# AP Physics B - Satellite/Orbit problem?

A satellite of mass m is in an elliptical orbit around the Earth, which has mass Me and radius Re. The orbit varies from closest approach of a at point A to maximum distance of b from the center of the Earth at point B. At point A, the speed of the satellite is vo.Express your answers in terms of a, b, m, Me, Re, vo, and G.

a. Write the expression for the gravitational force between the satellite and Earth at point b.

b. The potential energy of the satellite when it is a distance r from the center of the Earth is given by:

Ug=(-GMem)/r

Determine the total energy of the satellite when it is at A.

c. Determine the velocity of the satellite as it passes point B in its orbit.

As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth.

d. determine the speed of the satellite for this circular orbit.

e. calculate the work done in changing the orbit

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I honestly don't know where to start with this problem...any initial help would be very much appreciated :)

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Hi ohmygosh123 welcome to PF!

Please show an attempt at the question, like a relevant equations and what you think should be the correct way to solve this problem.

-yinx-

Ok this is what i have so far:

A: Fg = (GmM)/r^2 = (GmMe)/bRe^2

B: Total Energy = KE + PE = (-GMem)/a + 1/2mvo^2

C: (-GMem)/a + 1/2mvo^2 = 1/2mv^2 ???

D: change in KE = 1/2mv^2 - 1/2mvo^2 => 2(change in KE) = mv^2 - mvo^2

E: W = Fdcos / W = Change in KE or Change in Energy / W = 1/2mv^2 - 1/2mvo^2

W = m[(v^2-vo^2)/2]