Patched Local Lunar Gravity Solutions Using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into 12 regions and 2 polar caps, with a resolution of 0.15 ° × 0.15 ° (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Orbit determination of the Lunar Reconnaissance Orbiter: Status after Seven Years

The Lunar Reconnaissance Orbiter (LRO) has been orbiting the Moon since 2009, obtaining unique and foundational datasets important to understanding the evolution of the Moon and the Solar System. The high-resolution data acquired by LRO benefit from precise orbit determination (OD), limiting the need for geolocation and co-registration tasks. The initial position knowledge requirement (50 meters) was met with radio tracking from ground stations, after combination with LOLA altimetric crossovers. LRO-specific gravity field solutions were determined and allowed radio-only OD to perform at the level of 20 meters, although secular inclination changes required frequent updates. The high-accuracy gravity fields from GRAIL, with <10 km spatial resolution, further improved the radio-only orbit reconstruction quality (<10 meters). However, orbit reconstruction is in part limited by the 0.3-0.5 mm/s measurement noise level in S-band tracking. One-way tracking through Laser Ranging can supplement the tracking available for OD with 28-Hz ranges with 20-cm single-shot precision, but is available only on the nearside (the lunar hemisphere facing the Earth due to tidal locking). Here, we report on the status of the OD effort since the beginning of the mission, a period spanning more than seven years. We describe modeling improvements and the use of new measurements. In particular, the LOLA altimetric data give accurate, uniform, and independent information about LRO's orbit, with a different sensitivity and geometry which includes coverage over the lunar farside and is not tied to ground-based assets. With SLDEM2015 (a combination of the LOLA topographic profiles and the Kaguya Terrain Camera stereo images), another use of altimetry is possible for OD. We extend the 'direct altimetry' technique developed for the ICESat mission to perform OD and adjust spacecraft position to minimize discrepancies between LOLA tracks and SLDEM2015. Comparisons with the radio-only orbits are used to evaluate this new tracking type, of interest for the OD of future lunar orbiters carrying a laser altimeter. LROC NAC images also provide independent accuracy estimation, through the repeated views taken of anthropogenic features for instance.

Lunar impact basins revealed by Gravity Recovery and Interior Laboratory measurements

Observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission indicate a marked change in the gravitational signature of lunar impact structures at the morphological transition, with increasing diameter, from complex craters to peak-ring basins. At crater diameters larger than ~200 km, a central positive Bouguer anomaly is seen within the innermost peak ring, and an annular negative Bouguer anomaly extends outward from this ring to the outer topographic rim crest. These observations demonstrate that basin-forming impacts remove crustal materials from within the peak ring and thicken the crust between the peak ring and the outer rim crest. A correlation between the diameter of the central Bouguer gravity high and the outer topographic ring diameter for well-preserved basins enables the identification and characterization of basins for which topographic signatures have been obscured by superposed cratering and volcanism. The GRAIL inventory of lunar basins improves upon earlier lists that differed in their totals by more than a factor of 2. The size-frequency distributions of basins on the nearside and farside hemispheres of the Moon differ substantially; the nearside hosts more basins larger than 350 km in diameter, whereas the farside has more smaller basins. Hemispherical differences in target properties, including temperature and porosity, are likely to have contributed to these different distributions. Better understanding of the factors that control basin size will help to constrain models of the original impactor population.

Analytical theory of an artificial satellite of the moon

The dynamics of an artificial satellite of the moon is quite different from the dynamics of an artificial satellite of the Earth. Indeed, the C(22) term is only 1/10 of the J(2) term, and the effect of the Earth on the lunar satellite is much larger than the effect of the Moon on a terrestrial satellite. The method used here is the Lie method for averaging the Hamiltonian of the problem, in canonical variables. The solution is developed in powers of the small factors linked to J(2) and C(22). Short period terms (linked to l, the mean anomaly) are eliminated first, and then the long period terms (linked to g, the mean argument of the periaster, and to h, the longitude of the ascending node), which finally gives the secular motion. The results are obtained in a closed form, without any series developments in eccentricity or inclination. Thus, the solution applies for a wide range of values, except for few isolated critical values. The results are only very preliminary. As a side result, we were able to check the solution given by Kozai for the effect of the J(2) term on an artificial satellite.

Improved gravity field of the moon from lunar prospector

An improved gravity model from Doppler tracking of the Lunar Prospector (LP) spacecraft reveals three new large mass concentrations (mascons) on the nearside of the moon beneath the impact basins Mare Humboltianum, Mendel-Ryberg, and Schiller-Zucchius, where the latter basin has no visible mare fill. Although there is no direct measurement of the lunar farside gravity, LP partially resolves four mascons in the large farside basins of Hertzsprung, Coulomb-Sarton, Freundlich-Sharonov, and Mare Moscoviense. The center of each of these basins contains a gravity maximum relative to the surrounding basin. The improved normalized polar moment of inertia (0.3932 +/- 0.0002) is consistent with an iron core with a radius of 220 to 450 kilometers.