Differentiable Description of Irregular Eclipse Conditions
Background
Determining eclipse regions is a frequent and critical challenge in astrodynamics. This determination impacts various factors, including the acceleration induced by solar radiation pressure, the spacecraft power input, and its thermal state all of which must be accounted for in various phases of the mission design [1,2,3]. When an object with a high area-to-mass ratio is in motion around small bodies with a weak gravitational potential, the solar radiation pressure can become one of the main perturbing forces, and the precise computation of eclipse conditions becomes essential to have an accurate prediction of their motion and its stability [4,5,6].
Project goals
This study leverages recent advances in neural image processing to develop fully differentiable models of eclipse regions for highly irregular celestial bodies. By utilizing test cases involving Solar System bodies previously visited by spacecraft, such as 433 Eros, 25143 Itokawa, 67P/Churyumov–Gerasimenko, and 101955 Bennu, we propose and study an implicit neural architecture defining the shape of the eclipse cone based on the Sun's direction. Employing periodic activation functions, we achieve high precision in modeling eclipse conditions. Furthermore, we discuss the potential applications of these differentiable models in spaceflight mechanics computations.
In this project, we introduce EclipseNETs [7], a technique to obtain a neural-based implicit representation of cylindrical shadows cast by irregular bodies. This novel approach leverages the latest advances in neural processing of images to model complex geometries in a fully differentiable and computationally efficient manner, enabling highly precise numerical propagation of orbits that include solar radiation pressure effects. Our method builds on recent advances in implicit neural representations, particularly Neural Radiance Fields (NeRFs) and their variants, which have demonstrated remarkable success in capturing intricate details of 3D scenes from 2D images through neural networks trained on photometric consistency [8]. Implicit neural representations, as explored in the works of Sitzmann et al. [9], utilize periodic activation functions to represent high-frequency details and complex shapes implicitly. These implicit representations are particularly well-suited for modeling the shadows cast by celestial bodies because they can accurately and efficiently represent the intricate geometries and dynamics involved.
Our approach integrates these ideas into the domain of orbital dynamics, where traditional methods like ray-tracing are limited by their lack of differentiability and computational inefficiencies. By using neural implicit representations, EclipseNETs can handle the precise calculation of eclipse conditions more robustly. This technique transforms the problem into one that can be efficiently solved with Taylor-based methods, ultimately improving the reliability and accuracy of eclipse event detection during orbital propagation.
References
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Oblate earth eclipse state algorithm for low-earth-orbiting satellites.
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[2] Jia, X., Xu, M., Pan, X. and Mao, X.:
Eclipse prediction algorithms for low-earth-orbiting satellites.
IEEE Transactions on Aerospace and Electronic Systems, 53(6), pp.2963-2975 (2017).
[3] Srivastava, V.K., Kumar, J., Kulshrestha, S., Kushvah, B.S., Bhaskar, M.K., Somesh, S., Roopa, M.V. and Ramakrishna, B.N.:
Eclipse modeling for the Mars orbiter mission.
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[4] Lang, A., Chen, G. and Guo, P.:
Heliotropic orbits at asteroid 99942 Apophis: Considering solar radiation pressure and zonal gravity perturbations.
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[5] Lang, A.:
Spacecraft orbital stability zones around asteroid 99942 Apophis.
Acta Astronautica, 182, pp.251-263 (2021).
[6] McMahon, J.W., Scheeres, D.J., Chesley, S.R., French, A., Brack, D., Farnocchia, D., Takahashi, Y., Rozitis, B., Tricarico, P., Mazarico, E. and Bierhaus, B.:
Dynamical evolution of simulated particles ejected from asteroid Bennu.
Journal of Geophysical Research: Planets, 125(8), p.e2019JE006229 (2021).
[7] Acciarini, G., Biscani, F. and Izzo, D.
EclipseNETs: a differentiable description of irregular eclipse conditions.
Proceedings of the 1st SPAICE Conference on AI in and for Space, 210, (2024).
[8] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R. and Nerf, R.N.:
Representing scenes as neural radiance fields for view synthesis.
Commun. ACM, vol. 65, no. 1, pp. 99–106, https://doi.org/10.1145/3503250 (2021).
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Implicit neural representations with periodic activation functions.
Advances in neural information processing systems, 33, pp.7462-7473 (2020).