Improved Initial Guesses for Numerical Solutions of Kepler's Equation

TL;DR

This paper introduces new initial guess methods for solving Kepler's Equation, significantly enhancing computational efficiency especially for hyperbolic orbits through symbolic regression and genetic algorithms.

Contribution

It presents novel initial guess formulas derived via symbolic regression and genetic learning, improving the speed of iterative solutions for elliptical and hyperbolic orbits.

Findings

Modest speed improvements for elliptical orbits

Major speed improvements for hyperbolic orbits

Simple implementation of new initial guesses

Abstract

Numerical solutions of Kepler's Equation are critical components of celestial mechanics software, and are often computation hot spots. This work uses symbolic regression and a genetic learning algorithm to find new initial guesses for iterative Kepler solvers for both elliptical and hyperbolic orbits. The new initial guesses are simple to implement, and result in modest speed improvements for elliptical orbits, and major speed improvements for hyperbolic orbits.