Question:

Consider a binary star system to find the mass of the stars. The distance between them is found out to be \(a\), and the period of revolution \(T\). Assume that the masses of two stars are equal. Find the mass from the conditions.

Answer:

This method allows us to find the total mass of the system in laboratory by knowing the distance between stars and the period. Kepler’s third law indicates the relationship between the period and distance.

\[  \frac{T^2}{a^3} = \frac{4\pi^2}{G(m_1+m_2)}  \]

where \(G\) is the gravitational constant. Since \(m_1+m_2 = 2m\), we can solve for the mass.

\[  m = \frac{2\pi^2 a^3}{GT^2}  \]

This gives the mass of one star.