An application of symplectic integration for general relativistic planetary orbitography subject to non-gravitational forces

Abstract

Spacecraft propagation tools describe the motion of near-Earth objects and interplanetary probes using Newton’s theory of gravity supplemented with the approximate general relativistic n-body Einstein–Infeld–Hoffmann equations of motion. With respect to the general theory of relativity and the long-standing recommendations of the International Astronomical Union for astrometry, celestial mechanics and metrology, we believe modern orbitography software is now reaching its limits in terms of complexity. In this paper, we present the first results of a prototype software titled General Relativistic Accelerometer-based Propagation Environment (GRAPE). We describe the motion of interplanetary probes and spacecraft using extended general relativistic equations of motion which account for non-gravitational forces using end-user supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between four-velocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiter-like test particles subject to a radiation-like four-force. The accuracy of the numerical procedure is maintained using a 5-stage, 10^mathrm{th}-order structure-preserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10^{-32}.