Bifurcation of frozen orbits in a gravity field with zonal harmonics

TL;DR

This paper introduces a methodology to analyze bifurcation sequences of frozen satellite orbits considering higher-order gravitational effects and relativistic corrections, using geometric analysis of normal forms.

Contribution

It develops a novel approach combining normal form analysis and invariants to study bifurcations in complex gravitational models of satellite orbits.

Findings

Identifies bifurcation sequences in augmented gravity models.

Provides a geometric framework for understanding frozen orbit stability.

Enhances prediction accuracy for satellite orbit behavior.

Abstract

We propose a methodology to study the bifurcation sequences of frozen orbits when the 2nd-order fundamental model of the satellite problem is augmented with the contribution of octupolar terms and relativistic corrections. The method is based on the analysis of twice-reduced closed normal forms expressed in terms of suitable combinations of the invariants of the Kepler problem, able to provide a clear geometric view of the problem.