# Basic 3-body problem

1. Mar 19, 2006

### Stam

I hope i'm on the right thread!!
So i have the following problem...I have a homework on the three body problem. I want to simulate a 2D periodic circular problem using the Lagrange configuration. The masses of the three bodies are all equal to 1.
Can anyone tell me what initial conditions to use???

2. Mar 19, 2006

### pervect

Staff Emeritus
You'll basically have an equilateral triangle rotating about the center of mass. Calcluating the angular frequency, w, at which the rotation occurs is a bit tricky, though.

Do you expect this case with three equal masses to be stable?

3. Mar 19, 2006

### Stam

I know that with equal masses it will be unstable....I know that in the bibliography there are some specific initial condititions for which a periodic orbit on a equilateral triangle will occur. I found the initial conditions (x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3) for the figure-8 orbit but i cannot found anywhere about the lagrange.

4. Mar 19, 2006

### tony873004

http://orbitsimulator.com/BA/3-body.GIF
It is stable for a few orbits, then it falls apart.

Like Pervect said, its an equalateral triangle, so x,y,&z should be easy to find.

There's a wide range of velocities that will give you varying eccentricities.
sqrt(2GM/r) is what I used in the above picture. sqrt(3GM/r) gives you more circular orbits.

5. Mar 19, 2006

### Stam

Or I'm too stupid or too tired ...Anyway i'm stuck. Can anyone give me a set of initial conditions because i have to hand in a homework tomorrow? Thanks for all the answers!!

6. Mar 19, 2006

### enigma

Staff Emeritus
Sorry Stam,

We _help_ with homework, but we won't _do_ your homework here.

Assuming you're qualified to be in the class you're in, what tony and pervect provided is more than enough to get a solution.

7. Mar 19, 2006

### Stam

Yes it's true. But my homework was to search the internet and find specific intial conditions and not to calculate them. My professor has given me a mathematica program to calculate three body orbits and all i have to do is search the internet, find exact numbers for the lagrange and figure-8 orbit, plot the orbit in mathematica and create a .gif with that orbit. I've found initial conditions for figure-8 but nothing for the lagrange orbit. Sorry for not mentioning that earlier!