Question

Is the angular momentum of a planet conserved as it orbits a star? Explain your answer using torque. Conservation of angular momentum:

The angular momentum of an object or system is conserved whenever the total external torque on the object or system is zero. τ ⃗_ext=0 → ∆L ⃗=0

Answer 1

Yes, angular momentum of a planet is conserved about the star it is orbiting.

Torque = r F sin, where r is position of the point where force is applied relative to the point where force is calculated, F is force and is the angle between r and F.

Consider torque about the star. Only force acting on the planet is the gravitational force due to the star. For this force, r is pointing from the star towards the planet, while force(gravitational ) is pointing towards the star from the planet(because gravitational forces are attractive). So, r and F are pointing opposite to each other and hence,=180 degrees.

So, torque = r*F*sin180 = 0.

Now, according to law of conservation of angular momentum, angular momentum of an object is conserved if no net external torque acts on the object. Here, external torque is 0. So, angular momentum is conserved.