Newton's gravitational drill process

Newton, after some mathematical calculus, calculated gravitational F from the speed of the moon in the celestial body. So what formula did he use to calculate step by step?

First of all, the speed at which he travels around the Earth from the Moon divides the circumference of his orbit around the Earth by its orbit around the Earth as follows by an algebraic formula:

V月=2πr/T

Here 2πr is the circumference of the Moon around the Earth, r is the orbital radius, and T is its lunar cycle around the Earth.

On this basis, the centripetal acceleration of the Moon is obtained, that is, the square of the speed of the Moon's flight around the Earth is divided by its orbital radius. Its algebraic formula is:

a月=(V月)²/r

The Moon is known to have an orbital period of 27.3 days and the Moon orbits the Earth at a speed of 3.8X100000000 m/s

Solution based on known data: a month = 0.0027m/s²

Applied to the gravitational pull of the apple landing, its acceleration a is equal to the free-fall acceleration, a=9.8m/s², since its own weight is negligible relative to the Earth.

From the above conclusions, the gravitational acceleration relationship between Apple and the Moon can be derived from Kepler's three laws, and finally the following is obtained:

F=GMm/r²

That is, objects are attractive to each other, and the magnitude of this force is only related to their respective masses and the distance between them, which is the famous law of universal gravitation.

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