Kepler's laws were originally developed to describe the motion of planetary bodies, but
they are just as relevant for theoretical satellite orbits around the earth.
 Each planet moves around the sun in a ellipse with the sun at one focus (i.e motion is
in a plane).
 A line from the sun to a planet (radius vector) sweeps out equal areas in equal
intervals of time.
 The ratio of the square of the orbit period (T) to the cube of the semimajor axis (a)
is a constant (i.e T^{2}/a^{3} = constant)
The geometry of an ellipse:
and: c^{2}=a^{2}b^{2}
Eccentricity (e) is defined as:
e^{2}=1(b/a)^{2}
Newton's universal law of gravitation tells us that:
F=(G.M.m)/r^{2}
From Newton's Second Law of Motion we get:
F=m.a
Centripetal acceleration (assume circular motion for simplicity):
a=v^{2}/r
Taking these three expressions, and simplifying we get the following equation:
v=(G.M/r)^{0.5}
i.e ω=(G.M/r^{3})^{0.5}
