Question

how did newton guess the inverse square rule?​

Answer 1

Answer:

For a uniform circular orbit of radius rr, the acceleration is

a = ω2r,ω = 2πT,(A)(A)a = ω2r,ω = 2πT,

where TT is the orbital period. Comparing eq. (A) with Kepler's third law

T2 ∝ r3,(B)(B)T2 ∝ r3,

we conclude that the gravitational acceleration

a ∝ r−2(C)(C)a ∝ r−2

is proportional to the inverse square distance rr.

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Answer 2

Answer:

Kepler's third law of planetary motion was used by Newton to guess how the force of gravitation of the earth is weakened by distance. ... According to the inverse-square law of gravitaion, the force of gravitation on a planet should decrease as the square of the distance of the planet from the sun.

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