Calculate the magnitude of the Earth's translational (orbital) angular momentum relative to the Sun when the Earth is at location A and when the Earth is at location B as displayed in the representation of the situation in the representations. The mass of the Earth is $6$ x $10^{24}kg$ and its distance from the Sun is $1.5$ x $10^{11}m$.

The Earth makes one complete orbit of the Sun in 1 year, so its average speed is:

$v = \frac{2\pi(1.5 \times 10^{11}m)}{(365)(24)(60)(60)s} = 3.0 \times 10^4 m/s$

At location A

$\vec{p} = \langle 0, 6 \times 10^{24}kg \cdot 3.0 \times 10^{4} m/s, 0 \rangle$

$\vec{p} = \langle 0, 1.8 \times 10^{29}, 0 \rangle kg \cdot m/s$

$\mid\vec{p}\mid = 1.8 \times 10^{29} kg \cdot m/s$

$\mid\vec{L}_{trans,Sun}\mid = (1.5 \times 10^{11} m)(1.8 \times 10^{29} kg \cdot m/s) sin 90^{\circ}$

$\mid\vec{L}_{trans,Sun}\mid = 2.7 \times 10^{40} kg \cdot m^2/s$