Kepler's Laws

Johannes Kepler found the following three laws by observing the trajectories of the planets in the solar system. These laws are not only valid for planets orbiting around our sun but for all celestial bodies such as the moon or artificial satellites orbiting around the earth or planets in other planetary systems. Even for the movements of stars around black holes, these laws seem to be valid. However, it has to be kept in mind that these formulas require a very small mass of the orbiting object compared to the central body which is approximately the case for most of the planetary systems. The first law is easily understandable by taking a look at the earth orbiting around the sun. Distinguishing this movement from an exact circle is almost impossible because the eccentricity of the ellipse is very small. Nevertheless, faster objects such as asteroids can follow an elliptical trajectory with huge semi-major axes. The second law is not directly obvious and will be proven with the help of the conservation of the angular momentum. The third law is simply an observation by Keppler and will be used to derive Newton's law of gravitation in the following section.