Satellite Motion And Angular Momentum

Step 1: Orbital radius

Given:

Step 2: Orbital velocity using gravitational and centripetal force balance

For circular motion, gravitational force provides the centripetal force: Simplifying, we get:

Step 3: Angular momentum of the satellite

The angular momentum of the satellite is:

Step 4: Substituting given values

Satellite mass: Orbital radius: Orbital speed:

Step 5: Substitute into the formula for angular momentum

Simplify:

Step 6: Simplifying the square root

Therefore,

Step 7: Alternative given form of angular momentum

It is given that:

Step 8: Equating both expressions

Cancel and (since both are non-zero):

Step 9: Squaring both sides

Final Answer:

Concept :

• Gravitational force acts as the centripetal force for orbital motion.
• Orbital velocity for a circular orbit: .
• Angular momentum of a satellite: .
• Simplify carefully when combining constants under square roots.