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 )

Step-by-step solution

The energy of artificial satellite at the surface of the earth E₁=- G M m R When the satellite is intended to move in a circular orbit of radius 7 R , then energy of artificial satellite E₂=- 1 2 G M m 7 R The minimum energy required E=E₁-E₂=- G M m R + 1 2 ( G M m 7 R )= -14 G M m+G M m 14 R =- 13 G M m 14 R