Advanced Modeling of Optimal Low-Thrust Lunar Pole-Sitter Trajectories
- Paper number
IAC-09.C1.5.4
- Author
Mr. Daniel Grebow, Purdue University, United States
- Coauthor
Mr. Martin Ozimek, United States
- Coauthor
Prof. Kathleen Howell, Purdue University, United States
- Year
2009
- Abstract
Recently, Grebow et al. discovered low-thrust trajectories in the Restricted Three-Body Problem (RTBP) that maintain direct line-of-site with the lunar south pole for very long periods. The trajectories might be used to support communications for a sustained human presence at the south pole, one current interest of NASA. The results have general implications, however, including long-term exploration of the polar regions of other planets, as well as planetary moons. NASA is investigating the coverage capabilities of a small 500 kg spacecraft with an NSTAR thruster. Originating in International Space Station (ISS) orbit, the mission is characterized by three phases: (1) spiral out to the Moon, (2) optimize pole-sitting position, and (3) spiral down to an end-of-life lunar stable orbit. The end-of-life orbit corresponds to a frozen orbit, serving as part of a larger constellation for continued surveillance and lunar operations. The RTBP study successfully implemented all three phases. The results indicate that the motion seems to be confined to a deformed surface corresponding to the halo orbit families. Though these types of solutions have been useful in the design of missions like ISEE-3, WIND, SOHO, MAP, and Genesis, clearly the nature of the pole-sitter trajectories requires further validation with higher fidelity models. This investigation proposes the transition of preliminary designs to include the effects of lunar librations, planetary ephemerides, solar powered thrust-modeling, shadowing, solar radiation pressure, and actual departure from the ISS. \vspace{3 mm} \noindent {\bf Methodology} \vspace{2 mm} The problem will be solved with collocation including path constraints to restrict the spacecraft to a bounded region below the actual lunar south pole. The algorithm removes unnecessary arcs, automatically determines when it is necessary to thrust, and appropriately aligns the thruster. Direct transcription is a natural transition from collocation to optimize the coverage time. \vspace{3 mm} \noindent {\bf Expectation of Results} \vspace{2 mm} Currently, the actual performance under higher fidelity models is unknown. In the previous study, several parameters were computed for a feasible and optimized mission. (See Table 1.) Of particular note, lunar librations are expected to result in a decrease of the minimum elevation angle of 13$^\circ$ from the lunar south pole. Since the initial goal of 365 days was far exceeded in the RTBP study, a comparable total time for phase two under the new model will also be emphasized. \begin{table}[h] \caption{Preliminary Performance Characteristics of Pole-Sitter Mission.} \label{tab:specs} \centering \begin{tabular}[c]{llrr} \hline \hline & & Feasible & Optimal \\ \hline {PHASE $1$} & Fuel Mass Consumed (kg) & 22.13 & 13.58 \\ & Total Time (days) & 42.81 & 34.14 \\ \hline & No. of Thrust Arcs & 35 & 35 \\ {PHASE $2$} & Fuel Mass Consumed (kg) & 264.19 & 273.09 \\ & \bf{Total Time (days)} & \bf{447.04}& \bf{554.18} \\ & \bf{Min. Elevation Angle ($^{\circ}$)} & \bf{13.0} & \bf{13.0} \\ \hline {PHASE $3$} & Fuel Mass Consumed (kg) & 1.76 & 1.41 \\ & Total Time (days) & 2.36 & 2.37 \\ \hline\hline \end{tabular}\end{table} \vspace{4 mm} \noindent {\bf References} \vspace{2 mm} \noindent Grebow, D., Ozimek, M., and Howell, K., “Design of Optimal Low-Thrust Lunar Pole-Sitter Missions,” Paper No. AAS 09-148, {\it 19th AAS/AIAA Spaceflight Mechanics Meeting}, Savannah, Georgia, February 8-12, 2009.- Abstract document
- Manuscript document
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