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Initial orbit determination methods yield only a point solution, with no information about the quality of or confidence in the solution. However, probabilistic information may be inferred directly from the initial orbit determination process, given measurement uncertainty characteristics. A state uncertainty estimate is derived directly from Gauss's angles-only initial orbit determination method using a novel technique based on sigma points. This method is tested across a range of simulated orbit types and observation geometries. Comparisons with a standard least-squares-based approach are made, and the direct uncertainty estimates are shown to be more realistic than the least-squares estimates. The state and uncertainty estimates from this method are also shown to be suitable to initialize an unscented Kalman filter for processing further measurements. [ABSTRACT FROM AUTHOR]

Relative motion of one satellite about another in circular orbit, where the two objects have the same semimajor axis, is periodic in the linearized approximation. A set of orbital elements, the geometric relative orbital elements, which are an exact geometric analogy to the classical orbital elements, can be defined. The relative orbit is manifestly seen to be an ellipse or circle in apocentral coordinates, analogous to perifocal coordinates in inertial motion and different from the local-vertical local-horizontal Cartesian coordinates customarily used for analysis of relative motion problems. These provide a way to do relative motion trajectory design and guidance that stands in contrast to the use of Cartesian coordinates. Algorithms are presented for computing the delta-r and timing for impulsive maneuvers to change a single element: two that change the plane and one that changes the size of the relative orbit. The change in size is a two-maneuver transfer and uses the solution of the three-point periodic boundary value problem, also solved and presented here. This solution permits the direct computation, with no iteration or searching, of the periodic relative orbit that connects two points. Optimization to minimize fuel use can be done with a one-dimensional search. [ABSTRACT FROM AUTHOR]

Tungsten dust used as an artificial atmosphere to aid in deorbiting of space debris should be deployed soon after a fragmentation to be effective, before the delta- v imparted to each fragment and orbit perturbations spreads the debris so far apart that an unpractically large amount of dust must be used. Maneuvering a spacecraft carrying a sufficient amount of dust and launched in advance of need is one way of reaching the target region quickly; the question addressed here is whether a significant fraction of possible fragmentations can be reached with a vehicle with a realistic fuel capacity. Lambert targeting is computed to reach the point of need at the correct elapsed time from the dispatch time and place. The time delay may be varied above some presumed minimum needed for fragmentation detection, communication, and maneuver initiation. With more than one vehicle on orbit, the fraction of fragmentations reachable in the requisite time increases. With just two vehicles, it is possible to reach 69 % of orbits in the most populous altitude and inclination band of satellites, with a minimum 30 min delay between fragmentation and dispatch of cleanup vehicle. [ABSTRACT FROM AUTHOR]

There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure. [ABSTRACT FROM AUTHOR]

Time evolution of a Hamiltonian system can be viewed as a canonical transformation; therefore perturbations, giving rise to near-identity deviations from an unperturbed solution, can be represented by products of Lie transformations, or, together with the unperturbed solution, Lie transfer maps. In this paper I broaden the applicability to all perturbed Hamiltonian systems the method of Dragt and Finn and subsequent co-workers, who developed a representation using a product of Lie transformations factored by phase space variable order. In the present paper, perturbation parameters are no longer necessarily associated with the phase space variables; this method treats both "internal" and "external" perturbations on an equal footing, and a rank is assigned to each variable to reflect the degree of perturbation it represents. With the companion program PGLT, analytic development of the Lie transfer maps is relatively easy for many systems. [ABSTRACT FROM AUTHOR]