The force of attraction between two objects with the following formula.
F=g(m1*m2)/d^2
Whereas g is the gravitational constant of the universe. A number so close to one that for this purpose we'll call it one.
m1 and m2 are the mass of the two objects in question. In this case the Earth and the Moon. Multiply those two and divide by the square of the distance (d) between the two objects.
@Jezibaba Thank you for this little mental exercise, it was yummy 😊
Even with out plugging in all the numbers we know the mass of the Earth is several times that of the Moon. So unless the object was very close to the Moon, the Earth is going to win out in this one.
Of course an object directly between the Earth and the Moon wouldn't drop like a rock pushed off a table top. Depending upon it's initial velocity it would end up moving towards the Earth.
/end