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EclipseNETs: a differentiable description of irregular eclipse conditions

Giacomo Acciarini, Francesco Biscani, Dario Izzo

TL;DR

EclipseNETs introduces a differentiable implicit representation to model eclipses cast by irregular small bodies, addressing the non-differentiable and slow nature of traditional ray-tracing approaches in spaceflight mechanics. By encoding the eclipse geometry as a scalar function $F$ learned by SIREN-based networks and conditioning on the Sun direction, the approach enables accurate, fast propagation of orbits under solar radiation pressure. The method is trained on four well-studied bodies (Bennu, Itokawa, 67P, Eros) and demonstrates centimeter-scale accuracy after a few orbits, with inference speeds surpassing vectorized ray-tracing by over two orders of magnitude. This differentiable eclipse model holds promise for efficient mission design and real-time trajectory optimization in irregular-gravity environments, where precise shadow computation is critical for SRP, thermal, and power considerations.

Abstract

In the field of spaceflight mechanics and astrodynamics, determining eclipse regions is a frequent and critical challenge. 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. 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.

EclipseNETs: a differentiable description of irregular eclipse conditions

TL;DR

EclipseNETs introduces a differentiable implicit representation to model eclipses cast by irregular small bodies, addressing the non-differentiable and slow nature of traditional ray-tracing approaches in spaceflight mechanics. By encoding the eclipse geometry as a scalar function learned by SIREN-based networks and conditioning on the Sun direction, the approach enables accurate, fast propagation of orbits under solar radiation pressure. The method is trained on four well-studied bodies (Bennu, Itokawa, 67P, Eros) and demonstrates centimeter-scale accuracy after a few orbits, with inference speeds surpassing vectorized ray-tracing by over two orders of magnitude. This differentiable eclipse model holds promise for efficient mission design and real-time trajectory optimization in irregular-gravity environments, where precise shadow computation is critical for SRP, thermal, and power considerations.

Abstract

In the field of spaceflight mechanics and astrodynamics, determining eclipse regions is a frequent and critical challenge. 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. 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.
Paper Structure (8 sections, 3 equations, 3 figures, 2 tables)

This paper contains 8 sections, 3 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Methods
  4. Eclipse Function
  5. Irregular Bodies
  6. Spacecraft dynamics
  7. Training and dataset creation
  8. Author Contributions

Figures (3)

  • Figure 1: Basic definition of the eclipse function $F_\mathcal{B}$ here introduced and other relevant quantities.
  • Figure 2: On the left three panels: three views of a spacecraft trajectory around Churyumov-Gerasimenko, with initial conditions, and entry and exit eclipse conditions highlighted; on the right panel: error in positional coordinates between a trajectory found computing the silhouette with Möller–Trumbore, against the one found using a neural network.
  • Figure 3: A) 3D model for of Bennu, Churyumov-Gerasimenko, Eros, and Itokawa. B): contour plot of the eclipse function, for a fixed view; C): examples of points where the eclipse function was sampled to construct the training set. D) Predictions of the eclipse for a Sun direction not on the training set. In red, an EclipseNet of 2,369 was used, in blue 50,561 parameters.