Answer to Question #146011 in Astronomy | Astrophysics for Abdul Salam

Question

.The two stars in a binary system have an orbital period of 5 years and an orbital separation, a, of 10AU. What is their combined mass?

Answer 1

According to the third Kepler's law,

$\displaystyle (m+M) P^2 = a^3 \; \; \Rightarrow \; \; m+M = \frac{a^3}{P^2} = \frac{10^3}{5^2} =\frac{1000}{25} = 40$ solar masses.

Answer: 40 solar masses.