Question

There is a moon orbiting an Earth-like planet. The mass of the moon is 5.49 × 1022 kg, the center-to-center separation of the planet and the moon is 2.32 × 105 km, the orbital period of the moon is 21.2 days, and the radius of the moon is 1710 km. What is the angular momentum of the moon about the planet?

Answer 1

To find the angular momentum of the moon about the planet, one must first calculate the moon's orbital velocity using its orbital period, and then use the formula for angular momentum, L = mvr, substituting the calculated velocity and given mass and orbital radius.

Step-by-step explanation:

The student is asking for the calculation of the angular momentum of a moon orbiting an Earth-like planet. To determine the angular momentum, we can use the formula L = mvr, where m is the mass of the moon, v is the orbital velocity, and r is the radius of the orbit (distance between the centers of the planet and the moon).

However, we need the orbital velocity, which can be calculated using the orbital period (T) and the orbit's circumference. The orbital velocity (v) is given by v = 2πr/T. Once the velocity is determined, we plug it back into the angular momentum formula.

The steps are as follows:

1. Convert the orbital period from days to seconds to maintain consistent units (1 day = 86400 s).
2. Calculate the moon's orbital velocity using v = 2πr/T.
3. Finally, calculate the angular momentum using L = mvr.

Note that for all calculations, it's important to convert distances from kilometers to meters to maintain SI units.