Question

how did newton guess the inverse square rule

Answer 1

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.

Newton further showed that the gravitational force is proportional to the product of the masses of the two objects. 

Thus, Newton formulated the universal law of gravitation.

Answer 2

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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