in section 12 on dynamos. A more technical discussion is part of "All things electric and magnetic", home page
    I hope that reading such web sites can also make science interesting to you.

          As shown there, to create an electric current in a circuit by its motion in a magnetic field, part of the circuit has to move relative to the rest of it. No electric circuit fixed to the Earth and rotating with it satisfies this. Sorry--you cannot tap the Earth's rotation to run your motor! A circuit that is in part in the solar wind flowing past Earth and in part tied to Earth can indeed produce a current, and such circuits are believed to power bright aurora, but no practical way exists to tap them.

    499.  Change in Earth gravity following Tsunamis

          Good afternoon! I wanted to see if you could answer a question for me that a student brought up in class.
          It involves the movement of land masses from the tsunami and earthquakes, along with the slight tilt in the earth position in space, Does that change the Gravitation Force?


          Dear Tracy
          A tsunami does not change the mass of the Earth, so the average gravity--the gravity calculated by condensing all mass to the Earth's center--will not change.

          What may change is the distribution of the asymmetric part of mass. That asymmetry is small--just as the oceans follow a smooth surface, the continents also seem to even out, because the enormous weight of mountains etc. overcomes rigidity at their foundations, which yield as if they were a tacky fluid.

          However, these adjustments require long time, on a geological scale, while shifts in the Earth's crust that lead to tsunamis are rather quick. Asymmetries caused by such events could be observed by the twin GRACE satellites as "gravity anomalies." See .
          I do not know what changes GRACE observed after the Japan Tsunami, but they were observed.  

    500.  Science fair expt. on light output of CFL lightbulbs

          [Note: the lightbulb project is only in the reply]

          I've notice quite a bit of discussion on the Internet regarding whether sunspots cause earthquakes (In my field, economics, there are stories that one statistical model says earthquakes cause sunspots.)

          My 12 year old son and I thought that researching this question would be a great science fair project. State curriculum guidelines require that the science fair projects test a hypothesis. So, I thought this is great! We have a hypothesis and, thanks to USGS, NASA, and the European Space Agency, we have tons of data.

          I have two issues that I hope you can help me with. First, my son has the worst science teacher in the world. She seems to think that the only way to test a hypothesis is to run a laboratory type experiment. One of her ideas of an "outstanding" project was when--ugh--students "test the amount of water or other substances like coke or fertilizer that they water plants with." Can you help me convince her that this is a cool and doable project?

          The second issue is a bit more complicated. Do you have any tips on how a 12 year old can test his hypothesis. I am economist and statistician, so I can use all types of fancy pants statistical models.  However, it seems from your website that you have certain panache for making these topic understandable to the masses.

          I apologize for the length of this email. I would appreciate any tips you can give.
    All the best.


          Your son's proposed investigation does not sound promising, and will probably lead to a zero result. Sunspots are magnetic phenomena, and while they are associated with magnetic changes and plasma flows in interplanetary space, it beats me how they could affect tectonic plates on Earth.

          A more logical question might be, does the position of the Moon in the sky affect earthquakes? By raising tides in the oceans and also in the solid Earth, the Moon periodically deforms our globe and exerts a non-trivial force on it. I vaguely recall this question has been asked before, but not what was found. For this project, your son will need a list of earthquakes and their times, a calendar tracking the Moon in the sky, and probably a computer code to derive for each earthquake the relative position of the Moon. It's not a quick job.

          As an alternative, let me propose a project that is altogether different. We are told that a 13W compact fluorescent lightbulb (CFL) emits as much light as a 60 W bulb with an incandescent filament, which uses 4 times as much electric power. But is it true?

          Your son will require two table lamps or equivalents, an incandescent 60W bulb and two CFLs of 13W. He will also need a yardstick, a homemade paper screen (mounted over a large hole in a cardboard screen), a smidgen of margarine or cooking oil, and probably a handheld calculator.

