A satellite of mass m revolves around the earth in a circular orbit of radius r. Find the angular momentum of the satellite with respect to the centre of the orbit.

Explanation

Angular momentum of the satellite about the centre of the orbit is L = mvr, where , v is the orbital speed of the satellite . For motion in a fixed orbit,
centripetal force = force of attraction due to gravity
`or, (mv^2)/r =(GMm)/(r^2)`
or, `mv^2r=GMm or, (mvr)^2=GMm^2r`
or, `mvr =m sqrt(GMr)`
`therefore L=msqrt(GMr)`.