Revisiting Kepler's Laws of Equal Areas and Ellipses for the Earth
  Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyze the angular velocity--or the reciprocal of the distance--for the Earth's orbit around the Sun, and can be defined as a periodic function by analyzing the available data, which helps explain the law of ellipses for the Earth. 
Wu-Yi Hsiang, Hai-Chau Chang, Herng Yao, Pon-Jen Chen
physics.hist-ph physics.class-ph