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Initial value and two point boundary value solutions to the Clohessy-Wiltshire equations

The nonhomogeneous Clohessy-Wiltshire (C-W) equations are formulated and solved as an initial value problem in the form structure of linear systems theory. The state transition matrix (STM) and its inverse are obtained explicitly in both Newtonian and Hamiltonian form. It is shown that the STM for the C-2 equations possesses a special property making its inverse easily obtainable. Since solutions to the C-W equations are needed in two-point boundary value form to construct a good mission design tool for orbit transfer, the Lambert problem is solved in the context of the C-W equations.

Mullins, Larry D.↗

Development of Formation Deployment and Intialization Concepts

NASA's Cross-Cutting Technology Development Program identified formation flying as a key enabler for the next generation Earth and Sciences campaign. It is hoped that this technology will allow a distributed network of autonomous satellites to act collaboratively as a single collective unit paving the way for extensive co-observing campaigns, coordinated multi-point observing programs, improved space-based interferometry, and entirely new approaches to conducting science. APL as a team member with GSFC, funded by the Earth Sciences and Technology Organization (ESTO), investigated formation deployment and initialization concepts which is central to the formation flying concept. This paper presents the analytical approach and preliminary results of the study. The study investigated a simple mission involving the deployment of six micro-satellites, one at a time, from a bus. At the initialization state, the satellites fly in an along-track trajectory separated by nominal spacing. The study entailed the development of a two-body (bus and satellite) relative motion propagator based on Clohessy-Wiltshire (C-W) equations with drag from which the relative motion of the micro-satellites is deduced. This code was used to investigate cluster development characteristics subject to "tip-off' (ejection) conditions. Results indicate that cluster development is very sensitive to the ballistic coefficients of the bus and satellites, and to relative ejection velocity. This information can be used to identify optimum deployment parameters, along with accuracy bounds for a particular mission, and to develop a cluster control strategy minimizing global fuel and cost. A suitable control strategy concept has been identified, however, it needs to be developed further.

Badesha, Surjit S.↗

Time-Varying Expression of the Formation Flying along Circular Trajectories

Usually, the formation flying associated with circular orbits is discussed through the well-known Hill s or C-W equations of motion. This paper dares to present and discuss the coordinates that may contain time-varying coefficients. The discussion presents how the controller s performance is affected by the selection of coordinates, and also looks at the special coordinate suitable for designating a target bin to which each spacecraft in the formation has only to be guided. It is revealed that the latter strategy may incorporate the J2 disturbance automatically.

Kawaguchi, Jun'ichiro↗

Chronic Lunar Dust Exposure on Rat Cornea: Evaluation by Gene Expression Profiling

Lunar dust is capable of entering habitats and vehicle compartments by sticking to spacesuits or other objects that are transferred into the spacecraft from the lunar surface and has been reported to cause irritation upon exposure. During the Apollo missions, crewmembers reported irritation specifically to the skin and eyes after contamination of the lunar and service modules. It has since been hypothesized that ocular irritation and abrasion might occur as a result of such exposure, impairing crew vision. Recent work has shown that both ultrafine and unground lunar dust exhibited minimal irritancy of the ocular surface (i.e., cornea); however, the assessment of the severity of ocular damage resulting from contact of lunar dust particles to the cornea has focused only on macroscopic signs of mechanical irritancy and cytotoxicity. Given the chemical reactive properties of lunar dust, exposure of the cornea may contribute to detrimental effects at the molecular level including but not limited to oxidative damage. Additionally, low level chronic exposures may confound any results obtained in previous acute studies. We report here preliminary results from a tissue sharing effort using 10‐week‐old Fischer 344 male rats chronically exposed to filtered air or jet milled lunar dust collected during Apollo 14 using a Jaeger‐NYU nose‐only chamber for a total of 120 hours (6 hours daily, 5 days a week) over a 4‐week period. RNA was isolated from corneas collected from rats at 1 day and 7 days after being exposed to concentrations of 0, 20, and 60 mg/m3 of lunar dust. Microarray analysis was performed using the Affymetrix GeneChip Rat Genome 230 2.0 Array with Affymetrix Expression Console and Transcriptome Analysis Console used for normalization and secondary analysis. An Ingenuity iReport"TM" was then generated for canonical pathway identification. The number of differentially expressed genes identified increases with dose compared to controls suggesting a more severe response to the lunar dust insult at higher levels. Pathways of interests that have been identified in all exposed samples include oxidative stress response, mitochondrial dysfunction, fibrosis, epithelial healing, TGF-Beta signaling, and extracellular matrix remodeling. Several biological processes related to cell migration, cellular proliferation, and eye development were also identified to be altered by exposure to lunar dust. Our preliminary results suggest that even a chronic insult of lunar dust as low as 20 mg/m(exp 3) elicits a molecular response in cornea tissue. Lunar dust on the surface of the moon would have the added properties of ionization and activation potentially leading to further damage to the cornea and greater sensitivity to any other environmental insult such as exposure to radiation. Additional studies are required to fully assess the risk of vision impairment and the mechanistic responses initiated in cornea exposed to lunar dust as well as the potential for long‐term effects to astronaut health

Theriot, C. A.↗

Quantification of Numerical Uncertainty via Nonlinear Dynamical Approach

Motivations (Ensure a Higher Level of Confidence in the Predictability & Reliability of Numerical Simulation for Multiscale Complex Nonlinear Fluid Problems) - The last two decades have been an era when computation is ahead of analysis & when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems & non-traditional fields (Especially when computations offer the ONLY way of generating this type of data limited simulations). - At present some of the numerical uncertainties can be explained and minimized by traditional numerical analysis and standard CFD practices. However, such practices, usually based on linearized analysis, MIGHT NOT be sufficient for strongly nonlinear and/or stiff problems. - We need a good understanding of the nonlinear behavior of numerical schemes being used as an integral part of code verification, validation and certification.

HEC↗