(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is no general analytical solution for the motion of a three-body gravitational system. However, there do exist analytical solutions for very special initial conditions. The figure below (see attachment) shows three stars, each of mass m, which move in a two-dimensional plane along a circle of radius r. Calculate how long this system takes to make one complete revolution. (In many cases, three-body orbits are not stable: any slight perturbation leads to a breakup of the orbit.)

2. Relevant equations

This course focuses heavily on the Momentum Principle.

mv^{2}/R=GMm/R^{2}

v=(GM/R)^{1/2}

v=(2(pi)R)/T

(2(pi)R)/T=(GM/R)^{1/2}where T is the time it takes to complete one complete revolution.

3. The attempt at a solution

I thought you could just replace Mm with m^{3}since the stars all have equal mass and then solve for T, but it's not in the answer choices. The answer is one of the choices in the attachment.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Time it takes a 3-body gravitational system to complete one orbit?

**Physics Forums | Science Articles, Homework Help, Discussion**