Explicit Solution to the Constant Radial Acceleration Problem

TL;DR

This paper presents an explicit, closed-form solution to the long-standing constant radial acceleration problem in orbital mechanics, expressed through Weierstrass elliptic functions, providing new insights and unifying previous results.

Contribution

It introduces the first explicit solution in closed form for the problem, connecting it with elliptic functions and enhancing understanding of its integrability.

Findings

Explicit solution expressed via Weierstrass elliptic functions

Reveals new insights and unifies previous results

Demonstrates the problem's integrability in closed form

Abstract

While the constant radial acceleration problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to a time parameter, has eluded all researchers so far. It is here shown how such a solution exists and is elegantly expressed in terms of the Weierstrass elliptic and related functions. Previously known facts can be derived from the new explicit solution and new insights are revealed.