Brahe & Kepler The Final Battle !@$?!!! Yay!!! Yay!!! Geocentric Heliocentric

Ptolemy’s Geocentric Model The Earth was at a point off center called the eccentric. The planet orbits a point in an epicycle. The point follows a path called the deferent. There is another point, called the equant, at which you observe uniform motion. C E

Copernicus’ Heliocentric Model All the heavenly spheres revolve around the Sun. The distance from the Earth to the sphere of Stars is much greater than the distance from the Earth to the Sun. The Earth spins on its axis, which explains the motion of the planets. The motion of the Sun relative to the stars results from the annual revolution of the Earth around the Sun.

Tycho Brahe (1546 - 1601) A brilliant astronomer whose major claim to fame was his ability to make and record extensive observations of the heavens.

Tycho Brahe When Brahe was a child his uncle kidnapped him and supported him. In 1572, made many observations of a supernova. This made him famous.

Tycho Brahe Because of this King Frederick II of Denmark offered Brahe an observatory on the island Hven. Here Brahe began the first comprehensive observational program.

Tycho Brahe Brahe also had a very complicated model of the “universe” In his model the Sun orbited the Earth. The other planets orbited the Sun. His model was not very accurate.

Tycho Brahe Old Tycho had some major personal problems. He had a metal nose because it was cut off in a duel with his friend whose wife he was “involved”.

Tycho Brahe After King Frederick II died, Brahe was asked to leave Denmark and moved to Prague. Ask me how Brahe died.

Tycho Brahe In Prague, Brahe took on an assistant named Johannes Kepler. This was probably the most important thing Brahe did.

Kepler’s Heliocentric Model Kepler used Brahe’s data to develop a model of the Solar System that is mostly correct even today. To do this he applied a condition on his model: That predictions must match observations!

Kepler’s Heliocentric Model Between 1609 and 1618, Kepler developed his three Laws of Planetary Motion. These are still used today !!!!!

Law 1 : The Law of Ellipses The orbit of each planet is an ellipse, with the Sun at one focus. An ellipse is like an oval where the distance from one focus to a point on the ellipse and back to the focus is the same. a1 b1 b2 a2 a1+ b1 = a2 + b2

Law 1: The Law of Ellipses We can tell how close an ellipse is to a circle by its eccentricity (e). The eccentricity (e) is defined as the ratio of the distance from the center of the ellipse to a focus (c) and the distance from the center of the ellipse and the farthest point on the ellipse from the center (a). a The eccentricity of an ellipse is between 0 & 1 since c < a. c = 0 so e = 0 As the foci move towards the center of the ellipse, the ellipse becomes a circle. The eccentricity of a circle is 0.

Law 2 : Law of Equal Areas A line drawn from a planet to the Sun sweeps out equal areas in equal time. What this means : The farther a planet is from the Sun the slower it moves. This law describes the orbit of ONE planet as it orbits the Sun. Faster orbital speed Slower orbital speed

Law 3 : Harmonic Law The square of the orbital period (the time it takes a planet revolve around the Sun one time) of a planet is directly proportional to the cube of the planet’s average distance from the Sun. The planets farther from the Sun take longer to orbit the Sun. (Much weaker than the above statement) This law compares the orbits of TWO planets.  

Where’s the Science ? Gravity Each of these models, from Aristotle to Kepler had one problem in common. None of these models had a CORRECT scientific reason that explains why the Solar System (universe) was structured the way each model described. It took Isaac Newton, with a little help from Galileo, to establish a central force that held the universe (Solar System) together. Gravity