In the XVI and XVII centuries, more than 1400 years after Ptolemy, his geocentric model was finally replaced by a much better (and much simpler!) one. The essential steps were due mainly to the contributions from the following four people.
 

  Copernicus: The Foundation

• Nicholas Copernicus (Polish, 1473-1543): Proposed the first modern heliocentric model, motivated by inaccuracies of the Ptolemaic model and based on aesthetic principles – only indirectly on evidence.
• Features of the model: It was still based on circles and epicycles, and was not more accurate than the Ptolemaic model; However, it allowed the calculation of distances to planets in AU, and provided the correct explanation for retrograde motion.
• What happened: Copernicus' model was not widely read or accepted right away, because it is difficult to change established ideas (although it did spark debates, and eventually condemnation by the Catholic church), because of its limitations, and because it did not address some of the better arguments in favor of geocentric models.

Tycho Brahe: The Data

• Tycho Brahe (Danish, 1546-1601): The greatest pre-telescope astronomer; Became famous after observing a (super)nova in 1572 and a comet in 1577, and proving that they were farther than the Moon: Heavens can change! Was given an island on which to build his observatory.
• His Solar System model: Believed in a mixed model, with the Sun and Moon orbiting the Earth (no stellar parallax!); Few people ever believed in it.
• The observations: He made the best and most systematic naked eye observations up to that time, accurate to 1', kept extensive detailed records of them, ... and hired Johannes Kepler as his assistant.

  Galileo: Observations and Response to Aristotle

• Galileo Galilei (Italian, 1564-1642): Introduced the concept of inertia, with which he could address Aristotle's objection to a moving Earth.
• Observations: The first to use telescopes in astronomy (1609) and publish his results; Saw stars in Milky Way (so stars can be so distant that they don't show parallax), features on Moon and Sun (so not all heavenly bodies are perfect), four "little stars" around Jupiter (so another body-and a moving one at that-can have orbiting moons), phases of Venus (a complete set); Why is this important?
• Ideas: He supported the Copernican Model, but was forced to recant. Thought that planets are "worlds," not just dots of light.
• Other observations: He also saw that Saturn sometimes has things sticking out from its sides (like ears), and looked for stellar parallax in Mizar.

Kepler: From Observation to Model of the Solar System

• Johannes Kepler (German, 1571-1630): Started trying to explain Tycho's data on Mars; Ended up developing the empirical model we still accept today for the solar system (basically).
• Laws of planetary motion: Three simple laws, 1. Ellipses: All planets move along ellipses, with the Sun at one focus; 2. Areas: Planets sweep out equal areas around the Sun in equal times (they move faster when closer to the Sun); 3. Periods: The period² is proportional to the distance³.
• [Verification: Helped by 1631 observations of a Mercury transit, and 1655 observations by Giandomenico Cassini of the Sun.]
• Are there other laws? Is there a pattern in the spacings or periods among the planets? Not the way Kepler hoped for, but there are resonances.
• How good are these laws? We now know that they need small corrections, but they hold for any planetary system, any moon around a planet.