Separating Masses in Kepler's Third Law

[KireeDendrall]

TL;DR Summary

Discussion of methods for separating the mass calculated of a two body system.

Hey everyone! I have been looking everywhere to try to find the answer to this question so I thought I'd pose it here. When we discuss finding the mass of orbiting bodies, it's easy to find the combined mass of the system using Kepler's Third Law in the form M1+M2=(4pi^2)(a^3)/((G)(T^2). My conundrum is that I can't seem to find how to separate the two masses. Anytime I've asked, I've gotten the answer that the combined mass is approximately the mass of the central object in the system and people won't elaborate past that.

I know there must be a way to separate these masses. Please help! Sorry if a thread like this has been posted previously, feel free to attach links for anything that would be relevant in pointing me in the right direction!

 

[phyzguy]

In many cases, like the solar system or an Earth satellite, the central mass is much larger than the orbiting body. Then assuming M1>>M2, you can see that M1+M2 ~ M1. If this is not the case, I think you need other data (beyond a and T) to determine both masses. For example, in the base of binary stars of similar masses, we can have spectroscopic data giving the velocities of the two stars. With this, together with a and T, we can determine both M1 and M2. Does this answer your question?