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.

Question

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.

anonymous · Answer

We also know that we are limited to planar motion, so we can look at four DEs:
One for x1, y1, x2, y2.

anonymous · Answer

With$$\vec r_1=<x_1, y_1>$$and etc. for r2.

anonymous · Answer

ah forget it im going to math se.

anonymous · Answer

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