How did Galileo help us understand orbits?

Answer 1

Galileo made many observations that supported the Sun-centered model of planetary motion. He had the best observing tool in the world at that time, the newly discovered telescope which he improved upon. With these instruments he was able to get considerably more detailed information about the apparent motion of planets and the moons of planets. This work did far more than simply undermine the Earth-centered models. It provided substantially more data to explain, especially data like phases of moons and planets and occultations.

Galileo and Kepler were contemporaries and corresponded, thought Kepler developed his first two laws (1605) before Galileo made his first telescope in 1609. Though Kepler and Galileo were in disagreement over many scientific issues of the time, each was well aware of the theories and observations of the other. There is, for example, specific reference in Kepler's work of the observation of the moons of Jupiter as supporting evidence for his own theories. In addition, Kepler built his own telescope based on Galileo's design and then substantially improved the design. There can be no doubt that some of Galileo's work and theories helped Kepler to complete his three laws on orbits in 1618.

Though Kepler is appropriately credited with arriving at the three laws of planetary motion, the work of Galileo, especially regarding the moons of Jupiter, helped matters along.

Answer 2: In fact Kepler's work was based on the observations of Tycho Brahe, the Danish nobleman who employed him and who had accurate equipment for the measurement of the positions of the planets. Kepler and Galileo corresponded very infrequently, and after a first exchange of letters in 1597 there was no more correspondence between them for twelve years during which time the major part of Kepler's work was completed.

Galileo's observations may have contributed towards Kepler's calculations in a general sense but not in any great detail. Apart from that, Galileo's contribution to science was very broad and significant, particularly his founding of the science of dynamics, but before 1610 everything he wrote was for private circulation. His first public pronouncement on the Copernican system came in 1613.