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XxBollWeevilx
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[SOLVED] Energy required to place a satellite in orbit
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)?
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!
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!