What is the form of a planetary orbit? The astronomers from Ptolemy to Copernicus had a clear (but wrong) answer to this question: A planet moves on a circle or at least on an orbit which can be explained by superposition of circular motions. It was Johannes Kepler who finished with this wrong idea in 1609. After he had analysed the large and precise observational data of Tycho Brahe, he found that the planets orbit on ellipses. The points of an ellipse are characterized by the property that the sum of their distances to the so-called foci is constant.
The following HTML5 app illustrates this law. A planet (blue) can be displaced with pressed mouse button on its orbit around the Sun (red). On the top right of the green panel you can select one of the nine planets or Halley's Comet. In addition, it is possible to investigate the orbit of an imaginary celestial body by entering its semimajor axis and numerical eccentricity (less than 1). The program will calculate the length of the semiminor axis and the current, the minimal and the maximal distance from the Sun. These lengths are given in astronomical units (AU). 1 AU = 1.49597870 × 1011 m is defined as the average distance between Earth and Sun. On the bottom right you can decide whether the elliptical orbit, the axes of the ellipse respectively the connecting lines between the celestial body and the foci (F and F') shall be drawn.