Newton´s derivation of Gravity´s law

[mprm86]

How did Newton come to his gravity´s law? Could someone please explain his deduction of the law, or he just said: the force exerted by gravity between two planets is F = -Gm1m2r^-2 ?

Thanks in advance.

 

[Chi Meson]

Newton's first assumption was that the same law that governs falling objects on Earth must also govern objects going around the Earth (as opposed to a different set of rules for planetary objects).

It was a short leap for him to realize that the Earth's gravity could be acting as a centripetal force. The trick was guessing at the proportionality. Obviously, the bigger the object, the more it weighed, but his insight was that the force of gravity must depend on the mass of two objects. The product of the two masses made more sense than the sum, so he investigated that relationship. Also, the force must get weaker as the distance increases. Following the rule for the intensity of light, he assumed an inverse-square proportionality. Newton realized that a constant of proportionality was needed, but he never knew what "G" would be.

He took his assumptions and checked it out regarding the motion of the Moon around the earth. THe data did not support his hypothesis, so he put his theory away for 20 years. Later, better data was measured, and he rechecked his prediction and this time it turned out correct.

So it was the scientific process that got him there: an assumption, an insight, a hypothesis, a prediction, and a validation. That's pretty much what everyone does (other than those who accidentally stumble into a discovery).

 

[Adrian Baker]

Don't forget Kepler's earlier Laws of Planetary motion. Newton would have been aware of these and this too would have helped him. Particularly so the relationship - Time period of planet squared is proportional to distance of planet cubed.

 

[Chi Meson]

Don't forget Kepler's earlier Laws of Planetary motion. Newton would have been aware of these and this too would have helped him. Particularly so the relationship - Time period of planet squared is proportional to distance of planet cubed.

Yes, that's right, the "shoulders of giants" and all. Newton was already aware of the geometrical aspects of planetary motion (thanks to Keppler). This allowed him to know what sort of calculations to do to make his predictions. Sadly, Keppler did not have the advantage of knowing Newton's laws of motion and was still under the dillusion* that there must be a propelling force in the direction of motion for all planets. Poor guy!

* edit: I guess this word is a combination of "disillusion" and "delusion"