Keppler's 1st Law: Examining a Proof

[rg057]

Homework Statement

i am examining a proof of kepplers first law for my conics project and I am 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

 

[Kurdt]

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.

 

[rg057]

thanks, altho the more I am looking at this the more i don't understand it,
can anyone explain where the negative comes from?

 

[rg057]

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

 

[Kurdt]

The negative is there because the force of gravity is attractive.