#22 Frames of Reference:
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: |
"Frames of Reference: The Basics," section #22: on disk Sframes1.htm, on the web http://www.phy6.org/stargaze/Sframes1.htm
"The Aberration of Starlight," section #22a: on disk Saberr.htm, on the web http://www.phy6.org/stargaze/Saberr.htm
"TheTheory of Relativity," section #22b: on disk Srelativ.htm, on the web
Goals: The student will learn|
Stories and extensions: The story of the aberration of starlight and of Bradley's observation on a boat in the river. About the solar wind and magnetosphere, and how aberration foiled a clever idea of downloading satellite data using a passive laser reflector.
Note to the teacher:
This lesson is closely related to the one on vectors (section #14 of "Stargazers", lesson plan #23). Some ideas expanded here were already introduced in #14--for instance, the motion of an airplane flying with velocity v1 relative to the air, which itself (because of the blowing wind) has a velocity v2 relative to the ground. In that example, the air and the ground represent two frames of reference moving with respect to the other, and we have already shown that the velocity of the airplane with respect to the ground is the vector sum v1+v2 .
Here, however, two additional aspects come into play. One, we are also concerned with accelerations and forces. These are the simplest cases, where all velocities are constant in magnitude and direction, so that shifting from one frame to the other adds no new forces or accelerations (That will no longer hold when we come to discuss rotating frames). And two, we study the changes created by the motion of the observer's own frame of reference.
Section (22a) is optional. It contains interesting stories, illustrating the lesson, but can be omitted (and perhaps assigned to some advanced students) if time runs short. It is also possible to teach only the first example, on the aberration of starlight and on its explanation by James Bradley.
Starting the Lesson
The starting paragraphs of Section #22 are quite appropriate for starting the lesson. After that, bring up the questions below, and continue with Section #22a.
Questions and tidbits:
--What is meant by a "frame of reference"?
--Can you give examples of frames of reference?
--Surface of the Earth, the Moon or Mars.
--A moving elevator, merry-go-round, roller coaster car or other ride.
--The frame of the wind carrying a run-away balloon, or of a river carrying a swimmer.
--Also, in certain contexts, the frame of the distant stars.
We have two frames of reference: A is the inside an elevator rising with constant velocity u, B is the frame of the building in which the elevator is located. A rider drops a penny inside the elevator. Is the velocity of the penny the same as seen from A and B?
In the preceding example, is the acceleration of the penny the same viewed inside the elevator and outside it?
You are the passenger in a car driving with velocity u on a rainy night. On the street outside, through the side window of the car, you see raindrops falling. They fall with a constant velocity v (because of air resistance, they no longer accelerate). As you watch them in the light of streetlights, how do they appear to move? What is their apparent velocity w? In what direction do they streak the windows?
Their velocity vector w has a vertical downwards component v (magnitude of v) and a horizontal component u (magnitude of –u) to the rear: in vector notation w = v–u = v+(–u). Since v and u are perpendicular to each other, by Pythagoras, w = SQRT(v2 + u2). Their streaks on the window are in the direction of w and the angle A between those streaks and the vertical satisfies sinA = u/w or tanA = u/v.
About the Aberration of Starlight
How are distances to stars measured by the parallax method?
If the directions to C are slightly different when viewed from A and B, then the difference gives the "parallax" angle between AC and BC. Using that angle one can calculate all other properties of the triangle ABC, including the distances AC abd BC from Earth to the star.
What changes were observed around 1700 in the position of Polaris?
How did astronomers know that it was not Polaris that did the moving?
--How did James Bradley know that the shift of Polaris was not a parallax effect?
--In the end, how did Bradley explain the strange shift in the position of Polaris and other stars?
--The aberration of starlight allows us to deduce that the Earth is indeed moving. Doesn't that contradict an earlier claim that absolute motion is undetectable?
[Optional further discussion by the teacher:
Actually, a systematic shift does exist, and from it we know that the solar system is moving at about 20 km/s towards a point known as the solar apex, near the star Vega. But in principle, it could also be that we are at rest and all those stars are moving in our direction, away from the solar apex. The physical effects would be exactly the same. It is only our logic that tells us it is more likely that our sun is moving, rather that a large number of distant suns happen to move on parallel tracks.]
[Harder poser--perhaps to take home] How do you think would a star on the ecliptic appear to move? Hint: it's not a circle--not even close!
About the Aberration of the Solar Wind
Why does the solar wind, on the average, appear to come not from the Sun but from a direction 4 degrees off the Sun?
What do you know about the "Solar Probe" mission?
How would instruments aboard the "solar probe" detect solar wind particles, even though they are shielded from direct sunlight?
About the Theory of Relativity
What is the principle of relativity?
How does the theory of relativity modify Newtonian mechanics?
Why did Newton's laws need to be modified? Don't they already satisfy the principle of relativity as they stand--only accelerations can be distinguished, while a constant velocity changes nothing?
What does relativity say about time in two moving frames of reference--especially if their relative velocity is close to the velocity of light??
In the late 1930s an unstable particle was discovered, named the muon (originally, "mu-meson"). Muons were fragments of collisions of very fast nuclei, and in the laboratory they decayed radioactively (into an electron and an unseen neutrino) in about 2 millionths of a second (microseconds). How far should muons traveling at the speed of light (300,000 km/s) be able to move, on the average, before decaying?
Muons moving close to the speed of light are produced in the atmosphere by collisions of fast atomic nuclei from space ("cosmic rays") at an altitude of about 12 kilometers. Yet a large fraction of them is still observed at sea level (they form the greater part of the cosmic radiation observed there). If they are so short-lived, how come they are not lost by decaying before reaching the ground?
[Comment: After relativity was introduced, Newtonian mechanics also became known as "classical mechanics" to distinguish it from "relativistic mechanics." Later still different modifications to Newton's mechanics were found to be appropriate for atomic dimensions, and these became known as "quantum mechanics." (And in case you wonder: yes, there also exist "relativistic quantum mechanics")] |
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Author and Curator: Dr. David P. Stern
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Last updated: 10-24-2004