Final answer:
The angular momentum of the Moon as it orbits Earth is calculated using the formula L = mvr, with values provided for the Moon's mass, orbital radius, and orbital period. The speed is found by dividing the orbit's circumference by the orbital period, then multiplied by the Moon's mass and radius to obtain angular momentum.
Step-by-step explanation:
The student is asking for the calculation of the angular momentum of the Moon as it orbits around the Earth. In classical physics, the angular momentum (L) of a body in circular orbit is given by the formula L = mvr, where m is the mass of the orbiting body, v is the orbital speed, and r is the radius of the orbit. To calculate the Moon's orbital speed (v), we can use the circumference of the orbit (2πr) and the orbital period (T).
To find v, we divide the circumference by the period:
v = 2πr / T
Using the given values, r = 3.84 x 10⁸ m, and T = 27.3 days (which we convert to seconds by multiplying by 24 hours/day, 60 minutes/hour, and 60 seconds/minute), the calculation would look like this:
v = 2π(3.84 x 10⁸ m) / (27.3 days * 24h/day * 60min/h * 60sec/min)
Now, to find the angular momentum L:
L = mvr = (7.35 x 10²² kg) * v * (3.84 x 10⁸ m)