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How much energy must be given to lift an artificial satellite of mass m from the surface of earth of mass m and radius r and put it in a circular orbit

with aradiusequal to twice the earth's radius?



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P.E. of satellite on ground =  PE1 = -G Me m / r
KE = KE1

PE of satellite in orbit of radius 2 r  = PE 2 = - G Me m / 2r

     m v² / 2 r  = GMe m / (2r)² = centripetal force
       1/2 m v² = KE2 = G Me m / 4 r

By using the Energy conservation principle,

   KE1 = PE2 + KE2 - PE1 = 3 G Me m / 4 r

 This is the energy required to send the satellite in to the orbit of radius 2 r.

2 5 2
 the energy required to send the satellite in to the orbit of radius 2 r.
to derive it use ke and pe formulas and substitute the values of each in eqns
1 5 1
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