Classical aberration of starlight

In summary: I couldn't find it anywhere in the book!It may be bad etiquette to keep answering my own post but the answer finally came to me when I ignored the book's approach to the problem. For the record:The change in aberration, if any, depends on the index of refraction of the medium in which the light travels. In this case, the medium is water which has a higher index of refraction than air. Consequently, the light travels at a slower speed in water than it does in air.
  • #1
mmwave
647
2
I have been trying to determine the change in angle required for a telescope due to the aberration of starlight when it is filled with water. The empty telescope is easily done with the law of sines.

The starlight reaches Earth at an arbitrary angle of theta from the vertical with a speed of c. The horizontal is the relative speed of Earth & star V. The hypoteneuse of the triangle is c' the Galilean relativity speed of V+c. The angle of the hypotenuse from the vertical is given by Theta_prime - Theta = V/c * cosine Theta.

Now fill the telescope with water & calculate the new angle theta_prime. I can't find any way to solve this! The only tools I have are law of sines and the law of cosines.

When theta equals zero I can see Theta_prime = Vn/c where n is the index of refraction of the water. I can extrapolate that the answer I want is
Theta_prime - Theta = Vn/c * cos Theta but I can do the analytic geometry to prove it.

Suggestions? (The special relativity answer is much easier to derive but I really want to know how to solve the classical case.)
 
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  • #2
While it's somewhat satisfying that no one else knows the answer but not as satisfying as learning the analytic geometry trick to make this doable.
 
  • #3
Unless you have fish in your ancestry, I can't for the life of me figure out why you'd want to have water in your telescope.
 
  • #4
Danger said:
Unless you have fish in your ancestry, I can't for the life of me figure out why you'd want to have water in your telescope.

The difference between classical & relativistic predictions for aberration in a water filled telescope is a 'proof' of the correctness of special relativity. I'm trying to work out the classical prediction and it seems much harder than the relativistic one!

(My aquatic ancestors are dolphins thank you very much!
:smile: )

mmwave.
 
  • #5
Hmm... it's a new one on me. Never heard of it (along with millions of other things). I have no idea what any of those math things mean. Out of curiosity, though... when you mentioned an 'empty' tube as opposed to a water-filled one, did you mean air-filled or actually evacuated? I mean, are you comparing the wave-propogation in water to that in air or in vacuum?
 
  • #6
Danger said:
Hmm... it's a new one on me. Never heard of it (along with millions of other things). I have no idea what any of those math things mean. Out of curiosity, though... when you mentioned an 'empty' tube as opposed to a water-filled one, did you mean air-filled or actually evacuated? I mean, are you comparing the wave-propogation in water to that in air or in vacuum?


The change in aberration, if any, depends on the relative speed of light in free space and in the tube. When Sir Airy did the experiment, it was water filled versus air filled but considering the difference in index of refraction between air and vacuum, it doesn't really matter.

mmwave.
 
  • #7
It may be bad etiquette to keep answering my own post but the answer finally came to me when I ignored the book's approach to the problem. For the record:

The time of flight is L/u where L is the length of the telescope, u is the speed of light in whatever medium u = c/n. The horizontal distance moved by the scope is vt. Sin theta equals vt/L = vL/u / L = v/u = vn/c. It's so simple...
 

What is classical aberration of starlight?

Classical aberration of starlight is a phenomenon that occurs when the Earth's motion around the Sun causes a change in the apparent position of stars in the sky. This change is due to the finite speed of light and the relative motion between the Earth and the stars.

How does classical aberration of starlight affect the appearance of stars?

Classical aberration of starlight causes stars to appear slightly shifted from their true position in the sky. This shift is typically less than one arcsecond, which is too small to be detected with the naked eye, but can be measured using precise instruments.

What is the cause of classical aberration of starlight?

The cause of classical aberration of starlight is the combination of the Earth's orbital motion around the Sun and the finite speed of light. As the Earth moves around the Sun, the direction of its velocity changes, causing the apparent position of stars to shift.

How is classical aberration of starlight different from other types of aberration?

Classical aberration of starlight is different from other types of aberration because it is caused by the Earth's motion around the Sun, rather than the motion of the observer or the motion of the light source. This is why it is also known as "annual aberration."

What is the significance of classical aberration of starlight in astronomy?

Classical aberration of starlight is an important factor to consider in making precise measurements of star positions. It also provides evidence for the Earth's motion around the Sun, as first observed by astronomer James Bradley in the 18th century.

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