The angular momentum of the Earth around the Sun is given by:
[tex]L=m \omega r^2[/tex]
where
m is the Earth's mass
[tex]\omega[/tex] is the Earth's angular velocity
r is the average distance of the Earth from the Sun
The Earth takes 365 days to make a complete revolution around the Sun, which corresponds to
[tex]t=365 d \cdot 24 \cdot 60 \cdot 60 =3.15 \cdot 10^7 s[/tex]
A complete revolution corresponds to [tex]2 \pi rad[/tex], therefore the Earth's angular velocity is
[tex]\omega = \frac{2 \pi rad}{3.15 \cdot 10^7 s}=1.99 \cdot 10^{-7} rad/s [/tex]
The average distance of Earth from the Sun is 149.6 million km:
[tex]r=149.6 Mkm = 149.6 \cdot 10^9 m[/tex]
And the Earth's mass is [tex]m=5.97 \cdot 10^{24} kg[/tex], therefore its angular momentum is
[tex]L=m \omega r^2 =(5.97 \cdot 10^{24} kg)(1.99 \cdot 10^{-7} rad/s)(149.6 \cdot 10^9 m)^2=[/tex]
[tex]=2.66 \cdot 10^{40} kg m^2/s[/tex]
