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Is the following DE solvable? For constants m1, m2, and G, find the position vectors r1 and r2 as functions of time. We know: \[m_1\frac{d^2\vec r_1}{dt^2}=G\frac{m_1 m_2 (\vec r_1-\vec r_2)}{|\vec r_1-\vec r_2|^3}\]\[m_1\frac{d^2\vec r_1}{dt^2}=-m_2\frac{d^2\vec r_2}{dt^2}\]General solution with constants is preferred. If you're interested, this is the two-body problem.

Mathematics
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We also know that we are limited to planar motion, so we can look at four DEs: One for x1, y1, x2, y2.
With\[\vec r_1=\]and etc. for r2.
ah forget it im going to math se.

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Other answers:

If any1's interested: http://math.stackexchange.com/questions/185593/solving-the-de-for-a-two-body-system

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