How Do You Calculate Gravitational Potential Energy Between Two Particles?

[woo]

Homework Statement

So this is my first post and, I've been working on this problem for a while and am having trouble wrapping my head around it... I tried searching but couldn't find anything that helped..
So here's the problem.

In one dimension, the magnitude of the gravitational force of attraction between a particle of mass M1, and one of mass M2 is given by:
F_x(x)=GM₁M₂/x²
Where G is a constant and x is the distance between the particles.

a) What is the potential energy function U(x)? Assume that U(x) -> 0 as x -> infinity.
b) How much work is required to increase the separation of the particles from x=x₁ to x=x₁+d?

Homework Equations

-dU(x)/dx=F_x(x)

The Attempt at a Solution

The solution given in the book is..a) U(x)=-Gm₁m₂/x
b) Gm₁m₂d/x₁(x₁+d)

Here is what I've been trying..
-dU(x)/dx=Gx₁x₂/x²

U(x)-U(x₀)=-$$\int$$(Gm₁m₂/x²)dx

 

[flatmaster]

Yep. Now simply do the integral. And apply your boundary condition U(inf) = 0