A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R . If the satellite is intended to move in a circular orbit of radius

Question

A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R . If the satellite is intended to move in a circular orbit of radius 7 R , the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant = G )

TestHub · Accepted Answer

The energy of artificial satellite at the surface of the earth E 1 ​ = − R GM m ​ When the satellite is intended to move in a circular orbit of radius 7 R , then energy of artificial satellite E 2 ​ = − 2 1 ​ 7 R GM m ​ The minimum energy required E = E 1 ​ − E 2 ​ = − R GM m ​ + 2 1 ​ ( 7 R GM m ​ ) = 14 R − 14 GM m + GM m ​ = − 14 R 13 GM m ​

Physics - Gravitation Question with Solution | TestHub

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