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.
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.
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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
to derive it use ke and pe formulas and substitute the values of each in eqns
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