LECTURE 6: TYCHO AND KEPLER

Key Questions:






TYCHO BRAHE (1546-1601)

Early work:

Extraordinary observations of planetary positions: Cosmological model:






JOHANNES KEPLER (1571-1630)

An enthusiastic Copernican from early on.
Astronomical work motivated by two overarching principles:

First principle could shade into mysticism, to a degree that seems "unscientific" from a modern perspective.
Second principle a modern one, breaking with long tradition (Aristotle through Copernicus) that laws of motion on Earth don't apply to heavens.

Early idea: orbital radii of planets (distances from Sun) determined by a geometry of the five regular polyhedra.
(Modern note: This idea is completely wrong.)
Knew this idea described the data approximately, but committed to testing it with best observations available.
Tycho had the best observations.
Kepler became his research assistant, in 1600. Tycho assigned him problem of detemining orbit of Mars.
Kepler inherited Tycho's position and, more importantly, data, after Tycho's death in 1601.






KEPLER'S PHYSICAL IDEAS








THE ORBIT OF MARS








KEPLER'S LAWS

Kepler's empirical results for motions of planets summarized by three "laws".
These completely replace the epicycles and other complications of the Ptolemaic and Copernican models.

First Law: The orbits of the planets are ellipses with the Sun at one focus.

An ellipse:

Second Law: The line joining the Sun and the planet sweeps out equal areas in equal times.

Third Law: The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.

Define one astronomical unit (AU) to be the semi-major axis of the Earth's orbit.
Third law can be expressed as an equation:

P2 = a3


P = period in years
a = semi-major axis in AU.

Kepler discovered third law 10 years after first two.
Delighted by implied harmony of cosmos.






EVALUATION OF KEPLER'S ACHIEVEMENTS

Results:

Methods:






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Updated: 2005 April 3 [dhw]