Non-dimensional Star-Identification

This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This algorithm is particularly suited to complement nominal lost-in-space algorithms, which may identify stars incorrectly when the focal length and/or optical axis offset deviate from their nominal operational ranges. These deviations may be caused, for example, by launch vibrations or thermal variations in orbit. The algorithm performance is compared in terms of accuracy, speed, and robustness to the Pyramid algorithm. These comparisons highlight the clear advantages that a combined approach of these methodologies provides.Comment: 17 pages, 10 figures, 4 table

Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory

This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly provides the osculating evolution of the system under the effects of any order of the zonal harmonics, and can be automated to obtain any level of accuracy in the approximated solution. Moreover, this paper defines a modified set of orbital elements that can be applied to any kind of orbit and that allows the Koopman operator to have a fast convergence. In that regard, several examples of application are included, showing that the proposed methodology can be used in any kind of orbit, including circular, elliptic, parabolic and hyperbolic orbits.Comment: 34 pages, 13 figure

Reliable and Repeatable Transit Through Cislunar Space Using the 2:1 Resonant Spatial Orbit Family

This work focuses on the identification of reliable and repeatable spatial (three-dimensional) trajectories that link the Earth and the Moon. For this purpose, this paper aims to extend the 2:1 resonant prograde family and 2:1 resonant retrograde family to three dimensions and to introduce spatial orbits that are not currently present in the literature. These orbits, named the 2:1 resonant spatial family, bifurcate from the two-dimensional families and smoothly transition between them in phase space. The stability properties of this new family of resonant orbits are discussed, and, interestingly, this family includes marginally stable members. Furthermore, this new family of orbits is applied to several engineering problems in the Earth-Moon system. First, this paper selects an appropriate member of 2:1 resonant spatial family on the basis of its stability properties and relationships with other multibody orbits in the regime. Next, this work combines this trajectory with momentum exchange tethers to transit payloads throughout the system in a reliable and repeatable fashion. Finally, this paper studies the process of aborting a catch and related recovery opportunities.Comment: 33 pages, 31 figure

2D Necklace Flower Constellations

The 2D Necklace Flower Constellation theory is a new design framework based on the 2D Lattice Flower Constellations that allows to expand the possibilities of design while maintaining the number of satellites in the configuration. The methodology presented is a generalization of the 2D Lattice design, where the concept of necklace is introduced in the formulation. This allows to assess the problem of building a constellation in orbit, or the study of the reconfiguration possibilities in a constellation. Moreover, this work includes three counting theorems that allow to know beforehand the number of possible configurations that the theory can provide. This new formulation is especially suited for design and optimization techniques

A Koopman Operator Tutorial with Othogonal Polynomials

The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combination of the eigenfunctions of the system. Coefficients are evaluated via the Galerkin method, using Legendre polynomials as a set of orthogonal basis functions. This tutorial provides a detailed analysis of the Koopman theory, followed by a rigorous explanation of the KO implementation in a computer environment, where a line-by-line description of a MATLAB code solves the Duffing oscillator application.Comment: 22 pages. arXiv admin note: text overlap with arXiv:2110.1211

Corrections on repeating ground-track orbits and their applications in satellite constellation design

The aim of the constellation design model shown in this paper is to generate constellations whose satellites share the same ground-track in a given time, making all the satellites pass over the same points of the Earth surface. The model takes into account a series of orbital perturbations such as the gravitational potential of the Earth, the atmospheric drag, the Sun and the Moon as disturbing third bodies or the solar radiation pressure. It also includes a new numerical method that improves the repeating ground-track property of any given satellite subjected to these perturbations. Moreover, the whole model allows to design constellations with multiple tracks that can be distributed in a minimum number of inertial orbits