Find the angular momentum of the earth
(a) about the sun due to its orbital motion and
(b) about its axis due to its spinning motion.

Explanation

(`a`)
`r`: distance between the sun and the earth
`M_(e)`: mass of the earth
`omega`: angular speed of the earth about the sun
`omega=(2pi)/(T)`, `T=365 days`
Orbital angular momentum is
`M_(e)vr=M_(e)(romega)r=M_(e)r^(2)omega`

`R_(e)`: radius of the earth
Moment of inertia of the earth about its axis
`I=(2)/(5)M_(e)R_(e)^(2)`
Angular velocity of the earth about its axis
`omega^(t)=(2pi)/(T')`, `T'=24h`
Spin angular momentum `=Iomega'=(2)/(5)M_(e)R_(e)^(2)omega`