The Moon's Gravitation

Proposition 4 Theorem 4

The moon gravitates towards the earth, and by the force of gravity is continually drawn off from a rectilinear motion, and retained in its orbit.

The mean distance of the moon from the earth in the syzygies in semi-diameters of the earth is:

• 60 to Vendelin and Huygens
• 60 1/2 to Copernicus
• 60 2/5 to Street
• 60 1/2 to Brahe when corrected

One revolution of the moon takes 27d 7h 43'.

• Earth’s circumference is 123,249,600 Paris feet.

If the moon, deprived of all motion, fell to the Earth, it will fall by 15.. Paris feet in a minute.

This is from a calculus, founded either on Prop. 36, Book 1 or (which comes to the same thing) upon Cor. 9, Prop. IV, of the same Book.

This calculus is founded on the hypothesis of the earth’s standing still; for if both earth and moon move about the sun, and at the same time about their common centre of gravity, the distance of the centres of the moon and earth from one another will be 60½ semi-diameters of the earth; as may be found by a computation from Prop. LX, Book I.

Scholium

Assume:

• many moons revolve around the Earth
• the smallest one would be nearest the Earth as to touch the mountaintops

If its centrifugal force stops, then it will fall to the Earth with the same velocity as bodies on mountains.