Revisiting Kepler's Laws of Equal Areas and Ellipses for the Earth

TL;DR

This paper presents simplified geometric and trigonometric derivations of Kepler's law of equal areas for Earth, and analyzes Earth's orbital velocity to explain the elliptical orbit using available data.

Contribution

It introduces more straightforward methods to derive Kepler's law of equal areas and applies data analysis to confirm Earth's elliptical orbit.

Findings

Derived the law of equal areas using simple geometric methods

Analyzed Earth's orbital velocity as a periodic function

Confirmed Earth's elliptical orbit through data analysis

Abstract

Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyze the angular velocity--or the reciprocal of the distance--for the Earth's orbit around the Sun, and can be defined as a periodic function by analyzing the available data, which helps explain the law of ellipses for the Earth.