Johannes Kepler was born poor and sickly in what is now Germany. His father left home when Johannes
was five and never returned. It is believed he was killed in a war. While Johannes was pursuing higher
education his mother was tried as a witch. Johannes hired a legal team which was able to obtain her
release, mostly on legal technicalities.
Although he had an eventful life, Kepler is most remembered for "cracking the code" that
describes the orbits of the planets.
Prior to Kepler's discoveries, the predominate theory of
the solar system was an Earth-centered geometry as described by Ptolemy. A Sun-centered theory
had been proposed by Copernicus, but its predictions were plagued with inaccuracies.
Working in Prague at the Royal Observatory of Denmark, Kepler succeeded by using the notes of his predecessor,
Tycho Brahe, which recorded the precise position of Mars relative to the Sun and Earth.
Kepler developed his laws empirically from observation, as opposed to deriving them
from some fundamental theoretical principles. About 30 years after Kepler died,
Isaac Newton was able to derive Kepler's Laws from basic laws of gravity.
Law 1. The orbits of the planets are ellipses, with the Sun at one focus.
Any ellipse has two geometrical points called the foci (focus for singular).
There is no physical significance of the focus without the Sun but it does have
mathematical significance. The total distance from a planet to each of the foci added together
is always the same regardless of where the planet is in its orbit.
The importance of this is that
by not assuming the orbits are perfect circles, the accuracy of predictions in the Sun-centered theory was
(for the first time) greater than those of the Earth-centered theory.
Law 2. The line joining a planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.
In any given amount of time, 30 days for instance, the planet sweeps out the same amount of area
regardless of which 30 day period you choose. Therefore the planet moves faster when it is nearer the Sun
and slower when it is farther from the Sun.
A planet moves with constantly changing speed as it moves about its orbit.
The fastest a planet moves is at perihelion (closest) and the slowest
is at aphelion (farthest).
Law 3. The square of the total time period (T) of the orbit is proportional to the
cube of the average distance of the planet to the Sun (R).
This law is sometimes referred to as the law of harmonies.
It compares the orbital time period and radius of an orbit of any planet, to those of the other planets.
The discovery Kepler made is that the ratio of the squares of
the revolutionary time periods to the cubes of the average distances from the Sun, is the same for