Keplers's Equation and Angular Momentum: Historical Perspective, Critical Analysis and Implications for Development of the Orbital Mechanics/Dynamics, Mathematics and Physics

TL;DR

This paper critically examines Kepler's Equation and angular momentum in orbital mechanics, exploring historical development, mathematical implications, and the connection between physical and mathematical continua in advanced dynamics.

Contribution

It provides a historical and critical analysis of Kepler's Equation, questions the derivation of transverse acceleration, and discusses implications for elliptic and symplectic integration methods.

Findings

Questions the existence of transverse acceleration in orbital mechanics.

Highlights implications for elliptic and symplectic integration.

Explores the connection between physical and mathematical continua.

Abstract

After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second ("Area") law, the subsequently -- in course of development of Orbital Mechanics -- to the 2nd law related and formally derived non-existent (zero-valued) transverse acceleration is questioned. Certain implications to Elliptic Integration, Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics/dynamics (with the augmented central and torquing forces) are also briefly hinted to.