Final answer:
The tidal force Earth exerted on the Moon when it was closer is calculated using Newton's law of universal gravitation and considering the differential gravitational force on the Moon's near and far sides. The closer proximity results in significantly stronger gravitational forces, greatly affecting the Moon's shape and orbit.
Step-by-step explanation:
To calculate the tidal force Earth would have exerted on the Moon shortly after the Moon formed, one must consider the gravitational pull on both the near side and far side of the Moon. The tidal force can be understood as the difference in gravitational forces at these two points.
The force of gravity is given by Newton's law of universal gravitation, F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. Since the Moon would have been at 1/10 of its current distance from Earth, the r in the equation would be much smaller, resulting in a significantly greater force as the force increases inversely with the square of the distance.
Given that gravity is stronger closer to the mass exerting it, the Earth would have a stronger gravitational pull on the side of the Moon that is nearer to Earth compared to the far side. The tidal force on Io is a result of this differential force, which tends to stretch an object along the line of gravitational influence, in the case of the Moon, towards and away from Earth. This also explains why the tidal force contributed to the shaping of the Moon's orbit over time.