Dynamics Homework Help

1. Feb 17, 2010

kaos4

1. The problem statement, all variables and given/known data

A Satellite is to be placed in an elliptic orbit about the earth. Knowing that the ration Va/Vp of the velocity at the apogee A to the velocity at perigee P is equal to the ration Rp/Ra of the distance to the center of the earth at P to that at A, and the distance between A and P is 80,000 km, determine the energy per unit mass required to place the satellite in its orbit by launching it from the surface of the earth.

Pic:

Va v-----Ra---------O----Rp----^ Vp

|---------80,000km---------|

2. Relevant equations
Conservation of Momentum: T1 + V1 = T2 + V2
T = .5mv^2
V = - GMm/r

3. The attempt at a solution
Va/Vp = Rp/Ra
Ra = 80,000 - Rp
E = T + V
E = 0.5mv^2 - GMm/r
E/m = .5v^2 - GM/r

I'm not sure where to go next. I know the final answer is 57.5 MJ/kg. How are all the 'r's and 'v's eliminated by just using the ratio? I'm generally able to solve these questions, but I've been working on this one for hours with no luck. Any help is greatly appreciated!

2. Feb 18, 2010

tiny-tim

Hi kaos4!

It's launched from the surface of the Earth …