Calculate Period & Center of Mass in Binary Star Systems | Newtons Law of Gravity & Kepler's 3rd Law

Commonly called the 'Two Body Problem' or the 'Kepler Problem', apply Newton's Law of Universal Gravitation to the circular motion of two celestial bodies in orbit around each other.

Looking at centripetal force, we can show that the two objects will orbit their mutual center of mass which is known as the Barycenter.

Then, relating the centripetal force we can calculate the period of orbit for the two bodies. The key concepts here are that the distance from one star to the other is the sum of the two orbitial radii. Additionally it is important to recognize that the orbital periods are the same, and the orbital velocities are different. Ultimately the derivation results in the equation commonly referred to as Kepler's 3rd Law.

This problem commonly comes up in early physics courses including AP Physics C Mechanics.

and yes I added a watermark. People have been ripping off my work.