Question

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​

Answer 1

Answer:

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

.