Posted by tom on Wednesday, November 24, 2010 at 2:08pm.
For (a) and (b), the satellite mass will not matter. The orbit distance from the center of the earth is R = 6378 + 210 = 6588 km. Speed is
V = 2 pi R/P
where P is the period.
Get the period from
G M/R^2 = V^2/R
G M = V^2*R = 4 pi^2 R^3/P^2
Solve for P
M is the earth's mass
Energy required = (1/2) m V^2 + GMm[1/Re - (1/(Re + 211,000m)]
m is the satellite mass
There is a small additional term (+ or - that takes into account the rotational speed of the earth at the launch point. That gives the rocket launcher a bit of a boost, especially at the equator.
I need a better explanation than that, and an answer to show you are right. thanks
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