Characterizing Planetary Orbits and the Trajectories of Light

TL;DR

This paper derives exact analytic formulas for planetary and light trajectories in Schwarzschild spacetime, introduces a new parameter space to classify orbits, and discusses potential extensions to Kerr geometry.

Contribution

It presents a novel parameter space for classifying all possible planetary orbits in Schwarzschild geometry and defines clear boundaries for different orbit types.

Findings

Defined regions in parameter space for orbit characteristics

Established direct links between observational data and parameter space points

Outlined potential extension to Kerr geometry

Abstract

Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.