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Math Help - 3-body problem

  1. #1
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    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 ?
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  2. #2
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    Quote Originally Posted by simplependulum View Post
    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.
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