Recall from basic physics that if the angular velocity of the smaller star is $\omega$ then its linear speed $v$ is given by $v = \omega r$. In terms of $v$, what is the time $t_1$ that it will take light emitted by the smaller star to reach Earth, if that light is emitted when the smaller star’s orbit has it moving directly away from Earth? (Again, assume—incorrectly—that light behaves as you would expect from everyday experience, with its base speed $c$ being increased or decreased by the motion of the source.)

In terms of $v$, what is the time $t_2$ that it will take light emitted by the smaller star to reach Earth if that light is emitted when the smaller star’s orbit has it moving directly toward Earth? (Again, assume—incorrectly—that light behaves as you would expect from everyday experience, with its base speed $c$ being increased or decreased by the motion of the source.)

In terms of $v$, what is the time $t_3$ that it takes the smaller star to move from the position relevant to part (A) to the position relevant to part (B)—that is, how long does it take the star to complete one half of a full orbit around the larger star?

What value of $\omega = v/r$ will result in the light emitted when the smaller star is traveling directly away from Earth reaching us at the same moment as the light emitted later, when the smaller star’s orbit has it moving directly toward earth?