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Precise orbit propagation for space debris objects using the Hermite integration scheme

Rodmann, Jens and Hampf, Daniel and Hasenohr, Thomas and Humbert, Leif and Riede, Wolfgang and Sproll, Fabian and Wagner, Paul (2017) Precise orbit propagation for space debris objects using the Hermite integration scheme. SEVENTH EUROPEAN CONFERENCE ON SPACE DEBRIS, 18.-21. Apr. 2017, Darmstadt, Deutschland.

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DLR's Institute of Technical Physics is actively developing laser-based optical tracking methods to determine 3D positions of LEO space debris objects to within a few metres. For Space Situational Awareness applications like collision avoidance or re-entry analyses, any initial high-precision orbit needs to be propagated, taking into account the various gravitational and non-gravitational forces perturbing the object's orbit. A key prerequisite for that is an accurate, fast, and versatile integration method allowing the prediction of trajectories from initial conditions. We will introduce a numerical integration technique based on the Hermite scheme, a self-starting, implicite predictor-corrector method originally developed and widely used for gravitational N-body systems. The Hermite scheme takes the acceleration and its first time derivative (also known as jerk) to predict future position and velocity vectors from previous values. The gist and beauty of the method relies on the fact that the second and third derivatives (sometimes called snap and crackle, respectively) can be explicitely calculated from the acceleration and jerk alone. These are then used iteratively to correct the object's state vector, yielding an integration method with fourth-order global error. The method can be used with constant or variable timesteps. For constant timesteps the Hermite integrator is time-symmetric, and shows no secular error in the semi-major axis and eccentricity. The code can integrate a large number of objects in parallel, with either shared or individual timesteps. This can be applied for predicting future states of a catalogue of space objects, or to propagate an object's state uncertainty (covariance) in a realistic manner. We will show first results from our orbit propagator development. The implementation of various physical models describing the gravitational and non-gravitational perturbations will be discussed.

Item URL in elib:https://elib.dlr.de/117680/
Document Type:Conference or Workshop Item (Poster)
Title:Precise orbit propagation for space debris objects using the Hermite integration scheme
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Rodmann, JensJens.Rodmann (at) dlr.deUNSPECIFIED
Hampf, DanielDaniel.Hampf (at) dlr.deUNSPECIFIED
Hasenohr, ThomasThomas.Hasenohr (at) dlr.deUNSPECIFIED
Humbert, Leifleif.humbert (at) dlr.deUNSPECIFIED
Riede, WolfgangWolfgang.Riede (at) dlr.deUNSPECIFIED
Sproll, FabianFabian.Sproll (at) dlr.deUNSPECIFIED
Wagner, PaulPaul.Wagner (at) dlr.deUNSPECIFIED
Date:April 2017
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Keywords:space debris; astrodynamics; numerical integration method
Event Location:Darmstadt, Deutschland
Event Type:international Conference
Event Dates:18.-21. Apr. 2017
Organizer:European Space Agency (ESA)
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben Einsatz von Lasern zur Detektion von Weltraumschrott
Location: Stuttgart
Institutes and Institutions:Institute of Technical Physics > Active Optical Systems
Deposited By: Rodmann, Jens
Deposited On:08 Jan 2018 10:07
Last Modified:08 Jan 2018 10:07

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