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Lunar Geophysics, Geodesy, and Dynamics
 proceedings of 13th International Workshop on Laser Ranging, October 711, 2002
, 2003
"... Experience with the dynamics and data analyses for Earth and Moon reveals both similarities and differences. Analysis of Lunar Laser Ranging (LLR) data provides information on the lunar orbit, rotation, solidbody tides, and retroreflector locations. Lunar rotational variations have strong sensitivi ..."
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Experience with the dynamics and data analyses for Earth and Moon reveals both similarities and differences. Analysis of Lunar Laser Ranging (LLR) data provides information on the lunar orbit, rotation, solidbody tides, and retroreflector locations. Lunar rotational variations have strong sensitivity to moments of inertia and gravity field while weaker variations, including tidal variations, give sensitivity to the interior structure, physical properties, and energy dissipation. A fluid core of about 20 % of the Moon’s radius is indicated by the dissipation data. The seconddegree Love numbers are detected, most sensitively k2. Lunar tidal dissipation is strong and its Q has a weak dependence on tidal frequency. Dissipationcaused acceleration in orbital longitude is dominated by tides on Earth with the Moon only contributing about 1%, but lunar tides cause a significant eccentricity rate. The lunar motion is sensitive to orbit and mass parameters. The very low noise of the lunar orbit and rotation also allows sensitive tests of the theory of relativity. Mooncentered coordinates of four retroreflectors are determined. Extending the data span and improving range accuracy will yield improved and new scientific results. Introduction – the Earth and Moon
Lunar Laser Ranging Science: Gravitational Physics and Lunar Interior and Geodesy
 In proc. “35th COSPAR Scientific Assembly
"... Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q = 33 ± 4 at a month and a weak d ..."
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Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q = 33 ± 4 at a month and a weak dependence on period. Lunar rotation depends on interior properties; a fluid core is indicated with radius ∼20 % that of the Moon. Tests of relativistic gravity verify the equivalence principle to ±1.4 × 10 −13, limit deviations from Einstein’s general relativity, and show no rate for the gravitational constant ˙ G/G with uncertainty 9 × 10 −13 yr −1. 1
Comparisons of the CubedSphere Gravity Model with the Spherical Harmonics
 Journal of Guidance, Control, and Dynamics
"... The cubedsphere gravitational model is a modification of a base model, e.g., the spherical harmonic model, to allow for the fast evaluation of acceleration. Themodel consists of concentric spheres, eachmapped to the surface of a cube and combined with an appropriate interpolation scheme. The paper ..."
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The cubedsphere gravitational model is a modification of a base model, e.g., the spherical harmonic model, to allow for the fast evaluation of acceleration. Themodel consists of concentric spheres, eachmapped to the surface of a cube and combined with an appropriate interpolation scheme. The paper presents a brief description of the cubedsphere model and a comparison of it with the spherical harmonic model. The model was configured to achieve a desired accuracy so that dynamical tests, e.g., evaluation of the integration constant, closely approximate that of the spherical harmonic model. The new model closely approximates the spherical harmonic model, with propagated orbits deviating by a fraction of a millimeter at or above feasible Earthcentered altitudes.
2004), Isostasy of the Moon from highresolution gravity and topography data: Implication for its thermal history, Geophys
 Res. Lett
"... [1] The Lunar Prospector lineofsight acceleration data after terrain correction have been inverted to the highresolution Bouguer gravity anomalies of the lunar nearside. Lithospheric thicknesses of the early Moon were investigated by comparing the gravity anomalies of craters and impact basins of ..."
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[1] The Lunar Prospector lineofsight acceleration data after terrain correction have been inverted to the highresolution Bouguer gravity anomalies of the lunar nearside. Lithospheric thicknesses of the early Moon were investigated by comparing the gravity anomalies of craters and impact basins of various dimensions. The lithosphere was already thick enough to support craters with diameters up to 300 km in the PreNectarian and Nectarian Periods. Degree of isostatic compensation of larger impact basins suggested lithospheric thickness of 20–60 km at that time, which depended more on localities rather than age
1Comparison of EKF and UKF for spacecraft localization via angle measurements
"... In this paper, the performance of two nonlinear estimators is compared for the localization of a spacecraft. It is assumed that range measurements are not available (like in deep space missions) and the localization problem is tackled on the basis of anglesonly measurements. A dynamic model of the ..."
