The Law of Closest Approach

TL;DR

This paper introduces the Law of Closest Approach, a new principle derived from conic orbit properties that enhances the calculation of orbital eccentricity by utilizing extremal speed and position conditions.

Contribution

It presents a novel law based on orbital mechanics that simplifies and improves eccentricity estimation by leveraging extremal orbital parameters.

Findings

The law states the minimal distance occurs at maximum speed with perpendicular velocity and position vectors.

The ratio of twice the kinetic energy to negative potential energy equals eccentricity plus one.

This law provides a more robust method for calculating orbital eccentricity.

Abstract

In this work, we introduce the Law of Closest Approach which is derived from the properties of conic orbits and can be considered an addendum to the laws of Kepler. It states that on the closest approach, the distance between the objects is minimal and the velocity vector is perpendicular to the position vector with maximum speed. The ratio of twice the kinetic energy to the negative potential energy is equal to the eccentricity plus one. The advantage of this law is that both speed and position are at extremum making the calculation of the eccentricity more robust.