Question

A binary star system consists of two stars of masses m1m1m_1 and m2m2m_2. The stars, which gravitationally attract each other, revolve around the center of mass of the system. The star with mass m1m1m_1 has a centripetal acceleration of magnitude a1a1a_1. Note that you do not need to understand universal gravitation to solve this problem.

Answer 1

Answer:

          $a_c_2=\dfrac{a_c_1\times m_1}{m_2}$

Explanation:

The question is: Find the magnitude of the centripetal acceleration of the star with mass m₂

The centripetal acceleration is the quotient of the centripetal force and the mass.

                $a_c=\dfrac{F_c}{m}$

Thus, you can write the equations for each star:

     

       $a_c_1=\dfrac{F_c_1}{m_1}$

       $a_c_2=\dfrac{F_c_2}{m_2}$

As per Newton's third law, the centripetal forces are equal in magnitude. Then:

       $a_c_1\times m_1=a_c_2\times m_2$

Now you can clear $a_c_2$:

          $a_c_2=\dfrac{a_c_1\times m_1}{m_2}$