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EDIT: last equation should be\[m_2\frac{d^2x_2}{dt^2}=\mp G\frac{m_1m_2}{(x_2-x_1)^2}\]

consider one of the mass to be at rest and another is accelerating.

You can't do that though! m_2 is accelerating too!

well if you want a dynamic system then ... it's going to be a system of second order DE.

not sure ... first order system is fairly complicated.

plus ... this is non linear :(( looks like there must be some other approach.

didn't get any solution from mathematica.

let dx/dt = v ... dv/dt = dv/dx *dx/dt = v dv/dx
not sure if you integrate it wrt dt ...

is \[\int v(t)dt=x(t)\]?

Cause that's all i did.

something like
|dw:1345580217154:dw|

I'm not sure for general case ... with non rest IC.

Okay thx i looked at the wiki link. I'm on to something on my own and I'll see if that works.

OK no one else is helping at physics so I'll repost the problem in the math section...

more over this is just 1D case ... for general 2d case the system of DE could me much worse.

Yeah I know it's 1D I was trying just to tackle this, let alone the 2D.

It's okay, I'll just do it out on my own using the CM. Don't worry about it.