Reestablishing Kepler_s first two laws for planets from the   non_stationary Earth
  The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the planet_Sun and Earth_Sun distances. The law of equal area for planets can hence be reestablished naturally from the moving Earth using the observed angular speed of a planet over the Sun. Furthermore, for the periodicity of a planet to the Sun, the distance from each planet to the Sun may be expressed as an angular periodic function. By coordinating with the observed data, this periodic distance function depicts an exact elliptical path. Here, we apply relatively simple mathematical skills to illustrate the invariant forms of planetary motions and indicate the key factors used to analyze the motions in complicated planetary systems. 
W. Y. Hsiang, H. C. Chang, H. Yao and P. S. Lee
physics.class-ph