Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.Comment: 33 pages, 10 figures, 7 tables. Part of the CMDA Topical Collection on "50 years of Celestial Mechanics and Dynamical Astronomy". Comments and feedback are encourage

Orbital Study of MSU CubeSath

The project is an orbital design study of a proposed CubeSat at Mississippi State University. The launch date is not specified. As for the mission, it is defined as forest fire detection. CubeSats are small satellites that are 10 x 10 x 10 cm in dimension and has a mass no more than 1 kg. They are currently used in different applications in many countries as an easy access to space. The analyses of this project have been carried out using a commercial software package, System Tool Kit (STK), developed by Analytical Graphics, Incorporated. This software provides a tool for performing simulations required for determining the orbit or the trajectory for satellites. In addition, a perturbation orbital study has been conducted and different propagators have been tested

Study and comparison of integrators for bodies orbiting the Earth

This Bachelor's thesis aims to study the behavior and performance of different open-source propagators for satellites orbiting the Earth. Analytical, numerical, and semi-analytical techniques have been used to solve the equations of motion governing the orbital dynamics of satellites. The thesis begins by establishing the theoretical framework of propagators, which encloses various aspects such as gravitational and non gravitational perturbations, coordinate systems, and time representations. A detailed investigation of the available open-source propagators is then undertaken preparing proper functions in Python and Matlab to use them. Subsequently, using the DSST propagator, each perturbation is individually evaluated to gain a comprehensive understanding of their specific effects on the satellite orbit, next to identifying the dominant perturbation. Furthermore, a comparison between propagators was conducted to evaluate their performance. The objective was to identify the propagator that not only closely matches the reference values obtained from GMAT but also demonstrates efficient CPU utilization analyzing different satellites orbiting in various altitude regimes. All the programming code created and used to execute the propagators has been grouped and organized making it available alongside the thesis. A README file is also attach to these resources, providing detailed explanations of their implementations, variables, and capabilities. Practical examples are also included to illustrate the usage of each propagator, facilitating a clear understanding of their functionalities and potential applications. This package is designed to enhance the user experience and simplify the integration of these tools into future projects. In conclusion, this Bachelor's thesis examines and compares open-source propagators for Earth-orbiting satellites. The research evaluates perturbations, their effects, and compares the available propagators. The findings provide insights into performance and suitability for accurate orbital dynamics modeling, alongside organized libraries in Python and Matlab

Dynamics of resonances and equilibria of Low Earth Objects

The nearby space surrounding the Earth is densely populated by artificial satellites and instruments, whose orbits are distributed within the Low-Earth-Orbit region (LEO), ranging between 90 and 2 000 $km$ of altitude. As a consequence of collisions and fragmentations, many space debris of different sizes are left in the LEO region. Given the threat raised by the possible damages which a collision of debris can provoke with operational or manned satellites, the study of their dynamics is nowadays mandatory. This work is focused on the existence of equilibria and the dynamics of resonances in LEO. We base our results on a simplified model which includes the geopotential and the atmospheric drag. Using such model, we make a qualitative study of the resonances and the equilibrium positions, including their location and stability. The dissipative effect due to the atmosphere provokes a tidal decay, but we give examples of different behaviors, precisely a straightforward passage through the resonance or rather a temporary capture. We also investigate the effect of the solar cycle which is responsible of fluctuations of the atmospheric density and we analyze the influence of Sun and Moon on LEO objects.Comment: 39 pages, 10 figure

Prediction of the position and velocity of a satellite after many revolutions

Position and velocity prediction method for satellite after many revolution

Guidance, Flight Mechanics and Trajectory Optimization. Volume 9 - General Perturbations Theory

General perturbations theory applications to spacecraft guidance, flight mechanics, and trajectory optimizatio

KAM Torus Orbit Prediction from Two Line Element Sets

A new method for orbit prediction, which is as accurate as numerical methods and as fast as analytical methods, in terms of computational time, is desirable. This paper presents Kolmogorov Arnol\u27d Moser (KAM) torus orbit prediction using Simplified General Perturbations 4 (SGP4) and Two-Line Element (TLE) data. First, a periodic orbit and its Floquet solution is calculated. After that, perturbations, which are on the order of 105 and smaller, are added to the periodic orbit plus Floquet solution. Then, the low eccentricity KAM torus is least squares fitted to the SGP4 and TLE data. The performance of the theory is presented in various ways. The new method is approximately five times more accurate for the best fits and three times more accurate for mean fits comparing to SGP4 and TLE. History of TLEs and KAM torus theory can be used to make accurate orbit predictions, which is conceptually similar to extrapolation. In addition, the new method may rival numerical methods and it can be used for collision avoidance calculations, and formation flight applications. However, high eccentricity, polar and critical inclination, air drag, and resonance problems should be addressed

Tethers in space handbook

The handbook provides a list and description of ongoing tether programs. This includes the joint U.S.-Italy demonstration project, and individual U.S. and Italian studies and demonstration programs. An overview of the current activity level and areas of emphasis in this emerging field is provided. The fundamental physical principles behind the proposed tether applications are addressed. Four basic concepts of gravity gradient, rotation, momentum exchange, and electrodynamics are discussed. Information extracted from literature, which supplements and enhances the tether applications is also presented. A bibliography is appended

Launch window analysis of satellites in high eccentricity or large circular orbits

Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions