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# Transferring a circular orbits radius using kinetic energy

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A space vehicle is in a circular orbit about the earth. The mass of the vehicle is 3,000 kg and the radius of the orbit is 2Re= 12,800km. The vehicle must be transferred to a circular orbit of radius 4Re.

a) What is the minimum energy expenditure required for the transfer?

b) An efficient way to accomplish the transfer is to use a semielliptical orbit (Hohmann transfer orbit). What velocity changes are required at the points of intersection between the original orbit and the semiellipse called A, and between the semiellipse and new circular orbit B?

#### Solution Preview

(a)
Energy (E1) = (-GMe.m/2Re) + (1/2) m.v1^2
Eneryg (E2) = (-GMe.m/4Re) + (1/2) m.v2^2

Here, v1 = sqrt(GMe/2Re)
and, v2 = ...

#### Solution Summary

This solution outlines the calculations needed to determine the energy and velocity changes required to modify the orbit of a space vehicle.

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