Invariant Speed of Light using Binary Stars and Tangential Velocity

So I was in class the other day and my professor mentioned that we can prove that light is invariant using a binary star system. His reasoning:

1. Assume a binary star system 1000-light years away from Earth, with the stars orbiting counterclockwise.

2. Assume stars rotating at 0.003c and stars positions at top and bottom of orbit. The time light takes to get from top star to earth is longer than the bottom star.

My question is how does this show that light is invariant?

• Are both the stars the same distance from Earth at this point? And are we assuming that we have a way to determine how long a light beam took to travel here? (Because that's not always guaranteed.) Jul 24, 2017 at 19:31
• Yea they are the same distance, and we're finding the difference between the times we see the stars on earth I believe Jul 24, 2017 at 19:33
• Wouldn't the invariance of $c$ mean that the light takes the same amount of time to reach us, regardless of the source? Jul 24, 2017 at 19:36
• But since the velocity of the top is moving away and the bottom is moving torwards, the distance is longer toa time takes longer according to d=ct Jul 24, 2017 at 19:39
• You just said the distance from each star to Earth was the same, though. Jul 24, 2017 at 19:48

Assuming we have a way to determine the time it takes light to reach us, this gives us a way to validate one of two hypotheses. Either:

1. The speed of light is not invariant, which means its speed is dependent on the source velocity, or

2. The speed of light is invariant, which means its speed is independent of the source velocity.

Under hypothesis 1, the light coming from one star is traveling faster than the other (since the two stars have different velocities relative to Earth), and under hypothesis 2, the light coming from each star has the same speed. Since the stars are the same distance away, under hypothesis 1, the faster light should reach us first, and under hypothesis 2, the light from both stars should reach us at the same time.

Experimentally, we have determined that hypothesis 2 is correct.

• Can you explain to me how experimentally? Does this have to do with the De Mite experiment or whatever? Jul 24, 2017 at 21:28
• @JeffreyChiu Usually the Michelson-Morley experiment is the one quoted for the discovery of the invariance of the speed of light. Jul 25, 2017 at 7:41

Binary system are quoted as a way to check the velocity of the star does not affect the speed of propagation of light, but, as far as I know the argument uses the amount of light observed at earth.

If the velocity of the rotating stars does not affect the speed of light we should observe the same amount of light no matter the phase of the orbital motion of the stars.