# 3-body problem

• Jul 27th 2009, 12:45 AM
simplependulum
3-body problem
There are 3 masses with mass $m_1 m_2 m_3$
Assume that the mass of $m_1$ is very large ( like the Sun comparing to the Earth and Mars ) the position of it remains in the origin

My question is what is the path of $m_2$ and $m_3$ ? Is the path also an ellipse ?
• Jul 28th 2009, 05:27 AM
aidan
Quote:

Originally Posted by simplependulum
There are 3 masses with mass $m_1 m_2 m_3$
Assume that the mass of $m_1$ is very large ( like the Sun comparing to the Earth and Mars ) the position of it remains in the origin

My question is what is the path of $m_2$ and $m_3$ ? Is the path also an ellipse ?

Perturbed ellipse.

Look at several possibilities:

1. Planet m2 has a circular orbit near m1; planet m3 has a circular orbit far from m1. As m3 orbits [m1;m2] the center of gravity changes, which will modify the orbit of m3.

2. m2 & m3 are of equal mass and have common center of mass orbit and far from m1.

2a. same as 2 but both are close to m1.

3. m2 & m3 are of equal mass and at equal distance but on opposite sides of m1.

You'll need to determine the orbital velocity that will maintain the longest stable orbit.