This is fascinating stuff. It's pretty clear to me that I've got a lot more to learn in way of calculus and mechanics.
Thank you all for the responses!
Oh, right. I don't know what I was thinking. So for the conservation of energy, that equation would look more like:
1/2 mv12 + 1/2 Mv22 - GMm/ r = c (constant)
(I'm including the kinetic energies of both masses because gravitational potential energy is written in terms of M and m )
The problem...
Oh neat! I hadn't considered conservation of energy. So something like this?
1/2 mv2 = -GMm / r
I'm cancelling out the mass (m) out from both sides because I can, but I don't know if I should.
1/2 v2 = -GM/r
let k = -GM
v = (2k/r)0.5
Where v is presumably dr/dt? In your second method you seem...
As far as stating the equation, I honestly can't say if I've done it correctly. The question is a matter of personal interest and didn't come from any textbook. I apologise for that. I just wanted to find a relationship between the time elapsed and the distance between two unbound masses. I find...
Homework Statement
Consider two masses of variable magnitude (M m) that are separated by a distance ( r ). Both masses are free to move. Calculate dr/dt.
Homework Equations
(See below)
The Attempt at a Solution
F = GMm / r2
a = Gm / r2
let k = Gm
da/dr = -2kr-3
dr/da = (-2k)-1 r3
dr/da *...