Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits

TL;DR

This paper compares optimal coplanar orbital transfers minimizing time versus energy, analyzing the geometric properties of the resulting metrics and their implications for transfer efficiency and convexity.

Contribution

It introduces a qualitative analysis of geodesic flow for time-minimal transfers using Finsler geometry, extending the understanding beyond the energy case.

Findings

Energy optimal transfers form a Riemannian structure with convexity properties.

Time optimal transfers are governed by a non-smooth Finsler metric.

Elliptic domain is proven to be geodesically convex.

Abstract

The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature computations, geodesic convexity), the time minimal case is associated to a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers. In particular we prove geodesic convexity of the elliptic domain.