A satellite of mass m is revolving in an orbit of radius r around a planet of mass m it lost some energy against the work in air resistance
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Velocity Vs of the satellite is given by
GMmsr2s=nsv2srs
vs=(GMrs)−−−−−−−√
KE=12msvs=12ms(GMns)
PE=−GMmsrs
E Total energy =KE+PE-----(1)
=−GMms2rs
Angular momentum
L=msvsrs
=ms(GMrs)1/2rs
=(GMm2srs)1/2
Substituting from (1)
L=(2Emsr2s)1/2
Hence a is the correct answer.
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