Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Publication
- Publication Type
Articles 1 - 4 of 4
Full-Text Articles in Astrodynamics
Euler's Three-Body Problem, Sylvio R. Bistafa
Euler's Three-Body Problem, Sylvio R. Bistafa
Euleriana
In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707-1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain …
Formation Flight Of Earth Satellites On Low-Eccentricity Kam Tori, Christopher T. Craft
Formation Flight Of Earth Satellites On Low-Eccentricity Kam Tori, Christopher T. Craft
Theses and Dissertations
The problem of Earth satellite constellation and formation flight is investigated in the context of Kolmogorov-Arnold-Moser (KAM) theory. KAM tori are constructed utilizing Wiesel’s Low-Eccentricity Earth Satellite Theory, allowing numerical representation of the perturbed tori describing Earth orbits acted upon by geopotential perturbations as sets of Fourier series. A maneuvering strategy using the local linearization of the KAM tangent space is developed and applied, demonstrating the ability to maneuver onto and within desired torus surfaces. Constellation and formation design and maintenance on KAM tori are discussed, along with stability and maneuver error concerns. It is shown that placement of satellites …
Orbital Resonances In The Vinti Solution, Laura M. Duffy
Orbital Resonances In The Vinti Solution, Laura M. Duffy
Theses and Dissertations
The Vinti Solution offers a more accurate model than the two-body problem as an orbital propagator. Unfortunately, the Vinti solution contains small divisors near orbital resonances in the perturbative terms of the Hamiltonian, which lead to inaccurate orbital predictions. One approach to avoid the small divisors is to apply transformation theory. The methodology of this research is to identify the perturbative terms of the Vinti Solution, perform a coordinate transformation, and derive the new equations of motion for the Vinti system near orbital resonances. The analysis in this research focuses on the 2:1 resonance, which includes the Global Positioning System. …
Space Object Self-Tracker On-Board Orbit Determination Analysis, Stacie M. Flamos
Space Object Self-Tracker On-Board Orbit Determination Analysis, Stacie M. Flamos
Theses and Dissertations
Due to the United States' growing dependence on space based assets and the in- creasing number of resident space objects (RSO), improvement of Space Situational Awareness (SSA) capabilities is more necessary than ever. As a way to aid in this need, the Air Force Institute of Technology (AFIT) is developing the Space Object Self-Tracker (SOS) as a proof-of-concept experimental satellite for RSO precision tracking and collision avoidance system in Low Earth Orbit (LEO). Specifically, SOS will use Global Positioning System (GPS) position estimates for on-board orbit de- termination. Currently, SOS will use the Simplified General Perturbations-4 (SGP4) algorithm as its …