# Kepplers first law

## Homework Statement

i am examining a proof of kepplers first law for my conics project and im a bit rusty on the physics, it begins withe the following line

## Homework Equations

To begin with, we will start off by applying Newton's law of motion and Newton's law of universal gravitation together to find that

m a = (-G m M/r^2) r

i think there is an extra r in this equation? if no where does it come from??

here is the link if it helps
http://members.kr.inter.net/joo/physics/curriculum/kepler/proof.html [Broken]

## The Attempt at a Solution

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## Answers and Replies

Kurdt
Staff Emeritus
Science Advisor
Gold Member
The r is in bold which indicates its a vector. So the force of gravity has a magnitude of (-G m M/r^2) along the unit vector r.

thanks, altho the more im looking at this the more i dont understand it,
can anyone explain where the negative comes from?

or if anyone knows of a link to a clearer proof, that would be appreciated also

Kurdt
Staff Emeritus
Science Advisor
Gold Member
The negative is there because the force of gravity is attractive.