Kepler's Confirmation(?) of the Mechanical Universe:

Kepler's (1571-1630) laws of Planetary Motion:

Kepler developed, using Tycho Brahe's observations, the first kinematic description of orbits. this description is strictly empirical.

Note: It was crucial to Kepler's method of checking possible orbits against observations that he have an idea of what should be accepted as adequate agreement. From this arises the first explicit use of the concept of observational error.

Kepler used Tycho's precision 20-year data set on Mars(approximately 9 complete orbits of Mars around the Sun)to arrive at this geometric description of the solar system:

• 1st law (law of elliptic orbits): Each planet moves in an elliptical orbit with the Sun at one focus.

Kepler's elliptical orbit for Mars

Note, the actual orbit of Mars deviates from that of a perfect circle by approximately 9% (The earth deviate's by 3%; Venus by less than 1%) so that after many orbits the positional discrepancy between a circular orbit and elliptical orbit is easy to measure. Had the orbit of Mars been nearly circular (like that of the Earth); Kepler would have not discovered his laws.

2nd law (law of equal areas): a line connection the Sun and a planet (called the radius vector) sweeps out equal areas in equal times

A planet must move faster in its orbit when its closer to the sun and slower in its orbit when its farthest from the sun a distance dependent phenomena.

3rd law (law of harmonics): The square of a planet's orbital period is proportional to its mean distance from the Sun cubed.

The 3rd law is used to develop a ``yardstick'' for the Solar System, expressing the distance to all the planets relative to Earth's orbit by just knowing their period (timing how long it takes for them to go around the Sun).

Although successful, Kepler's laws remained a set of empirical rules without a dynamical basis. The link between these laws and the physical world would be established about 50 years later by Isaac Newton (1642-1727).