Abstract
The analysis of range or Doppler data between sites on the Earth and Moon requires an accurate computation of the lunar orbit and detailed models of the orientation of the Earth and Moon. Models constructed to understand range and range rate can lack detail, but if they include the largest lunar orbit variations, tracking stations on a rotating Earth, and lunar sites on a synchronously rotating Moon, then they will display the largest effects for orbit elements, Earth orientation, tracking station locations, and lunar site coordinates. The range and range rate are expanded into periodic series. To understand accurate solutions, the largest periodic terms that are sensitive to various solution parameters indicate the sensitivity of data to solution parameters and the time spans needed for their determination. Conclusions include: cylindrical coordinates work well for sites on the rapidly rotating Earth, but Cartesian coordinates are more natural for the synchronously rotating Moon since the series for the three coordinate projections are distinct. For range and range rate data, daily, semimonthly, monthly, and longer periods are present. For Doppler data, the daily periods may be stronger and more useful than the long periods, particularly for terms associated with the terrestrial tracking station. Doppler data do not determine the lander coordinate toward the Earth well. Observational strategies for range and Doppler data are not identical. For all data types, one wishes a variety of hour angles, lunar declinations, times of month, and longer periods. A long span of high-quality range data can improve the lunar orbit, orientation of the Earth’s equator, and physical librations. The locations of new lunar sites or new tracking stations can be determined from shorter spans of data.
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Acknowledgements
At the Jet Propulsion Laboratory, Eq. (10) for interplanetary spacecraft is attributed to T. Hamilton and W. Melbourne. Early in the lunar laser-ranging effort, P. L. Bender of the University of Colorado at Boulder assessed the sensitivities of ranges to various parameters by considering separate orbit, terrestrial, and lunar components. That was a precursor to the expansions of this paper. Dale H. Boggs participated in the solutions of Table 9. Ryan Park advised on radio range and Doppler accuracies. Dmitry Pavlov provided a useful review. The research described in this paper was carried out at the Jet Propulsion Laboratory of the California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Government sponsorship is acknowledged.
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Williams, J.G. Insight-building models for lunar range and range rate. Celest Mech Dyn Astr 130, 63 (2018). https://doi.org/10.1007/s10569-018-9857-1
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DOI: https://doi.org/10.1007/s10569-018-9857-1