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An application of symplectic integration for general relativistic planetary orbitography subject to nongravitational forces
Author  Leary, Joseph; Barriot, JeanPierre; 
Keywords  Parker Data Used; General relativity; Nongravitational forces; Symplectic integration 
Abstract  Spacecraft propagation tools describe the motion of nearEarth objects and interplanetary probes using Newton s theory of gravity supplemented with the approximate general relativistic nbody EinsteinInfeldHoffmann equations of motion. With respect to the general theory of relativity and the longstanding 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 enduser supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between fourvelocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiterlike test particles subject to a radiationlike fourforce. The accuracy of the numerical procedure is maintained using a 5stage, 10$^th$order structurepreserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10$^32$. 
Year of Publication  2021 
Journal  Celestial Mechanics and Dynamical Astronomy 
Volume  133 
Number of Pages  56 
Section  
Date Published  dec 
ISBN  
URL  
DOI  10.1007/s10569021100517 