Giacomo Acciarini

Recent events, such as the loss of 38 satellites by SpaceX due to a geomagnetic storm have highlighted the importance of having more accurate estimation and prediction of thermospheric density. Solar and geomagnetic activities wield significant influence over the behavior of the thermospheric density, exerting an important impact on spacecraft motion in low-Earth orbit (LEO). The impending Solar Cycle 25's peak arrives at a time when the number of operational satellites in LEO is surging, driven by the proliferation of mega-constellations. This escalating satellite presence, spanning sectors from defense to commercial applications, increases the intricacy of the operational environment. The accuracy of thermospheric neutral density models, which underpin crucial safety-oriented tasks like satellite collision avoidance and space traffic management, is therefore pivotal. While the importance of solar events on thermospheric density is apparent, currently, the influence of the Sun in thermospheric density models is only included in the form of solar proxies (such as F10.7). This can be underwhelming, leading to mispredictions of thermospheric density values. A shared framework that supports the ingestion of inputs from various sources to devise thermospheric density models, and where thermospheric density models can be compared, is currently lacking. Furthermore, the recent advancements in machine learning (ML) offer a unique opportunity to construct thermospheric density models that use these models to describe the relationship between the Sun and the Earth's thermosphere. For this reason, this study introduces an open-source software package, called Karman, to help solve this problem. Essential for this, are three steps: first, the preparation and ingestion of input data from several sources in an ML-readiness fashion. Then, the construction of ML models that can be trained on these datasets. Finally, the creation of a benchmarking platform to compare ML models against state-of-the-art empirical models, evaluating their performances under varying conditions, such as geomagnetic storm strength, altitude, and solar irradiance levels.The utility of this framework is demonstrated through various experiments, showcasing its effectiveness in both benchmarking density models and discerning factors driving thermospheric density variations. The study compares the performance of traditional empirical models (NRLMSISE-00 and JB-08) with machine learning models trained on identical inputs. The results reveal a consistent 20-40\% improvement in accuracy, highlighting the potential of machine learning techniques.One particularly significant area addressed by this research involves the incorporation of additional inputs to refine density estimations. Current approaches rely on solar proxies for estimating the Sun's impact on the thermosphere. However, it is suggested that direct Extreme Ultraviolet (EUV) irradiance data could enhance accuracy. The framework outlined in this paper enables the integration of such inputs, facilitating the validation of hypotheses and supporting the evolution of thermospheric density models.In conclusion, this study presents a comprehensive framework for advancing thermospheric density modeling in the context of LEO satellites. Through the development of neural network models, an extensive dataset, and a benchmarking platform, the paper contributes significantly to the improvement of satellite trajectory predictions. As the space environment becomes increasingly intricate, tools such as the presented framework are crucial for maintaining the safety and effectiveness of satellite operations in LEO.

This paper explores the application of stochastic continuation methods in the context of mission analysis for spacecraft trajectories around libration points in the planar circular restricted three-body problem. Traditional deterministic approaches have limitations in accounting for uncertainties, requiring a two-step process involving Monte Carlo techniques for assessing the robustness of the deterministic design. This might lead to suboptimal solutions and to a long and time-consuming design process. Stochastic continuation methods, which extend numerical continuation techniques to moments of probability density functions, offer a promising alternative. This paper aims to pioneer the application of stochastic continuation procedures in mission analysis, incorporating and acknowledging the stochastic nature of spacecraft missions from the early design phases. By extending existing frameworks to handle fixed points of stroboscopic or Poincaré mappings, the study focuses on robustifying and enhancing trajectory design by considering uncertainties in the determination of periodic orbits. The proposed approach has the potential to discover new solutions that may remain hidden in deterministic analyses, offering improved mission design outcomes. Specifically, this work concentrates on the planar circular restricted three-body problem, assuming uncertainties in both initial conditions and the mass ratio parameter. Stochastic continuation is employed to identify equilibrium points and periodic orbits in this uncertain dynamical system. The generalization of steady states and periodic orbits in uncertain environments is discussed, demonstrating the effectiveness of stochastic continuation in identifying safe operational regions in uncertain astrodynamics problems.

The risk of collisions in Earth’s orbit is growing markedly. In January 2021, SpaceX and OneWeb released an operator-to-operator fact sheet that highlights the critical reliance on conjunction data messages (CDMs) and observations, demonstrating the need for a diverse sensing environment for orbital objects. Recently, the University of Oxford and the University of Surrey developed, in collaboration with Trillium Technologies and the European Space Operations Center, an opensource Python package for modeling the spacecraft collision avoidance process, called Kessler. Such tools can be used for importing/exporting CDMs in their standard format, modeling the current low-Earth orbit (LEO) population and its short-term propagation from a given catalog file, as well as modeling the evolution of conjunction events based on the current population and observation scenarios, hence emulating the CDMs generation process of the Combined Space Operations Center (CSpOC). The model also provides probabilistic programming and ML tools to predict future collision events and to perform Bayesian inference (i.e., optimal use of all available observations). In the framework of a United Kingdom Space Agency-funded project, we analyze and study the impact of megaconstellations and observation models in the collision avoidance process. First, we monitor and report how the estimated collision risk and other quantities at the time of closest approach (e.g. miss distance, uncertainties, etc.) vary, according to different observation models, which emulate different radar observation accuracy. Then, we analyze the impact of future megaconstellations on the number of warnings generated from the increase in the number of conjunctions leading to an increased burden on space operators. FCC licenses were used to identify credible megaconstellation sources to understand how a potential consistent increase in active satellites will impact LEO situational safety. We finally present how our simulations help understand the impact of these future megaconstellations on the current population, and how we can devise better ground observation strategies to quantify future observation needs and reduce the burden on operators.