Wolfram Alpha:

```Kepler's Laws
-------------
Kepler's three laws of planetary motion can be described as follows:

- The path of the planets about the sun is elliptical in shape,
with the center of the sun being located at one focus. (The
Law of Ellipses).

<- Rp -><------- Ra ------->
<- ea -><- ea ->   e = eccentricity
<------ a ----->

.     .
.              .
.                     m = planet
.                        .
perihelion .     Sun     o      +     . aphelion
.                         .
.                     .
.               .
.     .

Ra = a(1 + e)  Rp = a(1 - e)

- An imaginary line drawn from the center of the sun to the center
of the planet will sweep out equal areas in equal intervals of
time. (The Law of Equal Areas). This is an empirical law that
arises from conservation of angular momentum.  When the planet is
closer to the sun, it moves faster, sweeping through a longer
path in a given time.  Thus,

Laphelion = Lperihelion  where L = mvr

Thus,

vaphelionRa = vperihelionRp

- The ratio of the squares of the periods of any two planets is
equal to the ratio of the cubes of their average distances from
the sun. (The Law of Harmonies).  When the eccentricity of the
ellipse is very small the orbits approach circles.  This is the
case for all planets in the solar system except Pluto. Under
these circumstance we can derive the law as follows:

centripetal force = gravitational force

mv2/r = GMm/r2

mrω2 = GMm/r2

ω2 =(2π/T)2 = 4π2/T2

4π2r/T2 = GM/r2

T2 = (4π2/GM)r3

Geosynchronous Orbit (Earth)
----------------------------

T = 86,400 seconds (1 day), M =  5.9736x1024 kg => r = 4.2244 x107 m```