Gravity field of the Orientale basin from the Gravity Recovery and Interior Laboratory Mission.

The Orientale basin is the youngest and best-preserved major impact structure on the Moon. We used the Gravity Recovery and Interior Laboratory (GRAIL) spacecraft to investigate the gravitational field of Orientale at 3- to 5-kilometer (km) horizontal resolution. A volume of at least (3.4 ± 0.2) × 106 km3 of crustal material was removed and redistributed during basin formation. There is no preserved evidence of the transient crater that would reveal the basin's maximum volume, but its diameter may now be inferred to be between 320 and 460 km. The gravity field resolves distinctive structures of Orientale's three rings and suggests the presence of faults associated with the outer two that penetrate to the mantle. The crustal structure of Orientale provides constraints on the formation of multiring basins.

Limitations on the use of the power-law form of Sy(f) to compute Allan variance.

An exact solution to the well-known integral transform that relates the spectral density of the instantaneous fractional frequency deviation, Sy(f), to the Allan variance, sigma2y(tau), is presented for the case of a power-law representation of Sy(f). The approximate solution to this integral transform, which is found throughout the literature, also is derived. A graphical convergence analysis is presented, showing the range of applicability of the approximate solution. The results reinforce the use of the approximate solution, which converges quickly to the exact solution under virtually all reasonable measurement conditions.

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.

Ancient igneous intrusions and early expansion of the Moon revealed by GRAIL gravity gradiometry.

The earliest history of the Moon is poorly preserved in the surface geologic record due to the high flux of impactors, but aspects of that history may be preserved in subsurface structures. Application of gravity gradiometry to observations by the Gravity Recovery and Interior Laboratory (GRAIL) mission results in the identification of a population of linear gravity anomalies with lengths of hundreds of kilometers. Inversion of the gravity anomalies indicates elongated positive-density anomalies that are interpreted to be ancient vertical tabular intrusions or dikes formed by magmatism in combination with extension of the lithosphere. Crosscutting relationships support a pre-Nectarian to Nectarian age, preceding the end of the heavy bombardment of the Moon. The distribution, orientation, and dimensions of the intrusions indicate a globally isotropic extensional stress state arising from an increase in the Moon's radius by 0.6 to 4.9 kilometers early in lunar history, consistent with predictions of thermal models.

Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission.

Spacecraft-to-spacecraft tracking observations from the Gravity Recovery and Interior Laboratory (GRAIL) have been used to construct a gravitational field of the Moon to spherical harmonic degree and order 420. The GRAIL field reveals features not previously resolved, including tectonic structures, volcanic landforms, basin rings, crater central peaks, and numerous simple craters. From degrees 80 through 300, over 98% of the gravitational signature is associated with topography, a result that reflects the preservation of crater relief in highly fractured crust. The remaining 2% represents fine details of subsurface structure not previously resolved. GRAIL elucidates the role of impact bombardment in homogenizing the distribution of shallow density anomalies on terrestrial planetary bodies.

The crust of the Moon as seen by GRAIL.

High-resolution gravity data obtained from the dual Gravity Recovery and Interior Laboratory (GRAIL) spacecraft show that the bulk density of the Moon's highlands crust is 2550 kilograms per cubic meter, substantially lower than generally assumed. When combined with remote sensing and sample data, this density implies an average crustal porosity of 12% to depths of at least a few kilometers. Lateral variations in crustal porosity correlate with the largest impact basins, whereas lateral variations in crustal density correlate with crustal composition. The low-bulk crustal density allows construction of a global crustal thickness model that satisfies the Apollo seismic constraints, and with an average crustal thickness between 34 and 43 kilometers, the bulk refractory element composition of the Moon is not required to be enriched with respect to that of Earth.

The tides of Titan.

We have detected in Cassini spacecraft data the signature of the periodic tidal stresses within Titan, driven by the eccentricity (e = 0.028) of its 16-day orbit around Saturn. Precise measurements of the acceleration of Cassini during six close flybys between 2006 and 2011 have revealed that Titan responds to the variable tidal field exerted by Saturn with periodic changes of its quadrupole gravity, at about 4% of the static value. Two independent determinations of the corresponding degree-2 Love number yield k(2) = 0.589 ± 0.150 and k(2) = 0.637 ± 0.224 (2σ). Such a large response to the tidal field requires that Titan's interior be deformable over time scales of the orbital period, in a way that is consistent with a global ocean at depth.

Gravity field, shape, and moment of inertia of Titan.

Precise radio tracking of the spacecraft Cassini has provided a determination of Titan's mass and gravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxed body shaped by tidal and rotational effects. The inferred moment of inertia factor is about 0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock from ice or a core in which a large amount of water remains chemically bound in silicates. The equilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a-c) and 103 meters (b-c). The nonhydrostatic geoid height variations (up to 19 meters) are small compared to the observed topographic anomalies of hundreds of meters, suggesting a high degree of compensation appropriate to a body that has warm ice at depth.

Density of Mars' south polar layered deposits.

Both poles of Mars are hidden beneath caps of layered ice. We calculated the density of the south polar layered deposits by combining the gravity field obtained from initial results of radio tracking of the Mars Reconnaissance Orbiter with existing surface topography from the Mars Orbiter Laser Altimeter on the Mars Global Surveyor spacecraft and basal topography from the Mars Advanced Radar for Subsurface and Ionospheric Sounding on the Mars Express spacecraft. The results indicate a best-fit density of 1220 kilograms per cubic meter, which is consistent with water ice that has approximately 15% admixed dust. The results demonstrate that the deposits are probably composed of relatively clean water ice and also refine the martian surface-water inventory.

Amalthea's density is less than that of water.

Radio Doppler data from the Galileo spacecraft's encounter with Amalthea, one of Jupiter's small inner moons, on 5 November 2002 yield a mass of (2.08 +/- 0.15) x 10(18) kilograms. Images of Amalthea from two Voyager spacecraft in 1979 and Galileo imaging between November 1996 and June 1997 yield a volume of (2.43 +/- 0.22) x 10(6) cubic kilometers. The satellite thus has a density of 857 +/- 99 kilograms per cubic meter. We suggest that Amalthea is porous and composed of water ice, as well as rocky material, and thus formed in a cold region of the solar system, possibly not at its present location near Jupiter.