Stellar Aberration

Professor Richard Conn Henry

  The Earth, carrying a telescope tube,
moves around the Sun with velocity v.

At least as we normally think about it, light moves down the telescope tube with velocity c.

The stellar aberration angle is the negative of ψ.

The common analogy is falling rain: but in fact,
stellar aberration is a deep phenomenon of
Special Relativity.

       I have created a gif animation,
    showing the appearance of the sky when the Earth starts off,
    stationary, on Mar 21, and accelerates to 0.8 c over a one year period -
        small screen, black sky.
        small screen, white sky.
        big screen, black sky.
        big screen, white sky.

        Big screen, white sky: the non-relativistic sky at a steady 0.9 c.

Stellar Aberration was discovered in 1725 by Bradley,
in a marvelous example of how we poor humans do lurch (slowly and painfully) forward!
Since ancient times, dedicated investigators had tried ... and tried ... to find stellar parallax, hoping to prove that the Earth goes around the Sun.
Bradley was engaged in yet another such attempt ... when he stumbled across the unpredicted phenomenon of stellar aberration -
thereby proving that the Earth goes around the Sun!

WHY did no one, ancient or modern, predict the phenomenon?

By the time of Bradley, it was well determined that light moves with finite velocity.

If you stand still, in vertically-falling rain, only the top of your head gets wet.
But, if you stride forward, your chest gets wet, too!
The angle that the rain appears to fall at, clearly depends on both your speed, and that of the falling raindrops. See the formula!

How much is stellar aberration?
From Steele, "New Descriptive Astronomy" (no date, but maybe 1890):

"..the mean distance of the earth from the sun is about 93,000,000 miles,
and since light travels a little over 186,000 miles per second,
it follows that the time occupied by a ray of light in reaching us from the sun is about 8 1/3 minutes (8 min. 18 sec.);
so that, in fact, (1) we do not see the sun as it is, but as it was 8 1/3 minutes ago.
And since, during this time, the earth has moved in its orbit about   20 1/2"
(2), we do not see that luminary in the exact place it occupies at the time of observation."

The Johns Hopkins University's Professor Joseph Ames, with stunningly bad timing,
published "A Text Book of Physics" in 1904 (!) . Here is his material on aberration, the final paragraph being most interesting!

NASA is moving forward with the Space Interferometry Mission (SIM),
scheduled for launch in 2009, which will measure stellar aberration with sufficient precision that it will test special relativity!

Here is a derivation of the formula for Stellar Aberration, showing that it depends only on that part of the Lorentz Transformation that is responsible for the "shortening in the direction of motion."

FitzGerald-Newton Transformation

The Terrell Effect

Jim Terrell showed that the "shortening in the direction of motion" that is predicted by Special Relativity is invisible!
Here are the papers:

        Physical Review
        Letter to American Journal of Physics

Thanks to Scott Noble for calling my attention to this terrific web site

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