Formula for radius of planets barycenter using only orbit time and acceleration as input.

Question

I need a formula for a project to calculate the distance to the barycenter between two bodies from the main orbital body. I do not have the mass of either of the two bodies. But I do have the distance between them, the time of a full orbit, and the acceleration on the main body. Assuming the orbits are perfectly circular I need the radius of the main bodies orbit. I need velocity too but I know how to get that with the radius. Say the main body is Earth and the second is Luna but I don't know any more information about them.

Answer 1

Hi Blaine,

Anytime you have (or can assume) circular motion, always remember that the acceleration required to maintain circular motion is called "centripetal acceleration", which has its own special formula, independent of mass:

a_c = v²/r

If you know the velocity and acceleration for one of the bodies, you can figure out its orbital radius. The two bodies have to be on exactly opposite sides of the barycenter (since it is the center of mass of the two objects), so the total distance between the two bodies would be the sum of their orbital radii from the barycenter. I hope that helps!

Andy