kepler laws

Kepler's First Law or The Law of Ellipses

An ellipse is a closed, curved shape that is defined by two foci

The long one is called the major axis, and the short one is called the minor axis

The shape of an ellipse is measured by its eccentricity

Eccentricity can be from 0 ( a circle) to .95 (almost a line)

While the Earth makes a big circuit each year, the Sun also makes, a very small one, around the Sun-Earth center of gravity.

Kepler's Second Law or The Equal Areas Law

The motion this law describes also tells us that the average distance from a planet to the Sun is equal to the length of the semimajor axis

The line connecting the Sun to a planet sweeps equal areas in equal times.

although the orbit is symmetric, the motion is not. A planet speeds up as it approaches the Sun, gets its greatest velocity when passing closest, then slows down again.

If the orbit were exactly a circle (in which case what we call "long axis would be completely arbitrary, a diameter no different from any other), then by Kepler's 2nd law, the Earth would move at a constant speed and spend equal times in the summer half and the winter half of the year. Actually, it spends about 2 days fewer in the winter half!

But the axis of the Earth moves around a cone, in about 26000 years. In 13,000 years we will be closest to the Sun in midsummer, and climate will get harsher.

Kepler's Third Law: The Harmonic Law

a relation between the time of a planet's orbit and its distance from the Sun:

The squares of the orbital periods of the planets around the Sun are proportional to the cubes of the orbital semimajor axes.

or

P2=a3

Where P is the orbital period in Earth years and a is the length of the semimajor axis (average distance from the Sun) in Astronomical Units.