Half of the major axis is termed a semi-major axis. The third property of an ellipse: the longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis. Each ellipse has an eccentricity with a value between zero, a circle, and one, essentially a flat line, technically called a parabola. The flatter the ellipse, the more eccentric it is. The second property of an ellipse: the amount of flattening of the ellipse is called the eccentricity. The sum of the distances to the foci from any point on the ellipse is always a constant. The first property of an ellipse: an ellipse is defined by two points, each called a focus, and together called foci. Since the orbits of the planets are ellipses, let us review three basic properties of ellipses. Thus, in a twist of irony, Brahe unwittingly gave Kepler the very part of his data that would enable Kepler to formulate the correct theory of the solar system, banishing Brahe's own theory. But the reason Mars' orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.Īfter much struggling, Kepler was forced to an eventual realization that the orbits of the planets are not circles, but were instead the elongated or flattened circles that geometers call ellipses, and the particular difficulties Brahe hand with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which Brahe had extensive data. As it turned out, Kepler, unlike Brahe, believed firmly in the Copernican model of the solar system known as heliocentric, which correctly placed the Sun at its center. Based on this model, the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits the earth. It is believed that part of the motivation for giving the Mars problem to Kepler was Brahe's hope that its difficulty would occupy Kepler while Brahe worked to perfect his own theory of the solar system, which was based on a geocentric model, where the earth is the center of the solar system. He set Kepler, the task of understanding the orbit of the planet Mars, the movement of which fit problematically into the universe as described by Aristotle and Ptolemy. He, therefore, led Kepler to see only part of his voluminous planetary data. However, Brahe mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day. Tycho Brahe is credited with the most accurate astronomical observations of his time and was impressed with the studies of Kepler during an earlier meeting.

Due to religious and political difficulties common during that era, Kepler was banished from Graz on August 2nd, 1600.įortunately, an opportunity to work as an assistant for the famous astronomer Tycho Brahe presented itself and the young Kepler moved his family from Graz 300 miles across the Danube River to Brahe's home in Prague.

Kepler lived in Graz, Austria during the tumultuous early 17th century. The story of our greater understanding of planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler. The planets orbit the Sun in a counterclockwise direction as viewed from above the Sun's north pole, and the planets' orbits all are aligned to what astronomers call the ecliptic plane. They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet’s orbital period is proportional to the size of its orbit (its semi-major axis).Įxplore the process that Johannes Kepler undertook when he formulated his three laws of planetary motion. Kepler's three laws describe how planetary bodies orbit the Sun.

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