Ellipses

Eccentricity describes the shape of the orbit 

For a closed orbit 0< e< 1 (e=0 is circular). 
 

Kepler's first law 
Planets travel in elliptical orbits with the sun at one of the foci.  The elliptical path is due to the fact that gravity is a central force with an inverse squared power.  (In reality this "law" is more of an assumption- you are fixing the sun and not allowing it to move.  It does move, just not very much.)
 
 
 

Planet	Eccentricity (e)	Semimajor axis a (1010m)	Period T (y)	T2/a3 (10-34 y2/m3)
Mercury1	0.206	5.79	0.241	2.99
Venus	0.007	10.8	0.615	3.00
Earth	0.017	15.0	1.00	2.96
Mars	0.093	22.8	1.88	2.98
Jupiter2	0.049	77.8	11.9	3.01
Saturn2	0.056	143	29.5	2.98
Uranus	0.047	287	84.0	2.98
Neptune	0.009	4.50	165	2.99
Pluto	0.254	590	248	2.99

¹ Too close to the sun for observations.
² Moving too slowly for observations during a 16 year period.
Kepler did not know of the outer planets.
 
 

BTW: No telescopes were used in collecting Brahe's data!  He collected the data so carefully that Kepler was able to discover that planets travel in ellipses, not circles.  (Keep this in mind the next time you're in lab collecting data.)  :-)
 

For our purposes, we can approximate the orbits as being circular.  (This makes life much easier and doesn't sacrifice too much accuracy.)
 

Kepler's Third Law
This is nothing more than Newton's Second Law with gravitational force and centripetal acceleration.

Now substitute in v= 2pR/ T

So,

 
 

We'll examine Kepler's Second Law later, when we discuss angular momentum.