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Satellite: Hohmann transfer

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 V squared=2GM{(1/r)-(1/2a)}, where r is the distance from the massive body and a is the semi major axis of the ellipse(i.e., half the sum of the closest and farthest distances). A satellite can be transferred from one circular orbit (at radius r1) to a higher orbit (at r2) by boosting the circular speed v1 at r1 to the appropriate speed for an 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?

c) Check that the sum of your answers to parts (a) and (b) equals the difference in the total energies in the two circular orbits.

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