First slide
Gravitational force and laws
Question

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L . The magnitude of the areal velocity of the planet is:

Moderate
Solution

Assuming SAB a triangle 

 
A=12r2θ dAdt=12r2dθdt dAdt=12r2ω  Now, Angular Momentum, L=Iω=Mr2ω r2ω=LM Thus , dAdt=12LM

 Areal velocity=dAdt=L2M
 

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