Solution

Problem

*The accelerations of stars in a binary star system are $a_1$ and $a_2$. What is the mass of the second star if the mass of the first is $m_1$?*

Solution

The corresponding accelerations $a_1$ and $a_2$ are created solely by the forces of mutual interaction, then:
$$m_1 a_1 = F_1$$
$$m_2 a_2 = F_2$$

Since the interaction forces are equal in magnitude ($F_1 = F_2$), it follows that:
$$m_1 a_1 = m_2 a_2$$

Solving for the mass of the second star $m_2$, we obtain:
$$m_2 = \frac{m_1 a_1}{a_2}$$