Gravitational Energy for Satellite: r1 to r2

[Karol]

Homework Statement

A satellite orbits at radius r₁. What is the energy required to pass it to a greater radius r₂. express in terms of m and g

Homework Equations

The total energy of a satellite: $E=-\frac{GMm}{2r}$

The Attempt at a Solution

$$E=-\frac{GMm}{2r_2}+\frac{GMm}{2r_1}=-\frac{RGMm}{R2r_2}+\frac{RGMm}{R2r_1}=\frac{Rgm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2}\right )$$
The answer in the book:
$$\frac{R^2gm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2} \right)$$

 

[Orodruin]

A good first check is to make sure that the physical dimensions are consistent in every step. Your answer has dimensions energy/length and is therefore wrong. I suggest controlling the intermediate steps.

 

[Karol]

I found the mistake, Thanks, it helped