John D. Cook • 6/6/2026

From Kepler to Bessel

This article delves into the mathematical relationship between Kepler's equation and Bessel functions. It explains how mean anomaly and eccentric anomaly are related via Kepler's equation in elliptical orbits. The post discusses iterative and Newton's method approaches to solving the equation, then focuses on expanding eccentric anomaly in a sine series. It details the Fourier coefficient calculation, which leads to the integral representation of Bessel functions. The content is technical and mathematical, centered on celestial mechanics and applied mathematics.

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#Numerical Methods #Bessel Functions #Keplers Equation