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What is the minimum energy required to l...

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

A

`(2GmM)/(3R)`

B

`(GmM)/(2R)`

C

`(GMm)/(3R)`

D

`(5GmM)/(6R)`

Text Solution

Verified by Experts

The correct Answer is:
D
Energy of the satellite on the surface of the planet
`E_1=KE+PE=0+(-"GMm"/R)=-(GMm)/R`
Energy of the satellite in the circular orbit of radius (R + 2R) is
`therefore` Minimum energy required to launch the satellite is :
`DeltaE=E_f-E_i=-(GMm)/(6R)-(-"GMm"/R)=-"GMm"/(6R)+"GMm"/R="5GMm"/"6R"`
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