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Lunar Reconnaissance Orbiter: Designing the Mission Trajectory Frank Mycroft1 and Mark Beckman2 1 Research Associate, 2006 Goddard NASA Academy, Aerospace Engineering Dept., Princeton University 2 Principal Investigator, Flight Dynamics Analysis Branch, Code 595, NASA Goddard Space Flight Center Mission Profile Launch Date: Late October of 2008 through the end of that year. Launch Site: Cape Canaveral Time in Lunar Transit: Four to five days Nominal Mission Length: One year Mission Orbit: Selenecentric, circular, polar orbit at ~50 km altitude Acknowledgements We recognize the generous support and invaluable mentoring of Dave Folta, Joseph DiRienzi, Paul Black, the NASA Academy, and the New Jersey Space Grant Consortium. Project Overview This project seeks to identify those daily trajectories affording a minimum C3 energy, direct transfer to lunar orbit during the launch window under nominal conditions. The detailed characteristics for each mission phase from launch through the end of the nominal mission will be retrieved for each optimized launch opportunity. Future Work LRO will have a three-day launch window every two weeks during the final two months in 2008. Six optimized trajectories exist within each window, of which three exist with acceptable ground access for communications. All optimum solutions, including those that do not meet these constraints, will be found and fully characterized. Results from these analyses will be reviewed during LRO’s Critical Design Review in the fall of 2006. Mission Motivation The Lunar Reconnaissance Orbiter (LRO) marks the first step in NASA’s new vision to return men and women to the surface of the moon. Designed at NASA Goddard Space Flight Center, LRO will map lunar resources and provide an increased awareness of the moon’s topological and environmental challenges. Project Constraints Launch time must permit adequate communication between LRO and ground stations Capture about the moon will occur over the lunar South pole Launch date must result in a flight path that is approximately normal to the lunar dawn/dusk terminator at lunar solstice in order to identify lunar regions in permanent sunlight and shadow Trajectory Design: An Iterative Process Personal Responsibilities Include: Fully regenerate the previous LRO mission trajectory within AGI’s Satellite Tool Kit v.7.1. Develop more accurate engine sets and thruster models for finite burns. Further refine the trajectory model with better defined coordinate systems, propagators and gravity models. Write a MATLAB script employing STK/Connect to automate data retrieval for future trajectory analysis. (Over 700 lines of MATLAB code written) Iteratively solve for a daily trajectory solution which meets the project constraints. Using STK/Analyzer module, optimize each daily trajectory for minimum C3 energy direct transfer to lunar orbit. Generate plots showing the relationships between launch date and C3, lunar beta angle, and transfer time. One of two optimized daily direct transfer solutions to lunar orbit on October 28, 2008. Red represents rocket burns of significant duration, light blue and yellow represent coast phases. Thinner green and blue lines represent communication access between the Lunar Reconnaissance Orbiter and available Earth ground stations. Shown above are the two optimized solutions for a direct lunar transfer. Both fire trans-lunar injection (TLI) burns at the same point in space; however, both have different launch times, coast for different durations, travel within different orbital planes, and arrive at the moon at different times. Shown at left is a two dimensional rendering of the launch and coast phases of LRO’s trajectory coupled with one of the launch window’s primary limitations: communication. Talking with LRO immediately after the trans-lunar insertion (TLI) burn is critical, thus the burn must occur over available ground stations. Optimized trajectories that result in TLI burns in the 2nd or 3rd quadrants of the argument of latitude (highlighted in red) must be thrown out due to limited communication access. Acceptable trajectories have a TLI burn in the white segments. Each day, one of the two optimized solutions will exist in the white segment, thus, each day one launch opportunity exists. The worst TLI burn occurs over Australia, where 10 minutes will pass before LRO comes in contact with the nearest ground station. In order to perform a lunar capture, LRO trajectory analysts have defined a “B-plane” (shown in purple) which supports a robust lunar targeter in STK. The B-plane is constructed from a central body and the asymptote of the incoming trajectory. Constraints on the lengths of the two vectors, R and T, allow one to position the insertion over the lunar south pole as required for the LRO mission. Describing Position Upon entering the moon’s gravitational sphere of influence, a series of lunar orbital insertion (LOI) burns are performed. These burns (shown in red) first enable capture about the moon, then reduce eccentricity and position the argument of periapsis to the point of a quasi-frozen orbit, known as the commissioning orbit. LRO remains in the energy efficient (minimal stationkeeping) orbit for one to two months before entering its lower, more circular, mission orbit (green). The non-uniformity of the moon’s density perturbs LRO away from mission orbit, requiring monthly stationkeeping maneuvers. The chart at right depicts a moon-centered universe, and is useful for visualizing LRO’s final mission trajectory requirement: a solar-beta angle near zero at lunar solstice. At a beta angle of zero, LRO’s orbit plane coincides with the sun-moon vector. This orientation allows LRO to better study the dawn-dusk line. Since LRO’s orbit is inertially-fixed about a rotating moon, our only control over the beta-angle is the launch date. One three-day launch window meets this constraint every two weeks. Earth-beta angles near 90° provide a full view of LRO’s orbit, and are thus desired during maneuvers. The six Keplerian elements, shown at left, have been used extensively in describing LRO’s orbital position. Other important definitions are given below: C3 Energy – The square of a body’s velocity upon leaving the sphere of influence of the reference body. Low C3 trajectories require the least amount of fuel. This number rests around -1.9 km2/s2 for optimized LRO mission trajectories. Periapsis – The point of closest approach to the reference body. Eccentricity – A measure of an orbit’s deviation from circular. Orbits with an eccentricity between 0 and 1 are elliptical. “This mission is the first concrete step in laying the groundwork for humans to go back to the moon.” -Jim Garvin, NASA Chief Scientist