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Newton new the distance between the Moon and the Earth, the radius of the Earth, the period of the Moon around the Earth, the centripetal acceleration of an apple falling from a tree on the Earth and the centripetal accelaration of the moon as it orbited the Earth. He compared this to the distance between the Moon and center of the Earth to the distance between the Apple on the Earth's surface and the Earth's center.
Where the acceleration is the centriptal acceleration supplied by gravity and the distance is the distance between the two bodies' centers.

But Newton's Law is not complete until in 1798 Henry Cavindish, (109 year later,) made the law a mathematical formula by finding exactly how the two side of Newton's law of universal gravity relate to each other.
According to his model the centripetal acceleration of the Moon and apple was caused by the gravitational pull from the Earth. In the third part of this book, Newton shows that he has figured out how the acceleration due to gravity and the distance are related.

The magnitude of this force depends on the product of their masses and the square of the distance between them.

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universal law of gravity worksheet

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