A satellite of mass `m` is in a circular orbit of radius `r` round the Earth. Calculate its angular momentum with respect to the centre of the orbit in terms of the mass `M` of the Earth and `G`.
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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=sqrt((2GM)/(r ))` as orbital speed of the satellite to obtain `L=m(sqrt((2GM)/(r )))rimpliesL=msqrt(2GMr)`
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