GRIAL: A High-Fidelity Simulator of Orbital Forces and Torques
Valerio LEVI, Adrián DE ANDRÉS TIRADO, Miguel GUEREÑU MIRA
Abstract. Precise orbit determination (POD) is essential for Earth observation missions and geodetic satellites operations. While current POD systems achieve centimetre-level accuracy, occasional residual discrepancies result from simplified spacecraft geometry models. Considering the true shape of the object, rather than relying on the typical box-wings approximation, can further increase the accuracy of the computation. Moreover, SST applications, such as collision risk assessment or re-entry predictions, can be enhanced by considering the real shape and attitude of space objects. In this regard, tools for attitude propagation and determination of tumbling objects are crucial, and require precise modelling of the torques affecting the satellite. This work presents GMV’s GRIAL, a GPU-powered library for high-fidelity computation of force and torque perturbations acting on the surfaces of space objects of any complex shape in any attitude motion. In particular, the library models perturbations arising from solar radiation pressure (SRP), atmospheric drag, and Earth’s albedo and infrared (IR) radiation. Utilizing the GPU enables highly efficient and precise calculations, allowing the forces and torques to be computed simultaneously at numerous points on the object’s surface, and then summed using the CPU. Moreover, the incorporation of an OpenGL layer in the tool enables shadow casting, that efficiently accounts for the self-shadowing that occurs between different parts of the object, which is particularly significant for convex shaped features or protrusions such as dish antennas or solar arrays.
Keywords
Orbital Forces Modelling, Orbital Torques Modelling, GPU-Powered Approach, In-Parallel Computation, SRP, Drag
Published online 7/20/2026, 22 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Valerio LEVI, Adrián DE ANDRÉS TIRADO, Miguel GUEREÑU MIRA, GRIAL: A High-Fidelity Simulator of Orbital Forces and Torques, Materials Research Proceedings, Vol. 69, pp 972-993, 2026
DOI: https://doi.org/10.21741/9781644904251-171
The article was published as article 171 of the book CEAS – AIDAA Conference 2025
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] T.L. Papanikolaou, GEORB: Release for precise orbit determination of low Earth orbiters and satellite gravity missions, Software Impacts 16 (2023) 100502. https://doi.org/10.1016/j.simpa.2023.100502
[2] B.N.C. Dalton, Orbit/Covariance Estimation and ANalysis (OCEAN).
[3] FocusPOD — GMV. Accessed: Sep. 03, 2024. https://www.gmv.com/en-es/products/space/focuspod
[4] L.I. Zardaín Rodríguez, Developing an efficient algorithm for computing solar radiation pressure, Master’s thesis, Universitat Politècnica de Catalunya, 2019.
[5] S. Tanygin, G. Beatty, GPU-accelerated computation of SRP and drag forces and torques with graphical encoding of surface normals, 2016.
[6] Zardaín, L.: High-Fidelity Modeling and Visualizing of Solar Radiation Pressure: A Framework for High-Fidelity Analysis
[7] Rodríguez, Z., Iván, L.: Developing an efficient algorithm for computing solar radiation pressure. Master’s thesis, Universitat Politècnica de Catalunya (2019). Accessed: Jul. 31, 2024. https://upcommons.upc.edu/handle/2117/176196
[8] S.F.R. Carnà, R. Bevilacqua, High fidelity model for the atmospheric re-entry of CubeSats equipped with the drag de-orbit device, Acta Astronautica 156 (2019) 134–156. https://doi.org/10.1016/j.actaastro.2018.05.049
[9] Smith, B.: A Comprehensive Examination of Low Earth Orbit Aerodynamic Accelerations for Satellite Formation Control (2019). https://doi.org/10.13140/RG.2.2.31390.89922
[10] CERES ERBE-like Time-Interpolated TOA Fluxes Terra and Aqua Crosstrack Edition4. Accessed: Sep. 30, 2024. https://asdc.larc.nasa.gov/project/CERES/CER_ES4_Terra+Aqua_Edition4
[11] A. Kasiri, F. Saberi, Agile multi-targeting spacecraft control via backstepping-sliding mode approach, in: Proceedings of the International Conference on Robotics and Mechatronics (ICRoM), 2019. https://doi.org/10.1109/ICRoM48714.2019.9071889
[12] Lin, H.-Y., Zhao, C.-Y.: Evolution of the rotational motion of space debris acted upon by eddy current torque. Astrophysics and Space Science 357(2), 167 (2015) https://doi.org/10.1007/s10509-015-2396-225
[13] Gómez, N.O., Walker, S.J.I.: Eddy currents applied to de-tumbling of space debris: Analysis and validation of approximate proposed methods. Acta Astro-nautica 114, 34–53 (2015) https://doi.org/10.1016/j.actaastro.2015.04.012
[14] Bergin, C.: Russian Rokot Launches Sentinel-3A. NASASpaceFlight.com. Accessed: Sep. 02, 2024. https://www.nasaspaceflight.com/2016/02/russian-rokot-sentinel-3a-launch/
[15] WMO OSCAR — Satellite: Sentinel-3A. Accessed: Sep. 02, 2024. https://space.oscar.wmo.int/satellites/view/sentinel_3a
[16] S3 Mission. Accessed: Sep. 26, 2024. https://sentiwiki.copernicus.eu/web/s3-mission
[17] Vallado, D.A., Wertz, J.: Fundamentals of Astrodynamics and Applications. Microcosm Press (2013)
[18] A. Vananti, Tumbling motion assessment for space debris objects, Technical report, ESA/ESOC, 2019. ESA/ESOC AO/1-9934/19/D/SR. https://nebula.esa.int/sites/default/files/neb_tec_studies/2745/public/GT17-152GR_EX.pdf
