Hohmann Transfer, energy for both boosts

[jcook735]

Homework Statement

For a circular orbit around a massive gravitating body, the speed depends on the radius according to Equation 8.3; for elliptical orbits, the speed varies according to the equation v²= 2GM[(1/r)-(1/2a)], where r is the distance from the massive body and a is the semimajor axis of the ellipse. A satellite can be transferred from one circular orbit at radius r₁ to a higher orbit at radius r₂ by boosting the circular speed v₁ at r₁ to the appropriate speed for an elliptical orbit whose distance varies between r₁ and r₂, and then boosting the speed in the elliptical orbit at r₂ to the circular speed v₂. this is called a Hohmann transfer. (a) How much energy is required for the first boost in such a transfer to take a 250-kg satellite from a circular orbit at a 400-km altitude to the altitude of a geosynchronous orbit? (b) how much energy is required for the second boost?

Homework Equations

Conservation of energy and the v₂ equation given in the problem

The Attempt at a Solution

Well, I used conservation of energy E₁ + E = E₂ and found the E required to move the satellite between the two orbits. However, this question is asking for the energy required for each boost, and I have no idea how to separate these. Any help would be greatly appreciated!

 

[gneill]

Presumably you can find the circular orbit velocity for r1 and r2. In order to get the satellite in circular orbit at r1 onto the Hohmann transfer ellipse, what velocity must it have at r1?