According to Newton's law of universal gravitation, any two bodies of masses, m1 and m2, separated by a distance "d" will attract each other with a force, which can be given by the following expression:
Force = Gm1m2/d^2
where G is the universal gravitational constant and has a value of 6.674 x 10^-11 m^3/kg/s^2.
It is this force of gravity which causes Earth and other planets to move around the sun in their respective orbits. And the same force causes the moon to orbit Earth.
Since we know the distances of various planets from the sun and that of the moon from Earth and also the masses of the sun, moon and planets, we can calculate the force of attraction between the sun and the planets, and Earth and the moon.
Gravity is also the reason fruits fall down from the trees and we stay on Earth's surface (instead of being launched into space).
Hope this helps.
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