# How did Newton get Universal Gravity?

Q:
Newton's derived his law of universal gravitation by considering moon and earth , so why we use his law everywhere ?
Karachi, Pakistan
A:

Newton had a few more pieces of data. He knew that Kepler's Third Law for the orbital periods of the planets implied an acceleration toward the Sun given by a fixed constant times 1/R2, where R is the distance. He knew, thanks to solving a tough math problem, that  the same 1/R2 acceleration law would give elliptical orbits with the Sun at one focus- Kepler's Second Law. He knew that all heavy things near Earth's surface accelerate down at about 10 m/s2 (although he didn't use those units). He knew what acceleration the 1/R2 law would imply for the Moon (thanks to solving another math problem for spherical sources), and that that matched the Moon's actual acceleration toward the Earth. He knew that Jupiter's moons were acelerating toward it in a similar fashion. So he had lots of pieces that fit together with the 1/R2 law but not with any other simple law.

If he wanted to fit that acceleration law with his force laws (F=ma and the forces between two objects are equal and opposite) then the only way it would work is to have the acceleration caused by any object be proportional to its mass, m.

It's still a big jump to say that the law applies to everything everywhere. Basic physics has done surprisingly well with making leaps like that when it finds beautiful laws.

Later, of course, it turned out that Newton's gravity law wasn't quite right. It had to be replaced with General Relativity. That's not the sort of alternate law Newton could have possibly considered, since it requires a completely different conception of space and time. When General Relativity in turn gets replaced with something that integrates with quantum mechanics, it probably will require another big leap.

Mike W.

(published on 12/10/2015)

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