astronomy question?

Question

1. You've just discovered a new X-ray binary, which we will call Hyp-X1 ("Hyp" for hypothetical). The system Hyp-X1 contains a bright, B2 main-sequence star orbiting an unseen companion. The separation of the stars is estimated to be 20.0 million kilometers , and the orbital period of the visible star is 4.00 days.

Use Newton's version of Kepler's third law to calculate the sum of the masses of the two stars in the system. Give your answer in both kilograms and solar masses.

Determine the mass of the unseen companion.(Hint: A main-sequence star with spectral type B2 has a mass of about )

Answer 1

The newtonian version of Kepler's third law is

P^2 = 4*r^3*π^2 / G*(m1+m2), where P is the orbital period. For circular orbit r is the radius. P = 4.00 days, r = 20*10^6 km. Solve for m1+m2:

M = m1+m2 = 4*r^3*π^2 / G*P^2

Convert P from days to sec for a result in kg. You should get 3.96*10^31kg. The solar mass is 1.99*10^30kg, so the sum of masses is 19.92 solar masses

You didn't give the mass of a B2 star; It is 10.5 solar masses. The mass of the unseen companion is then 19.92 - 10.5 = 9.42 solar masses