(a)

\

The earth is a uniform sphere.

\

The moment of inertia of a solid sphere is $\"image\"$ , where $\"image\"$ is mass of the earth and $\"image\"$ is radius of earth.

\

Earth completes the one complete revolution in $\"image\"$ .

\

The angular velocity of the earth is $\"image\"$ .

\

The angular momentum of the earth is $\"image\"$ .

\

Substitute $\"image\"$ and $\"image\"$ .

\

$\"image\"$

\

$\"image\"$

\

$\"image\"$

\

$\"image\"$

\

$\"image\"$ .

\

The angular momentum of the Earth about its rotation axis is $\"image\"$ .

\

Determine the angular momentum of the Earth in its orbit around the Sun (treat the Earth as a particle orbiting the Sun).

\

(b) \ \

\

The moment of inertia of a solid sphere is $\"image\"$ .

\

The moment of inertia of the earth about the sun is $\"\"$ , where $\"image\"$ is mass of the earth, $\"image\"$ is radius of earth and $\"\"$ is the distance between earth and sun. \ \

\

Earth completes the one complete revolution about the sun in $\"\"$ .

\

The angular velocity of the earth is $\"\"$ .

\

The angular momentum of the earth in its orbit around the sun is $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The angular momentum of the earth in its orbit around the sun is $\"\"$ .