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**[SOLVED] Energy required to place a satellite in orbit**

## Homework Statement

A 200-kg satellite is placed in Earth orbit 200 km above the surface. What is the minimum energy necessary to place this satellite in orbit (assuming no air friction)?

## The Attempt at a Solution

To solve this problem, I got an answer similar to the one my book says, but it is a little off and the book gives a different means of calculating the answer.

I first took the energy that the satellite would have on the Earth, which would be [tex]-\frac{GmM_E}{R_E}[/tex]

I then took the energy that the satellite would have in orbit, which would be [tex]-\frac{GmM_E}{2(R_E+h)}[/tex]

I then took the final minus the initial to find the difference. I received an answer of 6.43 x 10^9 J. However, the answer in my book says that I should get an answer of 6.45 x 10^9 J as given by [tex]\frac{mGM_E(R_E+2h)}{2R_E(R_E+h)}[/tex]

I have no idea how to derive this formula that the book gives, and I can't see where the 2h comes from. I know that my answer is pretty close, but I would really like to know how to derive this formula. Thanks!