Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally-intensive process. Indeed, it requires the propagation of a grid sampling the whole search space. This work proposes a novel ballistic capture search algorithm based on Taylor differential algebra propagation. This algorithm provides a continuous description of the search space compared to classical grid sampling research and focuses on areas where the nonlinearities are the largest. Macroscopic analyses have been carried out to obtain cartography of large sets of solutions. Two criteria, named consistency and quality, are defined to assess this new algorithm and to compare its performances with classical grid sampling of the search space around Mars. Results show that differential algebra mapping works on large search spaces, and automatic domain splitting captures the dynamical variations on the whole domain successfully. The consistency criterion shows that more than 87% of the search space is guaranteed as accurate, with the quality criterion kept over 80%.Ballistic capture (BC) allows a spacecraft to approach a planet and enter a temporary orbit about it without requiring maneuvers in between. As part of the low-energy transfers, it is a valuable alternative to Keplerian approaches. Exploiting BC grants several benefits in terms of both cost reduction (Belbruno and Miller, 1993) and mission versatility (Belbruno and Carrico, 2000;Topputo and Belbruno, 2015), in general at the cost of longer transfer times (Circi and Teofilatto, 2001;Ivashkin, 2002). In the past, the BC mechanism was used to rescue Hiten (Belbruno and Miller, 1990), and to design insertion trajectories in lunar missions like SMART-1 (Racca et al, 2002) and GRAIL (Chung et al, 2010). In the near future, BepiColombo will exploit BC orbits to be weakly captured by Mercury (Benkhoff et al, 2021;Schuster and Jehn, 2014). BC is an event occurring in extremely rare occasions and requires acquiring a proper state (position and velocity) far away from the target planet (Topputo and Belbruno, 2015). In fact, massive numerical simulations are required to find the specific conditions that support capture (Topputo and Belbruno, 2009) and only approximately 1 out of 10 000 states lead to capture (Luo and Topputo, 2015). In a first effort to reduce the computational burden, the variational theory for

Both the number of man-made objects in space and human ambitions have been growing for the last few decades. This trend causes multiple issues, such as an increasing collision probability, or the necessity to control the space system with high precision. Thus, the need to perform an accurate estimation of the position and velocity of a spacecraft. This article aims at using Taylor Differential Algebra (TDA), an uncertainty propagation method, by implementing an ephemeris propagation tool designed to propagate long term trajectories. It will be used in the case study of Snoopy, the lost lunar module of mission Apollo 10, to explore new scenarios thanks to Monte-Carlo estimations, performed on the data gathered by this propagator.

The return of human space missions to the Moon puts the Earth-Moon system (EMS) at the center of attention. Hence, studying the periodic solutions to the circular restricted three-body problem (CR3BP) is crucial to ease transfer computations, find new solutions, or to better understand these orbits. This work proposes a novel continuation method of periodic families using differential algebra (DA) mapping. We exploit DA with automatic control of the truncation error to represent each family of periodic orbits as a set 2D Taylor polynomial maps. These maps guarantee the access to any point of the family without any numerical propagation, providing a continuous abacus. When applied to the halo family at L 1 and L 2 , the planar Lyapunov at L 1 and L 2 , the distant retrograde orbit (DRO) family, and the butterfly family, we show that the DA-based 2D mapping is asymptotically more efficient than point-wise methods by at least two orders of magnitude, with controlled accuracy. To assist the computation of family

The return of human space missions to the Moon puts the Earth-Moon system (EMS) at the center of attention. Hence, studying the periodic solutions to the circular restricted three-body problem (CR3BP) is crucial to ease transfer computations, find new solutions, or to better understand these orbits. This work proposes a novel continuation method of periodic families using differential algebra (DA) mapping. We exploit DA with automatic control of the truncation error to represent each family of periodic orbits as a set 2D Taylor polynomial maps. These maps guarantee the access to any point of the family without any numerical propagation, providing a continuous abacus. When applied to the halo family at L1 and L2, the planar Lyapunov at L1 and L2, the distant retrograde orbit (DRO) family, and the butterfly family, we show that the DA-based 2D mapping is asymptotically more efficient than point-wise methods by at least two orders of magnitude, with controlled accuracy. To assist the computation of family of periodic orbits, we propose a novel DA-based automatic bifurcation detection algorithm that enables the continuous mapping of the family’s bifurcation criteria. A bifurcation study on the halo L2 shows identical results as point-wise methods while highlighting two undocumented families.