Question

The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 10 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 10⁵ m/s. What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass.

Answer 1

Given that,

T = 10 months = 2.628*10^7 s

v = 10^5 m/s

we know that,

v = 2*pi*r / T

r =  (2.628*10⁷*10⁵*6.684*10^-12 / 2*pi) AU = 2.795 AU

From kepler's law,

T^2 = r^3 / (m1 + m2)

T = 10 months = 0.833 Years

so, (0.833)^2 = (2.795)^3 / (m1 + m2)

m1 + m2 = 31.44 solar mass

m1 = m2 = 15.72 solar mass

m1 = m2 = 3.12*10^31 kg