Can you integrate the force with respect to time for both bodies to get momentum ( p = G.M.m.t/4r
2 + c ) bodies are initially at res thus c = 0, due to conservation momentum is the same for each body....
Then p = mv so
V
M = G.m.t/4r
2
and
V
m = -G.M.t/4r
2
Integrate to get equation for position constants will be r and -r,
x
M = G.m.t
2/8r
2 - r
and
x
m = r - G.M.t
2/8r
2
at the time they collide the positions will obviously be equal...
G.m.t
2/8r
2 - r = r - G.M.t
2/8r
2
2r = G.m.t
2/8r
2 + G.M.t
2/8r
2
16r
3 = G.m.t
2 + G.M.t
2
t
2 = 16r
3G(M+m)
t = (16r
3G(M+m))
1/2
hows that?
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