[Paper Review] Influence of Apophis' spin axis variations on a spacecraft during the 2029 close approach with Earth

S. Aljbaae, J. Souchay+3 more|arXiv (Cornell University)|May 28, 2021

Astro and Planetary Science3 references5 citations

TL;DR

This study investigates the destabilizing effects of Apophis' spin axis variations during its 2029 Earth close encounter on a spacecraft in orbit, using MEGNO, PMap, and Time-Series Prediction to analyze orbital stability. It finds that nearly all orbits become unstable due to Earth's gravitational perturbations, with only a few highly predictable, stable orbits identified via machine learning-based forecasting.

ABSTRACT

Tumbling asteroids belong to a small group of objects, whose angular velocity vector is unaligned with any of its principal axes of inertia. This leads to challenging efforts to model the trajectory of any spacecraft designed to orbit these bodies. In this work, we deepen a previous study on this topic, concerning the asteroid (99942) Apophis during its close encounter with the Earth in 2029. We analyze the orbital behaviour of a spacecraft orbiting the asteroid during this event, by including the effects of the changes of orientation of the spin axis of the asteroid, depending on two sets of initial conditions. The global dynamics of the spacecraft around the target are analyzed using three approaches, MEGNO, PMap, and Time-Series prediction. We confirm that no spacecraft with natural orbits could survive the high perturbations caused by the close encounter with our planet.

Motivation & Objective

• To assess the impact of Apophis' spin axis variations—induced by Earth's gravitational torque—on the orbital dynamics of a spacecraft during the 2029 close encounter.
• To improve upon prior models by incorporating realistic spin state evolution, including changes in obliquity (ε) and precession angle (ψ), based on Souchay et al. (2018).
• To evaluate orbital stability over a 60-day window (43 days before to 16 days after the encounter) under two extreme initial spin state conditions.
• To compare the effectiveness of three dynamical indicators—MEGNO, PMap, and Time-Series Prediction—in identifying stable or chaotic orbital regions.
• To explore the potential of machine learning-based Time-Series Prediction as a novel method for classifying orbital stability based on predictability.

Proposed method

• Adapted the spin state evolution model from Souchay et al. (2018), using classical celestial mechanics to compute changes in Apophis' angular momentum axis due to Earth's tidal potential.
• Employed a 3996-point-mass gravitational model of Apophis derived from polyhedral shape data (Brozović et al., 2018) to accurately represent the asteroid's non-spherical gravity field.
• Conducted 60-day numerical integrations of spacecraft orbits with varying initial semi-major axes (a₀) and eccentricities (e₀), focusing on proximity to the asteroid.
• Applied three stability analysis techniques: MEGNO for chaos detection, PMap (Perturbation Map of type II) for visualizing orbital evolution, and Time-Series Prediction using machine learning to assess orbital predictability.
• Calculated Pearson correlation coefficients to compare the consistency of results across the three methods, validating their reliability and complementarity.
• Used the Time-Series Prediction method to classify orbits based on forecast error, where lower error indicates higher stability and predictability.

Experimental results

Research questions

• RQ1 How do variations in Apophis' spin axis (specifically ε and ψ) during the 2029 Earth flyby affect the long-term stability of a spacecraft in orbit?
• RQ2 What is the extent of orbital disruption caused by Earth's gravitational perturbations on a spacecraft during the close encounter, particularly in comparison to pre-encounter stability?
• RQ3 How do the MEGNO, PMap, and Time-Series Prediction methods compare in identifying stable and chaotic orbital regions around Apophis?
• RQ4 Can machine learning-based Time-Series Prediction effectively identify stable orbits in a highly perturbed dynamical environment like the Apophis-Earth flyby?
• RQ5 Are there any regions of initial orbital elements (a₀, e₀) that remain stable despite the extreme perturbations, and if so, what are their characteristics?

Key findings

• The vast majority of spacecraft orbits become unstable during the 2029 close encounter, with most experiencing either collision with Apophis or escape from its gravitational influence.
• Orbits with initial semi-major axes below 1 km (e.g., a₀ = 0.5 km) are particularly prone to disruption, with one such orbit colliding after only 21 days.
• The PMap method revealed finer-scale orbital distinctions near the asteroid compared to MEGNO and Time-Series Prediction, especially for orbits within 1 km of Apophis.
• A strong positive correlation (Pearson coefficient) was found between PMap and Time-Series Prediction results, indicating consistency in identifying stable and unstable regions.
• Time-Series Prediction successfully identified a set of highly predictable orbits, suggesting they are likely stable, and demonstrated potential as a complementary tool to traditional chaos indicators.
• Despite the high perturbations, a small number of orbits—particularly those with moderate initial semi-major axes—survived the 60-day integration, indicating possible stable regions exist under specific initial conditions.