# How did newton figure out gravity

## Main Question or Discussion Point

How did Newton arrive at the conclusion that the force of gravity is directly proportional to the product of the masses of two objects, and inversely proportional to the square of their distance?

I know that he was the first to realise it's gravity that keeps the planets in orbit, but what observations enabled him to formulate his law of universal gravitation?

Did he figure out circular motion after he formulated his three laws of motion?

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I think he based his theory on Kepplers laws . And Keppler based his laws on observations made by an astronomer whose name I can never remember.

EL
LENIN said:
And Keppler based his laws on observations made by an astronomer whose name I can never remember.
Tycho Brahe
http://en.wikipedia.org/wiki/Tycho_brahe

Thank you EL.

somebody told me that gravity is not JUST caused by mass, it is caused by motion w/ it, if it would be at rest, it wouldn't have gravity, it is motion that creates the sucking effect. Since everything in this universe is in motion, I guess I can't prove him wrong. Do you guys has something to say about this?

rbj
Teegvin said:
How did Newton arrive at the conclusion that the force of gravity is directly proportional to the product of the masses of two objects, and inversely proportional to the square of their distance?
there are some good philosophical reasons to arrive at that even before the observational evidence. if the gravitational force (toward the center of the Earth) of two grapefruits (bundled together) is twice that of one grapefruit, the graviational force is proportional to $m$. if symmetry of relationship is to hold, then the gravitational force (toward the center of one grapefruit) of two Earths (bundled together) is twice that of one Earth. that makes the graviational force is proportional to $M$.

the inverse-square relationship to spacing $r$ between $M$ and $m$ comes from the concept of flux and equating (proportionately) the field intensity of graviation to flux density which is behind every inverse-square law (such as electrostatics). it comes from the fact that we live in a 3-spacial dimensional reality and that the surface area of any 3-D solid increases proportionally to the square of it's 1-D size. particularly, the surface area of a sphere is $4 \pi r^2$. the total amount flux emanating out of mass $M$ is constant (and proportional to $M$) and is distributed equally among the surface area $4 \pi r^2$ of the sphere of radius $r$ at the distance $r$ from the mass $M$. the flux density is equal to the flux per unit area which is, for the sphere, equal to the total flux divided by the total surface area making it proportional to $M / (r^2)$. that flux density is proportional to field strength and the gravitational field strength is multiplied by $m$ to get the force that is exerted by $M$ on $m$. the only way you satisfy all of this is to say that the force is proportional to $M m / (r^2)$ and the constant of proportionality is simply $G$.

see the wikipedia articles on Flux, Gauss's law, and Inverse-square law. this applies to electrostatics also.

then to tie it together, if the graviational force is proportional to $m$ if $M$ is kept constant, and if it is also proportional to $M$ if $m$ is kept constant, and keeping both $M$ and $m$ constant but seeing that the field strength decreases as $1/r^2$ (because the flux density decreases as $1/(4 \pi r^2)$ and we, as well as Gauss, postulate that field strength is proportional to flux density), the relationship that satisfies all of that is

$$F \propto \frac{Mm}{r^2}$$

Did he figure out circular motion after he formulated his three laws of motion?
and after he invented calculus. you need calculus to derive the acceleration due to circular motion.

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