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 semi-major axis (a)
is a constant (i.e T2/a3 = constant)
The geometry of an ellipse:
Eccentricity (e) is defined as:
Newton's universal law of gravitation tells us that:
From Newton's Second Law of Motion we get:
Centripetal acceleration (assume circular motion for simplicity):
Taking these three expressions, and simplifying we get the following equation: