What does Kepler's Law state?

What does the law state and what is the equation that is used with this law? Thanks in advance!
Kepler's Laws, three laws concerning the motions of planets formulated by the German astronomer Johannes Kepler early in the 17th century. See Solar System.

Kepler based his laws on planetary data collected by the Danish astronomer Tycho Brahe, to whom he was an assistant. The proposals broke with a centuries-old belief that the planets moved in circular orbits. This was a feature of the Ptolemaic system, advanced by the Alexandrian astronomer Ptolemy in the 2nd century ad, and of the Copernican system, put forward by the Polish astronomer Nicolaus Copernicus, in the 16th century. According to Kepler's first law, the planets orbit the Sun in elliptical paths, with the Sun at one focus of the ellipse. The second law states that the areas described by the straight line joining the centre of the planet and the centre of the Sun are equal for equal time intervals; that is, the closer a planet comes to the Sun, the more rapidly it moves. Kepler's third law states that the ratio of the cube of a planet's mean distance, d, from the Sun to the square of its orbital period, t, is a constant—that is, d3/t2 is the same for all planets.

These laws played an important part in the work of the 17th-century English astronomer, mathematician, and physicist Sir Isaac Newton, and are important for the understanding of the orbital paths of the Moon and of artificial satellites.
Kepler's Law states the following:
1) The orbit of each planet is an ellipse, with the Sun located at one of its foci.

2)A line drawn between the sun and the planet sweeps out equal areas in equal times as the planet orbits the sun.

3)The square of the sideral period of a planet(the time it takes a planet to complete one revolution about the sun relative to the stars) is directly proportional to the cube of the semimajor axis of the planet's orbit.

In terms of the equations of Kepler's law, if you want a rigorous physical treatment, it is too complicated to write here, primarily due the law of ellipses as well as conservation of angular momentum, using polar coordinates.

I hope this has answered your question.


Answers:
Kepler has three laws of planetary motion:

1. The orbit of a planet about a star is an ellipse with the star at one focus.

2. A line joining a planet and its star sweeps out equal areas during equal intervals of time.This is also known as the law of equal areas.

3. The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits. This one has an equation tied to it:

T^2 = xa^3, where T = orbital period of a planet and a = semimajor axis of orbit