The apparent path of Mars in 2005-2006 is shown above. Mars path will be retrograde in Fall 2005.
To account for uneven and retrograde motion in the Ptolemaic system, pre-Copernican astronomers invoked additional circles of motion called epicycles.
Epicycles could add speed to a planets orbit as in the above figure
Or they could induce retrograde motion as above.
Unfortunately, one epicycle was not enough to fit the observations. So astronomers added epicycle upon epicycle (up to 28 in Ptolemy's system) to try to get predicted positions that would agree with the observations. Moreover, some of the epicycles were not centered on previous orbital paths (the "deferent") but were offset. So simplicity was being sacrificed in order to keep "circular" motion alive.
"Nature, and Nature's Laws lay hid in Night,
In the Copernican view, planetary positions as seen from the earth correspond to solar system positions as shown in the figure at left and are referred to by a variety of terms. Opposition, Conjunction, and Elongation refer to how a planet is aligned with the line of site between Earth and Sun. Using these geometries, Copernicus was able to calculate the relative distances of each of the known planets from the Sun. He did remarkably well, as illustrated in the table to the right.
The period of a planet's orbit is the time it takes for it to go around once. The sidereal period is the time it takes to go around once relative to the stars (sidereal refers to the stars). The synoptic period (synoptic refers to taking the same point of view) is the time it takes for the planet to re-appear at an identical configuration as seen from earth (see figure at right).
Tycho Brahe used the parallax effect to show that a newly discovered Supernova was very distant. This same effect led him to believe the Copernican view was incorrect, however! This was because it implied that one should see the nearest stars wobble in position as the Earth moved in its orbit, and Brahe detected no such wobble. Stellar parallax (and the distance to the nearest stars) was not detected until the 19th century. The stars are much further away than anyone imagined in Brahe's day, and this fact makes the parallax effect very small and hard to measure! Currently, the US Naval Observatory Flagstaff Station has the premiere program to measure parallaxes of nearby faint dwarfs.
2) A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
P2 = a 3
At about the time Kepler was working out his laws of planetary motion, Galileo was turning a telescope to the heavens. His observations of Venus showed that the planet's size varied with phase in a way that could not be explained in the Ptolemaic System.
Galileo's observations of Jupiter's Moons showed four satellites orbiting another planet (i.e., not the Earth!) in a manner that obeyed Kepler's laws. This also supported the Copernican system.