# Separating Masses in Kepler's Third Law

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• KireeDendrall
In summary, the conversation discussed the difficulty in separating the masses of orbiting bodies when using Kepler's Third Law. It was suggested that in cases where the central object is much larger than the orbiting body, the combined mass can be approximated as the mass of the central object. However, in cases where the masses are similar, additional data such as spectroscopic data can be used to determine both masses.
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!

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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?

## 1. What is Kepler's Third Law?

Kepler's Third Law, also known as the harmonic law, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

## 2. How is mass involved in Kepler's Third Law?

In Kepler's Third Law, the mass of the planet is not explicitly mentioned. However, the mass of the planet does affect the semi-major axis of its orbit, which in turn affects the orbital period according to the law.

## 3. What does "separating masses" refer to in Kepler's Third Law?

"Separating masses" refers to the distance between two masses, such as the distance between a planet and its star. This distance is represented by the semi-major axis in Kepler's Third Law.

## 4. How does Kepler's Third Law apply to other objects in space?

Kepler's Third Law applies to any two masses in orbit around each other, not just planets and their stars. This law can be used to calculate the orbital period of moons around planets, or even stars around each other.

## 5. How can Kepler's Third Law be used in real-life applications?

Kepler's Third Law is used in various real-life applications, such as predicting the orbital period of satellites and spacecraft, calculating the masses of planets and stars, and even discovering new planets in distant solar systems.

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