Final answer:
The center of mass of the Earth-Moon system can be estimated using given information. The Moon does not solely rotate around the Earth. There are mutual gravitational forces between the Moon and Earth.
Step-by-step explanation:
The position of the center of mass of the Earth-Moon system can be estimated using the given information that it is located about 4700 km from the center of the Earth, with a depth of 1690 km below the surface. The center of mass is the point around which the Earth and Moon rotate.
To calculate the acceleration due to the Moon's gravity at that point, the formula for gravitational acceleration is used. The centripetal acceleration of the center of Earth as it rotates about the point can be calculated using the formula for centripetal acceleration.
It is important to note that while the Moon and Earth do rotate about their common center of mass, it is not an accurate approximation to say that the Moon rotates around the Earth, as both bodies exert gravitational forces on each other.