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Homework Statement
A satellite mass 481 is in circular orbit of 9.29x10^6 m above the surface of the Earth
the weight of a 65.1 kg astronaut inside the satellite
What work was done (ignoring friction) to put the satellite into this orbit. Assume it started at rest on the surface of the Earth
Also, A satellite of mass 730 kg is in circular orbit around the Earth, 3.12x10^6 m above the surface of the Earth. Find the minimum work needed to move the satellite outward and put it in circular orbit at a new height of 6.05x10^6 m above the surface of the Earth
Homework Equations
U = -GMm/r
fg = GMem/r^2
The Attempt at a Solution
For the first problem, I tried fg = GMem/r^2, (6.67x10^-11) x (5.97x10^24) x 65.1 / (9.29 x 10^6 + 6.371 x 10^6)^2 and got 105.69 N
For the second, U = -GMm/r; W = Ui-Uf
- (6.67x10^-11) x (5.97x10^24) x 481 / (6.371 x 10^6) - (- (6.67x10^-11) x (5.97x10^24) x 65.1 / (9.29 x 10^6 + 6.371 x 10^6) = -1.78E10 Should the work be negative? Is that the work done by gravity, so the work done to move the satellite is the same magnitude, opposite sign?
I tried a similar strategy for the third problem, and it did not work there either.
Hopefully you can help me understand what I am doing wrong. Thanks in advance.