Question

A binary star system consists of two stars of masses m1 and m2. The stars, which gravitationally attract each other, revolve around the center of mass of the system. The star with mass m1 has a centripetal acceleration of magnitude a1.

Note that you do not need to understand universal gravitation to solve this problem.
Find a2, the magnitude of the centripetal acceleration of the star with mass m2. Express the acceleration in terms of quantities given in the problem introduction.

Answer 1

Step-by-step explanation:

According to the Newton's second law

Force mass x acceleration

For the first star:

`F = m_(1)a_(1)` .... (1)

According to Newton's third law, there is an equal and opposite force on star 2 due to star 1 which is equal to the F.

For second star:

`F = m_(2)a_(2)` ..... (2)

By equation (1) and (2)

`m_(1)a_(1) = m_(2)a_(2)`

`a_(2)=(m_(1)a_(1))/(m_(2))`