Accounting for Solar Radiation Pressure in the Hamiltonian Normal Form of the Elliptic Restricted Three-Body Problem

TL;DR

This paper enhances the Hamiltonian normal form approach for the elliptic restricted three-body problem by incorporating solar radiation pressure, improving the accuracy of trajectory modeling for celestial bodies like the James Webb Space Telescope.

Contribution

It introduces a method to include solar radiation pressure into the Hamiltonian normal form of the elliptic restricted three-body problem, increasing model fidelity.

Findings

Normal forms of elliptic and circular problems are nearly equivalent in trajectory characterization.

Including solar radiation pressure improves the model's fidelity with ephemeris data.

The method enhances the accuracy of dynamical models for space missions.

Abstract

Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration points within the elliptic restricted three-body problem. The circular restricted three-body problem is a special case of the elliptic problem-- one that does not take into account the eccentricity of the true orbits of the primaries and thus provides a dynamical model of varying accuracy depending on the true anomaly of the primaries. This paper first shows that the normal forms of the elliptic problem offer nearly identical trajectory characterization capabilities to those of the circular problem and then demonstrates the difference in fidelity by comparing the circular and elliptic normal form representations of ephemeris data for the James Webb Space Telescope. Furthermore, methodology for including solar radiation pressure within the normal form is introduced, and the same ephemeris data is used to demonstrate the resulting increase in fidelity of the dynamical model.