Reestablishing Kepler_s first two laws for planets from the non_stationary Earth

TL;DR

This paper reestablishes Kepler's first two laws for planets by considering Earth's non-stationary motion, using observed angular speeds to derive planetary orbits as exact ellipses through simple mathematical relationships.

Contribution

It introduces a method to derive planetary laws from Earth's moving frame, providing a new perspective on planetary motion analysis.

Findings

Reestablished Kepler's laws considering Earth's motion

Derived planetary orbits as exact ellipses from observed data

Provided a simple mathematical framework for planetary motion analysis

Abstract

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.