Question

With the sun at the origin, compute the total angular momentum of the earth, and compare the magnitude of the contributions from the angular momentum of the center of mass and the angular momentum about the center of mass. You can make simplifying assumptions, like that the orbit is circular, that the earth is perfect sphere, etc.

Answer 1

The average distance of the earth from the sun is about 150 million km. Let's call this D.

So,

The angular momentum of the earth has two contributions, one about its center of mass, due to a rotation about its axis, and the other of its center of mass due to its revolution around the sun.

Since we can assume that the earth is a sphere, its moment of inertia about an axis of rotation passing through its center of mass will be

where M= mass of earth = 6X10²⁴ kg and R=radius of earth = 6400km = 6.4X10⁶m.

The angular velocity of earth for rotation about its axis is

and for revolution around the sun, the angular velocity will be

The angular momentum about the center of mass will be

To find the angular momentum about the sun as origin, we need to find the moment of inertia about the sun, so we need to use the parallel axis theorem, so