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Standard IX

Physics

Energy and It's Sources

an artificial...

Question

an artificial satellite of mass m orbiting the earth in a circular orbit of radius twice the earth radius R. It is to be taken in another circular orbit of radius 4R. The energy needed to complete the job is GMm/kR. find k

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Solution

Dear student,
In circular orbit

GM_em/(R_e+h)²=mv²/(R_e+h)
R_e= R = h
GM_em/(2R)²=mv²/(2R)

Let us first find the total Energy of the satellite.

Total Energy = Kinetic Energy + Potential Energy

= 1/2 mv² + (-GM_em/2R)

= 1/2 m (GM_e/2R) - GM_em/2R

= -GM_em/4R
For orbit of Radius 4R
Total energy = -GM_em/4 (4R) =-GM_em/16R
Change in energy = -GM_em/16R+GM_em/4R=-3GM_em/16 R
Comparing from given equation
k = 16/3
Regards

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