Do not worry about your difficulties in mathematics, I assure you that mine are greater.
Johannes Kepler's Astronomia Nova
The title page of Johannes Keplers Astronomia Nova, published in 1609, is shown in Figure 1. In translation, the full title reads, New Astronomy Based upon Causes, or Celestial Physics, Treated by Means of Commentaries on the Motion of the Star Mars, from Observations of Tycho Brahe, Gent. Thus, using Tycho Brahes data, Kepler focused his work on the orbit of Mars. His ten-year investigation led him to conclude that the orbit of Mars was not a circle but another conic section, an ellipse. In Astronomia Nova, he substantiated and formulated the first two of his laws of planetary motion. Keplers First Law of Planetary Motion asserts that each planet orbits the sun on an elliptical path, with the sun serving as one focus of the ellipse.
Figure 1: Title page of Johannes Keplers Astronomia Nova (1609)
Figure 2. Page 132 of Astronomia Nova contains a discussion and comparison of planetary motion according to the models derived by Ptolemy, Copernicus, and Brahe.
Figure 3. This sketch from Astronomia Nova offers one explanation for the apparent retrograde motion of the planet Mars when it is viewed from Earth. Specifically, it shows the path of Mars from the year 1580 (marked just to the right of center) to the year 1596 (at left, near the 10 oclock position) according to Ptolemys model.
For a modern explanation of the apparent retrograde motion of Mars and other planets in our solar system when viewed from Earth, see the animation, Retrograde Motion in the Copernican System, at the University of Tennessees website for Astronomy 161: The Solar System.
For selections from Keplers Astronomia Nova in English, see Selections from Keplers Astronomia Nova, selected, translated, and annotated by William H. Donahue, Green Lion Press, Santa Fe, New Mexico, 2004.
For more about Keplers Astronomia Nova, see The Composition of Kepler's Astronomia Nova, by James R. Voelkel, Princeton University Press, 2001.