how did newton guess inverse square rule
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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.
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Newton actually derived his inverse square law from Kepler's third law of planetary motion which states that, “The square of time period of a planet around the sun is directly proportional to the cube of the semi-major axis of the orbit”. ... Which can be stated as, T2∝r3.
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