In this we design a simple and insightful way to achieve Kepler’s first two laws for planets. The
approach is quite different from what we have done for the Earth before. It is because the
planet–Sun distance can be determined only through the Earth–Sun distance in the analysis. By
applying the law of equal areas for the Earth and the observed angular speeds of a planet over the
Sun, the law of equal areas for planets can be re-constructed. 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 easy mathematical skills to illustrate the invariant
forms of planetary motions and indicate the key factors used to analyse the motions in complicated
planetary systems.