          The experiment would use a grease-spot photometer, like the one I described in Since it is his project, I will not spell out the set-up for getting his result--let him do it.

          Having two CFLs allows other question to be answered, e.g. how does the intensity of light from the side of a CFL compare to that from the top? How does the intensity of the light of a CFL switched on 5 minutes ago compare to that of one turned on just now?

          The experiment will also teach your son that measurements generally involve comparison, such as that of an unknown weight in one pan of balance scales to known weights placed in the other pan. (Often though, this comparison is conducted when an instrument is set up--say, spring scales in a bathroom--and is then known as its calibration.)

          I think your son's teacher will approve. And BTW, I doubt she is the worst science teacher in the world--there exists too much competition for that distinction!

          If your son does this, please e-mail me a copy of his project

    [In his response the dad wrote that his son was doing the lightbulb project]

    501.  Does iron Fe56 have the most stable nucleus?

          I'm an undergraduate student with interest in physics and chemistry, and it happened that I stopped by the amazing educational content that you provide on the internet. I want to thank you for your generous contributions, and ask a question about an article that you wrote on Stargaze about Nuclear Power, in In the article, and specifically in the last paragraph of the section (A Review of Nuclear Structure), you wrote the following:
      " In summary, then: iron nuclei are the most stable ones, and the best sources of energy are therefore nuclei as far removed from ironas possible."
          And this statement has been cited in Wikipedia (the Free Encyclopedia) as a source for the claim that iron (particularly Fe56) has the most stable nuclei. However, I came across a study published in the American Journal of Physics in 1995 by M. P. Fewell, who showed that the widely believed idea that Fe56 has the most stable nuclei is not true. Instead, his study showed that Ni62 has the highest binding energy, followed by Fe58, and Fe56 comes in third. This is a link to the study on the AJP website:

          Can you please elaborate on this particular subject and explain the difference, if any, between the statement found in your article and the results from Fewell's study?


    Dear Shadi
          I will add this point to the web file. The nickel isotope with higher binding energy has low abundance, while iron is very common. Its higher binding energy is well known, and the reason why iron is much more plentiful has been studied--see paragraphs below the illustration of the nuclear binding energy curve in  

    502.  "Black Light Telescope"

          I have always been interested in what humans cannot see and observe and was just reading an interesting article on black light photography and the applications of this. Most experiments are based on what we can actually see and observe but not much emphasis is being placed on what we cannot see or observe with the naked eye. Have there been any experiments performed using black light in conjunction with telescopes. Would be interested to know if there have and any results.


    Hello, Michael
          What is commonly called "black light" is really soft UV (ultraviolet), which the eye cannot see but which fluorescent dyes make visible.

          Light is an electromagnetic radiation, and many other types of such radiation exist--infra-red, far UV, X-rays, microwaves, even radio, and they all have been used by astronomers. The problem with many of them is that they are absorbed by the atmosphere or ionosphere, so studies are conducted from orbiting satellites--for instance, the X-ray observatory "Chandra."

          You may be interested in and the two sections that follow there.  

    503.  Message from New Jersey

    Dr. Stern,
          Just a thank you and kudos to you for providing such an outstanding website for the world to enjoy and enrich itself. As an MD I have always been a science lover and spend hours reading science topics for pure enjoyment even when I don't really feel I grasp them at all. Most texts and sources are poorly written from the standpoint of someone trying to learn (or review) the stuff as a non expert. You have one of the clearest and easy to grasp writing gifts I have ever stumbled upon. I always felt that I could understand most of science if someone could just explain it in easiest enough terms. This ability is truly a gift of god and I think requires a true understanding of the material to be able to turn it around and present it to laymen, students etc in a way we can all grasp. You have the best explanation of the coriolis effect I have seen! No other sites bother to explain the simple details (at least that I have seen). Please keep up the outstanding work for all of our sakes, and again thank you. It is time and effort well spent.

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Last updated 2-25-2012