Final answer:
To calculate the total angular momentum of the Earth-Moon system, consider the spins of both the Earth and the Moon on their axes, as well as the orbital angular momentum of the system.
If the Earth's rotation decreases due to tidal drag, the Moon's orbital radius will increase because the decrease in centrifugal force will be greater than the decrease in gravitational force.
Step-by-step explanation:
To calculate the total angular momentum of the Earth-Moon system, we need to consider the spins of both the Earth and the Moon on their axes, as well as the orbital angular momentum of the system.
The total angular momentum of an object is the sum of the angular momenta of its individual components. The angular momentum of an object spinning on its axis is given by the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In the case of the Earth, the angular momentum due to its spin is determined by the moment of inertia and the angular velocity of the Earth. The same applies to the Moon.
The orbital angular momentum of the Earth-Moon system can be calculated using the formula L = mvr, where L is the angular momentum, m is the mass of the Moon, v is its orbital velocity, and r is the distance from the Moon to the center of the Earth.
If the Earth's rotation decreases due to tidal drag, its moment of inertia and angular velocity will change, resulting in a change in its angular momentum. As a result, the total angular momentum of the Earth-Moon system will also change.
The Moon's orbital radius is determined by the balance between gravitational force and centrifugal force. If the Earth's rotation decreases, the Moon's orbital radius will increase because the decrease in centrifugal force will be greater than the decrease in gravitational force.