The diagram below shows the radial velocity curve of a double-line spectroscopic binary. Based on this radial velocity curve, which of the following statements is correct?

Question

Quizplus · Accepted Answer

The radial velocity curve of a double-line spectroscopic binary shows the velocity variations of both stars as they orbit around a common center of mass. The amplitude of the velocity variations depends on the masses of the stars and their separation, with larger masses and closer separations resulting in larger amplitudes.

In this particular curve, it can be seen that the velocities of both stars vary sinusoidally over a period of approximately 2 days. However, the amplitude of the variations for Star B (the lower curve) is larger than for Star A (the upper curve). This indicates that Star B is more massive than Star A, since larger masses result in larger amplitudes of velocity variations.

To determine the relative masses of the stars, we can use the fact that the ratio of their masses is equal to the ratio of the semi-amplitudes of their velocity variations. In this case, the semi-amplitude of Star B's velocity variations is approximately twice that of Star A's. Therefore, we can conclude that:

B) Star B is twice the mass of star A.

The Diagram Below Shows the Radial Velocity Curve of a Double-Line