An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km . From earth's surface to the orbit, the change in total m

Question

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km . From earth's surface to the orbit, the change in total mechanical energy of the ball is x 21 R e ​ GM e ​ m ​ . The value of x is (take R e ​ = 6370 km ) :

TestHub · Accepted Answer

​ h = 318.5 ≈ ( 20 R e ​ ​ ) T ⋅ E i ​ = R e ​ − GM e ​ m ​ T ⋅ E f ​ = 2 ( R e ​ + h ) − GM e ​ m ​ = 2 ( R e ​ + 20 R e ​ ​ ) − GM e ​ m ​ ⇒ T ⋅ E f ​ = 21 R e ​ − 10 GM e ​ m ​ ​ Change in total mechanical energy ​ = TE f ​ − TE i ​ = Re GM e ​ m ​ [ 1 − 21 10 ​ ] = 21 Re 11 GM e ​ m ​ ​

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