There are 3 masses with mass

Assume that the mass of 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 and ? Is the path also an ellipse ?

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- July 27th 2009, 12:45 AMsimplependulum3-body problem
There are 3 masses with mass

Assume that the mass of 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 and ? Is the path also an ellipse ? - July 28th 2009, 05:27 AMaidan
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.