- Modelling & Simulation
- Active Removal/Deflection of Uncooperative Targets
- Orbit and Attitude Estimation and Prediction
- IEEE Computational Intelligence in Aerospace Sciences
- Research Output

This research area forms the basis of every analysis or tool that aims to predict the evolution of the debris environment, the danger of an actual impact with an asteroid, the consequences of a deflection or removal action.

Aaron Rosengren, Fabien Gachet, Ioannis Gkolias

The dynamics of Near-Earth Asteroids (NEO) is strongly chaotic, being affected, by close encounters with major planets. State-of-the-art modelling of asteroidal orbits requires the solution of the *n*‑body problem, including the gravitational interaction of the asteroid with the major planets and the Sun [1]. This problem is known to be non-integrable; the corresponding dynamical behaviour might show regular or chaotic orbits. An accurate description of the asteroidal motion must also include the rotational dynamics in its full generality. The attitude dynamics must be coupled with the orbital motion in order to get a complete picture in a conservative setting first and then considering dissipative effects [2]. A better approximation of the dynamics requires to take into account tiny perturbations of various kinds, including relativistic terms, as well as non-gravitational effects like radiation pressure and the Yarkovsky and YORP effects; these latter, in turn, depend not only on the size and surface properties of the asteroid, but also on its rotation state. Likewise, a fundamental requirement for space debris is the knowledge of their dynamics in different orbital regimes. Many perturbations alter the simple Keplerian motion: higher order terms in the gravity field of the Earth and third-body perturbations, due mainly to the Sun and the Moon, radiation pressure, drag. The theoretical modelling of orbital resonances in Earth orbit is still not complete and, in turns, their correct modelling is extremely important in determining for example the stability and hence the lifetime of several class of orbits. The study of high area-over-mass (HAMR) objects is on-going and requires the correct modelling of the drag and solar radiation pressure coupled with gravity. Also for space debris the coupling between attitude and orbit motion is important and not completely understood.

*Objectives. To develop a coupled model of attitude and orbit for asteroids (single and binaries) and space debris, to study resonances, to study the orbital and attitude dynamics under dissipative effects, to study the combined contribution of gravity, light pressure and other force components for HAMR.*

Aaron Rosengren, Fabien Gachet, Ioannis Gkolias, Davids Amato

For space debris, the analytical theory of orbit propagation developed in the 1960’s under NORAD still forms the basis of the long-term orbit propagation codes commonly used. Fast and accurate orbital propagators are now particularly important to cope with the need of collision avoidance screening and escape procedures, applied to the growing number of objects catalogued and to the increasing accuracy of the sensors. The increasing computer power and development of affordable parallel computing facilities make numerical methods partly viable for these applications [3]. For asteroids, the predictability horizon of the NEA orbit is usually short due to close approaches with the planets. The averaging principle is normally used to compute long term evolutions but the crossings of planets’ orbits produce singularities in the averaged equations of motion and the averaged evolution does not give reliable results. New singularity extraction methods [4] exist but have been implemented and tested only with the planets on circular coplanar orbits. In both cases, if a special perturbation method is used for long-term trajectory prediction, the choice of the propagation model and integration scheme are fundamental. The trajectory propagation via special perturbation can be done using Cowell's, Encke's or the variation of parameters method. VoP methods that are singularity-free and regularised, like the Kustaaheimo-Stiefel and Sperling-Burdet regularizations, are much desired as they lead to an increased accuracy and computing speed. Recent formulations, like DROMO [5] represent a promising solution for both NEO and space debris orbit propagation.

*Objectives. The objective is to explore new special perturbation methods, like DROMO, to study integrators for long term propagation of coupled orbital and attitude motion and to investigate new analytical or semi-analytical theories for NEO’s and space debris.*

As the recent collision between Iridium-33 and Cosmos-2251 dramatically showed, high energetic catastrophic impacts in space are a reality [6]. As a result of the impact, two large clouds of debris were created and are currently orbiting the Earth. The early detection and full characterization of debris clouds in space is one of the main and most demanding tasks for a future Space Situational Awareness sensor network [7]. The global dynamics of debris clouds can, moreover, give way to complex interactions with large space assets, such as the satellite constellations in LEO, which can easily lead to strongly enhanced collision probability for long time spans. Therefore the development of tools and methods for the global characterization of debris clouds, such as orbital distance functions and similarity criteria, become important in the definition of the whole space debris population. In addition, recent work on the evolution of clouds of chipsats under the combined effect of light pressure and gravity, the advances on high-order Taylor series expansions and recent proposals on the use of smart clouds for asteroid deflection suggest some new avenues for research in this area. For example, the dynamics of clouds of HAMR particles is integrable: a partial differential equation can be formulated which describes the global time evolution of the debris cloud in orbital element space.

