Question

write an expression for angular momentum of satelite​

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.

Explanation:

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Answer 2

Answer:

Refer to the attachment for the diagram.

The General formula for calculating the Angular Momentum of a body is given as:

$\boxed{L = m \times v \times r}$

where,

'L' is the Angular Momentum, 'r' is the radius of the circle created by the rotating body and 'v' is the velocity of the body.

According to the diagram, let's assume

Mass of satellite = 'm'

Radius of orbit = 'r'

Mass of Earth = 'M'

We are already aware that,

$\boxed{\text{Orbital Velocity (v_0)} = \sqrt{\dfrac{GM}{r}}}$$\boxed{\text{Orbital Velocity}\: (v_0) = \sqrt{ \dfrac{GM}{r} }}$

Substituting that in the value of 'v' we get,

$\implies L = m \times r \times \sqrt{ \dfrac{GM}{r}}\\\\\\\implies L = m \times \dfrac{r}{\sqrt{r}} \times \sqrt{GM}\\\\\\\implies L = m \times \sqrt{r} \times \sqrt{GM}\\\\\\\implies {\boxed{ \bf{ L = m \times \sqrt{GMr}}}$

Hence the Angular Momentum of Satellite revolving Earth is m √(GMr).