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.

Answer 1

a₂ = m₁ / m₂ a₁

Step-by-step explanation:

For this exercise we note that the attraction between the two stars is an action and reaction force, therefore it has the same magnitude, but it is applied to each of the bodies

Let's apply Newton's second law on the star 1

F₁ = m₁ a₁

Newton's second law in star 2

F₂ = m₂ a₂

| F₁ | = | F₂ |

m₁ a₁ = m₂ a₂

a₂ = m₁ / m₂ a₁