The Main Problem in Satellite Theory Revisited

Abstract. Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal form of the main problem (J2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given through order four

Estimation of Untracked Geosynchronous Population from Short-Arc Angles-Only Observations

Telescope observations of the geosynchronous regime will observe two basic types of objects --- objects related to geosynchronous earth orbit (GEO) satellites, and objects in highly elliptical geosynchronous transfer orbits (GTO). Because telescopes only measure angular rates, the GTO can occasionally mimic the motion of GEO objects over short arcs. A GEO census based solely on short arc telescope observations may be affected by these ``interlopers''. A census that includes multiple angular rates can get an accurate statistical estimate of the GTO population, and that then can be used to correct the estimate of the geosynchronous earth orbit population

Orbit propagation with Lie transfer maps in the perturbed Kepler problem

The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another

Business Plan for a Sports Organizing Company

This product-based thesis presents a business plan for a sports organizing company in Helsinki, Finland, with a focus on organizing casual 8v8 football games for international young adults. Motivated by personal experience in event management, as well as being an international student in Finland who loves to play sports, the author recognized a lack of affordable, accessible, and low-commitment football activities. The business plan is for investors as well as a guide to implementation. It does not analyze the software development aspects of the business and none of the financial projections involved are finalized but are based off research. The theoretical framework discusses a variety of business theories that support the business plan. These include SWOT, AIDA, customer profiling and more. The structure of the business plan is then outlined with justifications. The research methods used were desktop research, interviews, and personal observation. The business plan outlines the company’s structure, customer segmentation, competitor analysis, marketing strategy, operational setup, and financial projections. The findings suggest good demand, manageable operational logistics, and financial feasibility. While challenges like third-party negotiations, cultural adaptation, and more exist, the plan serves as a satisfactory framework for the business. It will benefit the Helsinki metropolitan area by promoting community, cross-cultural communication, as well as physical and mental wellbeing. Creating this product-based thesis expanded the author’s knowledge on entrepreneurship, business management, and research development, as well as increasing critical thinking skills

Calais, After the Jungle

A short article discussing two projects, the film Calais Then (2016) and Then (2019), and a photo essay, Calais 2019

Design Unlikely Futures in the Jungle (paper)

A paper reflecting on four films made in the Calais Jungle camp

Student Projects for Space Navigation and Guidance

"Space Navigation and Guidance," taught every fall at the University of Maryland, is required of all space track undergraduate aerospace engineering majors. Every student is required to participate in a group project where real observations are used in the solution of a navigation problem with estimation from observations. In this paper, I discuss two such projects, an observatory project in which the students use a telescope to track a satellite and determine its orbit, and a GPS project in which they analyze GPS receiver data to determine the receiver's position

Lie Algebraic Methods for Treating Lattice Parameter Errors in Particle Accelerators

Orbital dynamics in particle accelerators, and ray tracing in light optics, are examples of Hamiltonian systems. The transformation from initial to final phase space coordinates in such systems is a symplectic map. Lie algebraic techniques have been used with great success in the case of idealized systems to represent symplectic maps by Lie transformations. These techniques allow rapid computation in tracking particles while maintaining complete symplecticity, and easy extraction of analytical quantities such as chromaticities and aberrations. Real accelerators differ from ideal ones in a number of ways. Magnetic or electric devices, designed to guide and focus the beam, may be in the wrong place or have the wrong orientation, and they may not have the intended field strengths. The purpose of this dissertation is to extend the Lie algebraic techniques to treat these misplacement, misalignment and mispowering errors. Symplectic maps describing accelerators with errors typically have first-order terms. There are two major aspects to creating a Lie algebraic theory of accelerator errors: creation of appropriate maps and their subsequent manipulation and use. There are several aspects to the manipulation and use of symplectic maps. A first aspect is particle tracking. That is, one must find how particle positions are transformed by a map. A second is concatenation, the combining of several maps into a single map including nonlinear feed-down effects from high-order elements. A third aspect is the computation of the fixed point of a map, and the expansion of a map about its fixed point. For the case of a map representing a full turn in a circular accelerator, the fixed point corresponds to the closed orbit. The creation of a map for an element with errors requires the integration of a Hamiltonian with first-order terms to obtain the corresponding Lie transformation. It also involves a procedure for the complete specification of errors, and the generation of the map for an element with errors from the map of an ideal element. The methods described are expected to be applicable to other electromagnetic systems such as electron microscopes, and also to light optics systems

Comparison Of Accuracy Assessment Techniques For Numerical Integration

See also dissertation of Matt Berry at http://scholar.lib.vt.edu/theses/available/etd-04282004-071227/Knowledge of accuracy of numerical integration is important for composing an overall numerical error budget; in orbit determination and propagation for space surveillance, there is frequently a computation time-accuracy tradeoff that must be balanced. There are several techniques to assess the accuracy of a numerical integrator. In this paper we compare some of those techniques: comparison with two-body results, with step-size halving, with a higher-order integrator, using a reverse test, and with a nearby exactly integrable solution (Zadunaisky's technique). Selection of different kinds of orbits for testing is important, and an RMS error ratio may be constructed to condense results into a compact form. Our results show that step- size halving and higher-order testing give consistent results, that the reverse test does not, and that Zadunaisky's technique performs well with a single-step integrator, but that more work is needed to implement it with a multi-step integrator