Question

write an expression of angular momentum of a satellite

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Answer 1

Answer:

We are asked about the angular momentum of the satellite with respect to the centre of earth. We know that the equation for angular momentum is given by, →L=r×→p, where 'L' is angular momentum, 'r' is radius and 'p' is momentum.

Answer 2

Given:

A a satellite is revolving around a planet.

To find:

Angular momentum of the satellite ?

Solution:

First of all , let's calculate the orbital velocity of the satellite. For that , we can say that gravitational force between the satellite and the planet provides the centripetal component of circular trajectory.

• Let mass of planet be M, mass of satellite be m and radius of trajectory be r .

$\sf\therefore \: \dfrac{GMm}{ {r}^{2} } = \dfrac{m {v}^{2} }{r}$

$\sf \implies \: v = \sqrt{\dfrac{GM}{r} }$

Now, the angular momentum be L :

$\sf \therefore \: L = mvr$

$\sf \implies \: L = m \times \sqrt{ \dfrac{GM}{r} } \times r$

$\sf \implies \: L = m \times \sqrt{ GMr}$

$\sf \implies \: L = \sqrt{ GM {m}^{2} r}$

So, the final expression is:

$\boxed{ \bf \: L = \sqrt{ GM {m}^{2} r} }$