Universal Gravitation
Newton's law of gravitation explains both the behaviour of objects on Earth and the dance of the planets.
Scientists of Newton's day realised that the Moon's orbit could be explained by a force from the Earth pulling on the Moon. However they didn't know what this force might be. Newton suggested that the force pulling on the Moon was the same force pulling a falling apple towards the ground.
Newton calculated that the Earth is pulling on an apple 3600 times stronger than it is pulling on the Moon. But the Earth's surface is 60 times closer to the centre of the Earth than the Moon—and 3600 = 60 x 60. These two 'pulls' could be explained with one force, if that force got weaker the further you got away by the inverse square of the distance.
Newton's equations included Galileo's discovery—all objects fall at the same speed. Gravity is stronger for more massive objects—but more massive objects are harder to speed up. These two effects cancel each other out exactly so all objects accelerate at the same rate under the influence of gravity.
