How Is Work Calculated in Gravitational Fields?

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Homework Statement

Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force:

$$F=\frac{Gm_{1}m_{2}}{r^2}$$

where r is the distance between the bodies and G is the gravitational constant. If one of the bodies is fixed, find the work needed to move the other from r=a to r=b.

Homework Equations

The Attempt at a Solution

$$W=F*x$$

$$F=\frac{Gm_{1}m_{2}}{r^2}$$

$$x=r$$

$$W=\frac{Gm_{1}m_{2}}{r^2}r = \frac{Gm_{1}m_{2}}{r}$$

$$r=b-a$$

$$W=Gm_{1}m_{2}(\frac{1}{b-a})$$

The answer states that $$W=Gm_{1}m_{2}(\frac{1}{a}-\frac{1}{b})$$. Did I make a mistake in setting up the problem?

 

[rl.bhat]

Two bodies are attracting each other. If you want to take on body away from the other, then the displacement and the force are in the opposite direction.
So W = F*x*cos(theta). Here what is theta?

 

[netheril96]

It seems that you have not learned calculus
The force here is not a constant,so you can't just use W=F*x