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.(adsbygoogle = window.adsbygoogle || []).push({});

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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# Classical aberration of starlight

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