Keplar devised three laws which describe the motions of the planets.

Keplar's First Law

Bodies move around the sun in elliptical orbits, with the sun at one
focus. The other focus is empty.

An ellipse is basically a squashed circle. All bodies orbit in an ellipse, although some are more elliptical than others.

The Earth's average distance from the sun in 150 million km. However, at perihelion* it is 148 million km from the sun, and at aphelion*, 152 million km. THe amount which an ellipse deviates from a perfect circle can be measured by 'eccentricity'. The Earth has an orbital eccentricity of 0.017 which is relatively circlular. Pluto has a much more eccentric orbit, with an eccentricity of 0.25, with perihelion and apthelion of 4400 and 7400 million km respectively.

If you're looking for loads of fun, the easiest way to construct an ellipse is by taking two drawing pins,
sticking them into a piece of paper, wrapping a loose piece of string around them, and then using moving a pencil around the loop, keeping it taught at all
times. With this method the pins represent the two foci.

Keplar's First Law is significant in that most ancient astronomers believed that the planets moved in circular orbits.

Keplars Second Law

The radius vector sweeps out equal areas in equal times.

This states that the line joining the planet to the sun sweeps the same area
in equal times. This means, given Keplar's First Law, that planets orbit
quickest when they are nearest the sun and the radius vector is
smaller, than when they are furthest from the sun.

Keplar's Third Law

The time period squared is directly proportional to the distance cubed.

This neat relationship was discovered by Keplar before Newton worked out what gravity was. Therefore, Keplar was unable to give a proof. However:

Proof:

Fudge 1: Assume the planets have circular orbits

The planets orbit experiencing a centripetal force towards the Sun:

Fc = mv²/r

Where Fc is the centripetal force, m is the planet's mass, r is the planet's distance from the Sun

This centripetal force is provided by the gravitational force of the Sun:

Fg = GMm/r²

Where Fg is the gravitational force from the Sun, G is the Universal gravitational constant and M is the mass of the Sun.

Fg = Fc

=> GMm/r² = mv²/r

Cancelling m:

GM/r² = v²/r --[1]

If the planet moves in a circular orbit, then the distance it moves in a circle is s = 2πr, and velocity in a circle is distance over time => v = 2πr/T

=> v² = 4π²r²/T²

Sub into eqn [1] and cancel r's:

GM/r² = 4π²r/T²

Multiply both sides by T²r²:

GMT² = 4π²r³

=> T² = 4π²/GM x r³

Since 4π²/GM is a constant for any central body (eg, the Sun)

=> T² ∝ r³

So he was right, after all.