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The Earth itself is not stationary but keeps revolving, and its motionfurther satisfies the law of equal area according to the heliocentric doctrine.That satisfaction can be used to construct the mathematical relationshipsbetween the planet_Sun and Earth_Sun distances. The law of equal area forplanets can hence be reestablished naturally from the moving Earth using theobserved angular speed of a planet over the Sun. Furthermore, for theperiodicity of a planet to the Sun, the distance from each planet to the Sunmay be expressed as an angular periodic function. By coordinating with theobserved data, this periodic distance function depicts an exact ellipticalpath. Here, we apply relatively simple mathematical skills to illustrate theinvariant forms of planetary motions and indicate the key factors used toanalyze the motions in complicated planetary systems.

Reestablishing Kepler_s first two laws for planets from the non_stationary Earth