taking the earth to be uniform sphere of radius 6400 km, calculate the total energy needed to raise a satellite of mass 2000 kg to a hight of 800 km above the ground and to set it into circular orbit at that attitude
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Explanation:
Initial energy= R
GMm
Here, m=mass of the satellite and M=mass of the earth
Final energy= (R+h)
GMm
Change in energy=Final energy-Initial energy
R+h
GMm
R
GMm =GMm[
R(R+h)
h
]=
R
2
GM
m[
R+h
Rh
]
Energy needed=g.m(
R+h
Rh
)
where,g=
R
2
GM
∴Energy needed =10×2000[
6400×10
3
+800000
6400×10
3
×800000
]=1.4×10
10
J
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