Don't tell me how to solve it, but I've been trying to use the following equation to get r which is distance) as a function of t.
$$\frac{GMm}{r^2}= -ma$$
I've been working on it for about a year now and I think I may have made a breakthrough, but I'm not sure. Here's what I did.
$$\frac{GM}{r^2}=-a$$ $$\frac{GM}{r^2}=-\frac{dv}{dt}$$ $$\frac{dr}{dv} \dot{} \frac{GM}{r^2}=-\frac{dv}{dt}\dot{}\frac{dr}{dv}$$ $$\frac{dr}{dv} \dot{} \frac{GM}{r^2}=-\frac{dr}{dt}$$ $$\frac{dr}{dv} \dot{} \frac{GM}{r^2}=-v$$
This is really convenient because I haven't taken differential equations, and this gets rid of the second derivative. The only problem is I've read something somewhere about not be able to treat derivatives as fractions. Is this okay to do, and if so why?