Question

Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 360 million kilometers and take 5.0 Earth years to orbit about a point midway between them. What is the mass of EACH?

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of each star = M

Distance between the two stars = D = 360 million km = 360 x 10⁶ km = 360 x 10⁹ m = 3.6 x 10¹¹ m

Radius of orbit of the stars = R

R = 1.8 x 10¹¹ m

Time period of orbit = T = 5 years = 5 x (365x24x60x60) sec = 1.5768 x 10⁸ sec

Orbital speed of the stars = V

V = 7172.6 m/s

The gravitational force of the stars on each other provides the necessary centripetal force for their circular motion.

M = 5.55 x 10²⁹ kg

Mass of each star = 5.55 x 10²⁹ kg