An artificial satellite of mass m orbiting the earth in a circular orbit of radius twice the earth's radius R . It is to be taken in another circular orbit of radius 4R. The transfer is accomplis

Question

An artificial satellite of mass m orbiting the earth in a circular orbit of radius twice the earth's radius R . It is to be taken in another circular orbit of radius 4R. The transfer is accomplished through an elliptical orbit as shown in the figure. The energy needed to complete the job is calculated to be equal to $\frac{1}{k} \frac{GMm}{R}$ where M is the mass of the earth. Find the value of k .

TestHub · Accepted Answer

Energy needed = mechanical energy in the 4R orbit − mechanical energy in the 2R orbit.

$E = - \frac{GM m}{2 ( 4 R )} - (- \frac{GM m}{2 ( 2 R )}) = \frac{GM m}{8 R}$

Comparing with $\frac{1}{k} \frac{GM m}{R}$ : k = 8.

Answer: 8.00

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