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Two particles are interacting through gravitational forces. How to find their positions in function of time?
Given the initial positions and velocities $r_1(0), r_2(0), v_1(0), v_2(0)$ of 2 particles interacting by a inverse square law force $F(r) = k/r^2$, what is their positions as a function of time?
I've spent my entire day trying to solve this. Every site seems to be ending up with a "solution" like:
$$r''(t) = k / r(t)²$$
But this is not a formula it is the same differential equation I started with. How I am supposed to actually evaluate this?
I've posted a similar question and I've been linked to this "duplicate". Unfortunatelly the formula provided there finds the time an object falling will hit the ground, which is quite different from the position of particles interacting in function of time. I don't know how to adapt.
