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The additional kinetic energy to be prov...

The additional kinetic energy to be provided to a satellite of mass `m` revolving around a planet of mass `M`, to transfer it forms a circular orbit of radius `R_(1)` to another of radius `R_(2)(R_(2)gtR_(1))` is

A

`GmM((1)/(R_(1)^(2))-(1)/(R_(2)^(2)))`

B

`GmM((1)/(R_(1))-(1)/(R_(2)))`

C

`2GmM((1)/(R_(1))-(1)/(R_(2)))`

D

`(1)/(2)GmM((1)/(R_(1))-(1)/(R_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Total energy of the orbiting satellite of mass m having orbital radius r is
`E=(GMm)/(2r)` where M is the mass of the planet.
Additional kinetic energy required to transfer the satellite from a circular orbit of radius `R_(1)` to another `R_(2)` is `=E_(2)-E_(1)`
`=-(GMm)/(2R_(2))-(-(GMm)/(2R_(1)))=-(GMm)/(2R_(2))+(GMm)/(2R_(1))`
`(GMm)/(2)((1)/(R_(1))-(1)/(2R_(1)))`
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