- #1

vasilicus

- 6

- 0

## Homework Statement

A satellite of mass m is in an elliptical orbit around the Earth, which has mass M and radius R. The orbit varies from closest approach of 'a' at point A to maximum distance of 'b' from the center of Earth at point B. At point a the speed of the satellite is v

_{o}. Assume Ug = 0 when masses are an infinite distance apart. Express your answers in terms of v

_{o}, a, b, m, M, R, and G.

A. Write the definite integral (including limits) that can be evaluated to show that Ug at distance r from the center of the Earth is given by Ug = -GMm/r

B. Determine the total energy at A.

C. Determine the angular momentum at A.

D. Determine the velocity at B.

As the satellite passes point a, it changes to a circular orbit of radius a around the center.

E. Determine the speed.

F. Determine the work done by a rocket engine to make this change happen.

## Homework Equations

Fg = GMm/r

f = GM/r

^{2}

g = Fg/m

U = -GMm/r

E = K + U = 1/2mv

^{2}- GMm/r

## The Attempt at a Solution

For a. I wasn't sure where to start. What am I supposed to do, reverse-derive the equation? If so could someone show me how because I really don't know.

b should just be E = mv

_{o}

^{2}/2 - GMm/r but I'm not sure this seems to easy.

c like b I already know that the equation is mv

_{o}a but again it seems to easy that it's just asking to repeat an equation I learned in class, there must be a catch.

d I thought v1r1 = v2r2 therefore v

_{b}= v

_{o}a/b would work but my teacher said this was the answer:

v

_{b}= square root of (v

_{o}

^{2}+ 2GM(1/b - 1/a)) I plugged in numbers and the % difference between the equations was approximately 1.8%. How did he get that equation? Why isn't mine right?

e my book says that v = square root of (GM/r) so I put square root (GM/a) but again it just seems way too easy.

f not sure where to start.