Chapter 16, Problem 58EAP

Angular Momentum of a Close Binary. Some close binary star systems have orbital periods as short as several days. Here we will estimate the angular momentum of such a system with two  $1M_{Sun}$ stars in a circular orbit having an orbital period of 10 days.

1. Determine the average orbital separation of this system using Newton’s version of Kepler’s third law.
2. Determine the average speed of each star with respect to the center of mass of the system.
3. The center of mass of this system lies at the midpoint between the two stars because their masses are equal. The distance of each star from the center of mass is therefore equal to half the orbital separation. What is the angular momentum of each star with respect to the center of mass?
4. Suppose the Sun had the same angular momentum as these two stars combined. Estimate the speed at which the Sun’s surface would be moving around the Sun’s rotation axis.
5. How does the speed from part d compare with the escape velocity from the Sun’s surface? What would happen if the Sun were spinning this fast?