Question

In a spectroscopic binary, if a pair shows a combined set of lines tonight, but a maximum split two nights later, what must its orbital period be?

Answer 1

Eight days.

Explanation:

Think of the splitting of the lines as two sine waves. They are 180 degrees out of phase because when Star A moves toward Earth making a blue shift, the Star B is moving away from Earth making a red shift.

Intial state: spectral lines together.

1/4 period: Star A reached its maximum blue shift (think of it as a peak in the sine wave), Star B reaches its maximum red shift (trough).

1/2 period: Spectral lines are back together.

3/4 period: Star A has a maximum red shift (trough), Star B a maximum blue shift (crest). Reverse of 1/4 period.

Full period: Back to the initial state for another cycle.