  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.
