(2-4)  Here is a binary star:

You can see that the orbiting star is just like Nefertiti on the merry-go-round, except that it’s hurling light instead of sardines at you. So if you assume that light’s velocity varies in the same way as that of a sardine, depending on the velocity of its source, you can adapt the merry-go-round analysis to figure out what’s going on. Here are the numbers:

D (the distance of the double star from Earth) = 70 light years (1 light year = 9.46 x 1015 m)

r (the radius of star B’s orbit around star A = 3.0 x 1010m

T (the time for one complete orbit) is 27.2 days

①  First calculate u, which is the velocity of star B in its orbit.

②  Using c = speed of light and taking account of u, write down expressions for t(1), the time it takes for light to reach the Earth from B at position 1, when B is approaching us, and t(2), the time it takes the light from position 2, when B is moving away.

③  Now deduce an expression for the difference between t(1) and t(2).  You can use the same kind of rearrangement we used in the sardine example to tidy this expression up, placing the terms over a single denominator.

④  Recognising that c >> u, simplify your expression in ③ further. This is the expression Willem derived in his original paper.

⑤  Plug in the numbers, to find out how much longer it takes light from the orbiting star to reach Earth when it is moving away than when it is moving towards you. Then, by comparing this with the period of one orbit, deduce what you would expect to see, observing from Earth.