Kepler’s Laws: All Three
Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.
1. Kepler’s Law 1: The Law of Orbits:
All planets move in elliptical orbits, with the sun at one focus.
This is the equation for an ellipse:
2. Kepler’s Law 2: The Law of Areas:
A line that connects a planet to the sun sweeps out equal areas in equal times.
3. Kepler’s Law 3: The Law of Periods:
The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
 Square of any planet’s orbital period (sidereal) is proportional to cube of its mean distance (semimajor axis) from Sun
 Mathematical statement: T = kR^{3/2} , where T = sideral period, and R = semimajor axis
 Example – If a is measured in astronomical units (AU = semimajor axis of Earth’s orbit) and sidereal period in years (Earth’s sidereal period), then the constant k in mathematical expression for Kepler’s third law is equal to 1, and the mathematical relation becomes T^{2} = R^{3}
Learn Kepler’s Laws : Live Classroom Video
Kepler’s laws were derived for orbits around the sun, but they apply to satellite orbits as well.
The Law of Orbits
All planets move in elliptical orbits, with the sun at one focus.
Orbit Eccentricity
The eccentricity of an ellipse can be defined as the ratio of the distance
Examples of Ellipse Eccentricity
Planetary orbit eccentricities

The Law of Areas
A line that connects a planet to the sun sweeps out equal areas in equal times.
This is one of Kepler’s laws.This empirical law discovered by Kepler 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. 
The Law of Periods
The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
Data: Law of Periods
Data confirming Kepler’s Law of Periods comes from measurements of the motion of the planets.
axis (10^{10}m) 
T (y) 
(10^{34}y^{2}/m^{3}) 

Mercury  5.79  0.241  2.99 
Venus  10.8  0.615  3.00 
Earth  15.0  1  2.96 
Mars  22.8  1.88  2.98 
Jupiter  77.8  11.9  3.01 
Saturn  143  29.5  2.98 
Uranus  287  84  2.98 
Neptune  450  165  2.99 
Pluto  590  248  2.99 