Thread: 3-body problem

There are 3 masses with mass $\displaystyle m_1 m_2 m_3$
Assume that the mass of $\displaystyle m_1$ 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 $\displaystyle m_2$ and $\displaystyle m_3$ ? Is the path also an ellipse ?

Originally Posted by simplependulum

There are 3 masses with mass $\displaystyle m_1 m_2 m_3$
Assume that the mass of $\displaystyle m_1$ 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 $\displaystyle m_2$ and $\displaystyle m_3$ ? 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.