Question

Two binary stars, mass 10-kg and 2x10 kg respectively rotate about
their common centre of mass with an angular velocity. Assuming
that only force on a star is the mutual gravitational force between
them, calculate angular
velocity of rotation if the distance between
the stars is 10° Km.​

Answer 1

Answer:

Deriving Kepler's Formula for Binary Stars

Explanation:

Your astronomy book goes through a detailed derivation of the equation to find the mass of a star in a binary system. But first, it says, you need to derive Kepler's Third Law.

Consider two bodies in circular orbits about each other, with masses m1 and m2 and separated by a distance, a. The diagram below, shows the two bodies at their maximum separation. The distance between the center of mass and m1 is a1 and between the center of mass and m2 is a1.

Diagram showing two bodies in circular orbits about their center of mass.