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Anderson R.L.,University of Colorado at Boulder | Anderson R.L.,Colorado Center for Astrodynamics Research | Lo M.W.,Jet Propulsion Laboratory | Lo M.W.,High Capability Computing and Modeling Group
Journal of Guidance, Control, and Dynamics | Year: 2010

In this analysis the relationship between a planar Europa Orbiter trajectory and the invariant manifolds of resonant periodic orbits is studied. An understanding of this trajectory with its large impulsive maneuvers should provide basic tools that can be extended to cases that approximate low thrust with many small maneuvers. This study therefore represents a step in understanding low-thrust trajectories. Unstable resonant orbits are computed along with their invariant manifolds in order to examine the resonance transitions that the planar Europa Orbiter trajectory travels through. The stable manifold of a Lyapunov orbit at the L2 libration point is used to show why a 5:6 resonance is necessary at this energy for capture around Europa. 2009. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. Source

Hudson J.S.,University of Michigan | Scheeres D.J.,University of Colorado at Boulder | Scheeres D.J.,Colorado Center for Astrodynamics Research
Journal of Guidance, Control, and Dynamics | Year: 2011

A method to evaluate the trajectory dynamics of low-thrust spacecraft is applied to targeting and optimal control problems. Averaged variational equations for the osculating orbital elements are used to estimate a spacecraft trajectory over many spiral orbits. Fourteen Fourier coefficients of the thrust acceleration vector represent the fundamental trajectory dynamics. Spacecraft targeting problems are solved using the averaged variational equations and a general cost function represented as a Fourier series. The resulting fuel costs and dynamic fidelity of the targeting solutions are evaluated. The goal of the method is not precise targeting, but easy reconstruction of the basic elements of the thrusting trajectory and control law. Copyright © 2011 by Jennifer Hudson. Source

Mullen J.,University of Colorado at Boulder | Schaub H.,University of Colorado at Boulder | Schaub H.,Colorado Center for Astrodynamics Research
Journal of Guidance, Control, and Dynamics | Year: 2010

A subfamily of attitude coordinates called the hypersphere stereographic orientation parameters (SOPs) (HSOPs), which contain both the previous MRPs (particular set of symmetric SOPs) and the asymmetric stereographic attitude parameters (ASOP), allowing for all this work to be combined into a single, minimal attitude parameter description, is reported. HSOPs are different than MRPs because of the different singular behaviors of each attitude coordinate set. This offers great flexibility, as the singular orientation can be placed at a full revolution or at particular rotations about particular body axes. In all cases, the kinematic differential equation only has quadratic nonlinear terms equivalent to those of the MRPs. Source

Leonard J.M.,University of Colorado at Boulder | Nievinski F.G.,University of Colorado at Boulder | Born G.H.,University of Colorado at Boulder | Born G.H.,Colorado Center for Astrodynamics Research
Journal of Spacecraft and Rockets | Year: 2013

Earth science satellite missions currently require orbit determination solutions with position accuracies to within a centimeter. The estimation of empirical accelerations has become commonplace in precise orbit determination for Earth-orbiting satellites. Dynamic model compensation uses an exponentially time-correlated system noise process, known as a first-order Gauss-Markov process, to estimate unmodeled accelerations. In this work, the use of a secondorder Gauss-Markov process is addressed to compensate for higher order spherical harmonic gravity accelerations, beyond J3. Improvements in precise orbit determination and orbit prediction through the implementation of an optimal second-order Gauss-Markov process for empirical acceleration estimation are assessed. The use of a single well-calibrated second-order Gauss-Markov process outperforms a first-order Gauss-Markov process and a poorly calibrated second-order Gauss-Markov process for both continuous observations and poor tracking data. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. Source

Pilinski M.D.,University of Colorado at Boulder | Pilinski M.D.,Research and Engineering Center for Unmanned Vehicles | Argrow B.M.,University of Colorado at Boulder | Argrow B.M.,Research and Engineering Center for Unmanned Vehicles | And 3 more authors.
Journal of Spacecraft and Rockets | Year: 2013

Orbits of launch-vehicle upper stages and spheres were observed by U.S. Air Force Space Command, and the resulting observations were converted by the Space Analysis Office to fitted ballistic coefficients by comparing the observed orbit with an orbit predicted by an atmospheric-drag model. The ballistic coefficients contain signals that result from atmospheric variability not captured by the model as well as signals that correspond to changes in the satellite-drag coefficient. For objects in highly elliptical orbits with perigee altitudes below 200 km a 50% change in ballistic coefficient can be observed. This drastic change is associated with both changes in the energy accommodation coefficient driven by atomic-oxygen adsorption and entry into a transition flow region where a diffuse shock forms ahead of the satellite near perigee. Furthermore, the observed ballistic coefficients for objects in near-circular orbits (7.5 km/s speeds) do not match those of objects in highly eccentric orbits (10 km/s speeds near perigee). This difference is attributed to a decrease in adsorption efficiency postulated by previous researchers that is formalized in this work into a semi-empirical model. The model parameters suggest that the average binding energy of atomic oxygen on satellite surfaces is about 5.7 eV. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. Source

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