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In this paper, the performance of two nonlinear estimators is compared for the localization of a spacecraft. It is assumed that range measurements are not available (like in deep space missions) and the localization problem is tackled on the basis of anglesonly measurements. A dynamic model of the spacecraft accounting for several perturbing effects, such as Earth and Moon gravitational field asymmetry and errors associated with the Moon ephemerides, is employed. The measurement process is based on elevation and azimuth of Moon and Earth with respect to the spacecraft reference system. Position and velocity of the spacecraft are estimated by using both the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The behavior of the filters is compared on two sample missions: EarthtoMoon transfer and geostationary orbit raising.
High resolution lunar gravity anomaly map from the lunar prospector
, 2003
"... lineofsight acceleration data ..."
1 Is it possible to test directly General Relativity in the gravitational field of the Moon?
, 2002
"... In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the postNewtonian LenseThir ..."
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In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the postNewtonian LenseThirring gravitomagnetic and the Einstein’s gravitoelectric effects on the satellites orbits are calculated and compared to the presentday orbit accuracy of lunar missions. It turns out that for SELENE’s Main Orbiter, at present, the gravitoelectric periselenium shift, which is the largest general relativistic effect, is 1 or 2 orders of magnitude smaller than the experimental sensitivity. The systematic error induced by the mismodelled classical periselenium precession due to the first even zonal harmonic J2 of the Moon’s nonspherical gravitational potential is 3 orders of magnitude larger than the general relativistic gravitoelectric precession. 1.
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, 2003
"... This report was prepared by the Center For Clean Air Policy in the course of performing ..."
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This report was prepared by the Center For Clean Air Policy in the course of performing
LowThrust Control of a Lunar Mapping Orbit
 Journal of Guidance, Control and Dynamics
"... Abstract A method is presented for generating and maintaining a lunar mapping orbit using continuous lowthrust hardware. Optimal control theory is used to maintain a lunar orbit that is lowaltitude, nearpolar, and Sunsynchronous; three typical requirements for a successful lunar mapping mission. ..."
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Abstract A method is presented for generating and maintaining a lunar mapping orbit using continuous lowthrust hardware. Optimal control theory is used to maintain a lunar orbit that is lowaltitude, nearpolar, and Sunsynchronous; three typical requirements for a successful lunar mapping mission. The analysis of the optimal control problem leads to the commonly seen twopoint boundary value problem, which is solved using a simple indirect shooting algorithm. Simulations are presented for a 50day mapping duration, in which it is shown that a very tight control is achieved with thrust levels below 1 N for a 1000 kg spacecraft. A straightforward approach for using the method presented to compute missions of any duration is also discussed.
SPACECRAFT LOCALIZATION VIA ANGLE MEASUREMENTS FOR AUTONOMOUS NAVIGATION IN DEEP SPACE MISSIONS
"... Abstract: This paper deals with spacecraft autonomous navigation in deep space missions. The considered problem is that of spacecraft localization based on angular measurements. The dynamic model of the spacecraft accounts for several perturbing effects, such as Earth and Moon gravitational field as ..."
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Abstract: This paper deals with spacecraft autonomous navigation in deep space missions. The considered problem is that of spacecraft localization based on angular measurements. The dynamic model of the spacecraft accounts for several perturbing effects, such as Earth and Moon gravitational field asymmetry and errors associated with the Moon ephemerides. The measurement process is based on elevation and azimuth of Moon and Earth with respect to the spacecraft reference system. Distance measurements are not employed. Position and velocity of the spacecraft are estimated by using both the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The performance of the filters are evaluated on an example of EarthtoMoon transfer mission.