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Calculating Stable Circular Orbits for Binary Stars
Binary stars are cool. But if you have two stars interacting with a gravitational interaction, there are technically 6 coordinates you need to deal with (3 vector components for each star). It’s possible to reduce this to an equivalent 1 dimensional problem, but I’m not going to go over that today. Instead, I’m going to show you two things: how to calculate the initial conditions for stable orbits and how to model a binary system in python.
Let’s get started.
Initial Conditions
Suppose we have two stars (because it’s really hard to have a binary star system with only one star). For now, I will just say that one star is twice the mass of the other star and they are separated by a distance “r”. Here’s what I want:
- The center of mass of the binary star system to be at my arbitrary origin (just because).
- Momentum of the center of mass to be zero (the zero vector).
- Circular orbits.
First the center of mass. I’m going to put my 2M star on the negative x-axis and then put my 1M star on the positive x-axis. Like this:
