Equation of motion of particle in gravitational field

[Gebar]

Homework Statement

We have two particles, m1 and m2 at positions x1 and x2, and we want to come up with the equation of motion of particle m1 due to the gravitational field of m2 (position of m1 as a function of time).

Homework Equations

F=Gm1m2/r^2
F=ma

The Attempt at a Solution

m1a=-Gm1m2/r^2
a=-Gm2/(x2-x1)^2
d^2x1/dt^2=-Gm2/(x2-x1)^2

Now, I don't know how to solve this. Any help will by appreciated.

 

[Aaron321]

im confused at what ur asking for but here we go it might give u a start

F= Gm1m2/r^2
F=ma

m1a=Gm1m2/r^2

a=Gm2/r^2

v/t=Gm2/r^2

v=Gm2t/r^2

then use Speed = dist/time

is that what u wanted?

 

[Gebar]

im confused at what ur asking for but here we go it might give u a start

F= Gm1m2/r^2
F=ma

m1a=Gm1m2/r^2

a=Gm2/r^2

v/t=Gm2/r^2

v=Gm2t/r^2

then use Speed = dist/time

is that what u wanted?

The accelaration changes since the distance between the particles changes, so I think this has to be solved analytically. I just don't know how to handle the final equation I gave, d^2x1/dt^2=-Gm2/(x2-x1)^2