a particle of mass m moving in a circular orbit of radius r has an angular momentum L about its centre, find the kinetic energy in terms of L, m, r
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The angular momentum of a particle of mass m moving in a circular path of radius r with a constant speed v is given by:
L=mvr.
Here, the satellite acts as a particle because its diameter is negligible compared to the diameter of the orbit. Therefore, its angular momentum about the centre of the orbit can be found by putting v=
r
2GM
as orbital speed of the satellite to obtain
L=m(
r
2GM
)r⇒L=m
2GMr
.
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