Kepler's Laws of Planetary Motion

• Uniform Circular Motion

• Kepler's First Law: All planets move about the sun in an elliptical orbit with the sun at one foci. In an elliptical orbit the distance between the planet and the sun is continuously varying:

  

• Keplers Second Law: Equal Areas in Equal Times

  Keplers Third Law: The Harmonic law which is mathematically stated as follows:

  

  In the above P is the orbital period measured in years and A is the semi-major axis measured in units of AU (the distance from the earth to the Sun). This empirical expression sets the scale of the solar system. For instance, if I observe an object to have an orbital period of 8 years then I know that it must have a semi-major axis of 4 AU, by the above expression. This solution is shown below:

Ptolemy's Desperate Attempt

The discovery of retrograde motion in the orbit of mars was a serious challenge to the standard geocentric cosmology which demanded that all the planets orbit the earth in the same direction. While retrograde motion has a natural explanation in a heliocentric cosmology, Ptolmey came up with an elaborate machine to both explain the observed retrograde motion and to keep the earth at the center of the Universe. This mechanism is shown in the movie below - thank goodness the real Universe doesn't work like this!:
• Ptolemy and his silly Epicycles