## Thursday, February 15, 2018

Published 5:37 PM by with 0 comment

# Planet Orbiting Binary Stars

I was curious what types of orbits you could get for a planet orbiting a binary star system, so I played with it a bit and collected some of the interesting results.

#### Background

Each of the simulations here consists of one Earth-sized planet and two Sun-sized stars. They are solutions to the general n-body problem. The stars are separated initially by 5 AU and the orbit maintains roughly that distance. The planet is moved to a variety of locations to see what types of orbits result from the initial conditions. All gifs are centered on one of the stars, so these are the orbits from its perspective. All simulations run for ~300 years and are calculated with 1 day time intervals. If you'd like the code to play with it, it's all very similar to the code here. That link contains a solution in both MATLAB and Python.

#### Halfway between the stars

First, I wanted to know what types of orbits were possible for a planet that starts halfway between the stars. Very few initial conditions led to orbits that were stable for any reasonable length of time, but a few ended up with cool orbits that involve the planet moving back and forth between the stars. My favorite is here:

Plotting the planet's distance from the center star yields this:

The planet started at 2.5 AU with an orbital speed of 1.73 AU/yr Pretty cool.

#### Near one star

It was very easy to get a stable orbit near one of the stars. Below is an example:

The planet started at 1 AU with an orbital speed of 2*pi AU/year (i.e., what Earth has).

#### Orbiting both stars

This was my favorite. You get a really cool apparent retrograde orbit effect from the planet. I don't know why, but I found the apparent stop/start thing fascinating:

The planet started at 15 AU with an orbital speed of 4.6 AU/yr.