*Objectives. To advance on the development of tools for global characterization of debris clouds, to investigate the use of new numerical techniques borrowed from fluid dynamics, to investigate the use of high-order expansions, to investigate the use of particle clouds for deflection purposes.*

Collision and impact modelling and simulation are of primary importance in assessing the consequences of an asteroid impact or a satellite collision, and how the impact risk evolves. Existing tools like Space Debris Mitigation long-term analysis program (SDM) or DAMAGE use the NASA Standard breakup model [8] to generate fragmentation debris resulting from explosions and collisions, and allow for a full 3D LEO to GEO simulation of the debris environment including all the main sources and sinks mechanisms influencing the space debris population down to the size of 1 mm. Tools like NEOMiSS [9] makes extensive use of global data to provide useful information across the Earth combining models of the physical effects of a potential NEO impact with historical knowledge of a variety of natural hazards, local building strength and information about the ability to evacuate a threatened region prior to an impact. These tools are fundamental to provide support to decision makers in the evaluation of the damage due to space debris and asteroids.

*Objectives. To extend and integrate these tools with the deflection/removal technologies and control actions developed in WP3 in order to evaluate the consequences of a deflection/removal action.*

The re-entry of single or fragmented objects involves the dependence of the results on various parameters that are difficult or impossible to predict. A probabilistic re-entry model is required that includes estimates of the uncertainties of heat transfer coefficients, emissivity, attitudes, release points, and other factors. The output from such a model would include a probability distribution for the impact footprint and for individual debris pieces of interest. A model incorporating some of these features was developed as part of the review of the Cassini mission re-entry. In that case, estimates were made of component attitude and rates and associated uncertainties during the peak heating phase, and these estimates were combined in an overall probability of survival of critical components. Using Monte-Carlo techniques, the total probability of ground impact can be determined for each surviving component. Total probability of ground impact can be determined and used for casualty expectation calculation. Recent advancement in uncertainty quantification in fluid dynamics suggests the use of DSMC simulations coupled with polynomial chaos (or analogous) uncertainty quantification to compute the aerodynamic forces during re-entry of debris and asteroids.

*Objectives. To investigate advanced CFD techniques for the re-entry of uncontrolled objects under uncertainty, to extend current statistical models for re-entry trajectory and on-ground impact probability.*

Identifying from where particular NEA may have originated is of primary importance to characterized the impactor. The recent availability of new data provides a new opportunity to connect many NEA with their origins. These links would, however, be crucial to test different models of transport from families of asteroids [10], to the known NEA population. If we can estimate the age of a family very accurately, then, by using plausible transport models [11] , we should be able to say what fraction of their members is present in the current NEA population. Knowing the composition of the members of families, one can infer distribution of spectral types of NEA. It is also very interesting to estimate the fraction of binary asteroids which can survive transport from the main belt to the NEA region, and thus, determine their contribution in the whole binary NEO population, which is estimated to represent 15% of the whole NEO population.

*Objectives: To test different models of asteroid transport from the Main belt to NEA population, to identify source locations in the Main belt, to estimate contribution of asteroids that belong to collisional families to the population of objects transported from the Main belt to the region of the terrestrial planets, to perform detailed study of asteroid families, including their dynamical and physical characterizations, to identified possible collisional families among NEA population.*

[1] Valsecchi, Milani, Gronchi and Chesley, Resonant returns to close approaches: Analytical theory, A&A 408, 2003. Milani, et al., Long term impact risk for (101955) 1999 RQ, Icarus 203, 2009.

[2] Celletti, Voyatzis, Regions of stability in rotational dynamics, Cel. Mech. Dyn. Astro. 107(1), 2010.

[3] Deleflie, Rossi, Portmann, Métris, Barlier, Semi-analytical investigations of the long term evolution of the eccentricity of Galileo and GPS-like orbits, Adv. Space. Res. 47, 2011.

[4] Gronchi, Generalized Averaging Principle and Proper Elements for NEAs, Lecture Notes in Physics 590, 2003.

[5] Peláez, Hedo, de Andréz, A special perturbation method in orbital dynamics, Cel. Mech. Dyn. Astro. 97(2), 2007.

[6] Rossi, Valsecchi, Farinella, Risk of collision for constellation satellites, Nature 399, 1999.

[7] Rossi, Valsecchi, Perozzi, Risk of Collision for the Navigation Constellations: Case of the Forthcoming Galileo, J. Astro. Sci. 52, 2004.

[8] Johnson, Krisko, Liou, Anz-Meador, NASA new breakup model of EVOLVE 4.0., Adv. Space Res. 28(9): 1377–1384, 2001

[9] Norlund, Lewis, Atkinson, Guo, NEOMiSS: A near Earth object decision support tool, IAA Planet. Def. Conf., 2011.

[10] Zappala, Cellino, Farinella, Knezevi, Asteroid families: I-Identification by hierarchical clustering and reliability assessment, J. Astro. 100, 1990.

[11] Novakovic, Tsiganis, Knezevic, Chaotic transport and chronology of complex asteroid families, MNRAS 402, 2010.

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