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 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 gammamcc, I think you are missing the point. The problem is not to integrate $d^2r/dt^2= 1/r^2$. He's alread done that. That results in $$v= \frac{dr}{dt}= \sqrt{c_1- \frac{2}{r}}$$ The question is how to integrate that.