Sander Goossens

Gravity Field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) Mission

The Holy GRAIL? The gravity field of a planet provides a view of its interior and thermal history by revealing areas of different density. GRAIL, a pair of satellites that act as a highly sensitive gravimeter, began mapping the Moons gravity in early 2012. Three papers highlight some of the results from the primary mission. Zuber et al. (p. 668, published online 6 December) discuss the overall gravity field, which reveals several new tectonic and geologic features of the Moon. Impacts have worked to homogenize the density structure of the Moons upper crust while fracturing it extensively. Wieczorek et al. (p. 671, published online 6 December) show that the upper crust is 35 to 40 kilometers thick and less dense—and thus more porous—than previously thought. Finally, Andrews-Hanna et al. (p. 675, published online 6 December) show that the crust is cut by widespread magmatic dikes that may reflect a period of expansion early in the Moons history. The Moons gravity field reveals that impacts have homogenized the density of the crust and fractured it extensively. 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.

Gravity Field and Internal Structure of Mercury from MESSENGER

Mercury Inside and Out The MESSENGER spacecraft orbiting Mercury has been in a ∼12-hour eccentric, near-polar orbit since 18 March 2011 (see the Perspective by McKinnon). Smith et al. (p. 214, published online 21 March) present the most recent determination of Mercurys gravity field, based on radio tracking of the MESSENGER spacecraft between 18 March and 23 August 2011. The results point to an interior structure that differs from those of the other terrestrial planets: the density of the planets solid outer shell suggests the existence of a deep reservoir of high-density material, possibly an Fe-S layer. Zuber et al. (p. 217, published online 21 March) used data obtained by the MESSENGER laser altimeter through to 24 October 2011 to build a topographic map of Mercurys northern hemisphere. The map shows less variation in elevation, compared with Mars or the Moon, and its features add to the body of evidence that Mercury has sustained geophysical activity for much of its history. Mercury’s outer solid shell is denser than expected, suggesting a deep reservoir of high-density material, possibly iron-sulfide. Radio tracking of the MESSENGER spacecraft has provided a model of Mercury’s gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 milli-Galileos (mgal). Mercury’s northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 ± 0.017, where M and R are Mercury’s mass and radius, and a ratio of the moment of inertia of Mercury’s solid outer shell to that of the planet of Cm/C = 0.452 ± 0.035. A model for Mercury’s radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.

GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data

We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the Gravity Recovery and Interior Laboratory (GRAIL) Primary (1 March to 29 May 2012) and Extended Missions (30 August to 14 December 2012). A power law constraint of 3.6 ×10−4/ℓ2 was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The models degree strength varies from a minimum of 575–675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November 2012 at 0.13 μm/s RMS, whereas the last month of Ka-Band Range-Rate data obtained from altitudes of 2–10 km fit at 0.98 μm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900.

Lunar interior properties from the GRAIL mission

The Gravity Recovery and Interior Laboratory (GRAIL) mission has sampled lunar gravity with unprecedented accuracy and resolution. The lunar GM, the product of the gravitational constant G and the mass M, is very well determined. However, uncertainties in the mass and mean density, 3345.56u2009±u20090.40u2009kg/m3, are limited by the accuracy of G. Values of the spherical harmonic degree-2 gravity coefficients J2 and C22, as well as the Love number k2 describing lunar degree-2 elastic response to tidal forces, come from two independent analyses of the 3u2009month GRAIL Primary Mission data at the Jet Propulsion Laboratory and the Goddard Space Flight Center. The two k2 determinations, with uncertainties of ~1%, differ by 1%; the average value is 0.02416u2009±u20090.00022 at a 1u2009month period with reference radius Ru2009=u20091738u2009km. Lunar laser ranging (LLR) data analysis determines (Cu2009−u2009A)/B and (Bu2009−u2009A)/C, where Au2009<u2009Bu2009<u2009C are the principal moments of inertia; the flattening of the fluid outer core; the dissipation at its solid boundaries; and the monthly tidal dissipation Qu2009=u200937.5u2009±u20094. The moment of inertia computation combines the GRAIL-determined J2 and C22 with LLR-derived (Cu2009−u2009A)/B and (Bu2009−u2009A)/C. The normalized mean moment of inertia of the solid Moon is Is/MR2u2009=u20090.392728u2009±u20090.000012. Matching the density, moment, and Love number, calculated models have a fluid outer core with radius of 200–380u2009km, a solid inner core with radius of 0–280u2009km and mass fraction of 0–1%, and a deep mantle zone of low seismic shear velocity. The mass fraction of the combined inner and outer core is ≤1.5%.

The gravity field, orientation, and ephemeris of Mercury from MESSENGER observations after three years in orbit

We have analyzed 3 years of radio tracking data from the MESSENGER spacecraft in orbit around Mercury and determined the gravity field, planetary orientation, and ephemeris of the innermost planet. With improvements in spatial coverage, force modeling, and data weighting, we refined an earlier global gravity field both in quality and resolution, and we present here a spherical harmonic solution to degree and order 50. In this field, termed HgM005, uncertainties in low-degree coefficients are reduced by an order of magnitude relative to earlier global fields, and we obtained a preliminary value of the tidal Love number k2 of 0.451±0.014. We also estimated Mercurys pole position, and we obtained an obliquity value of 2.06±0.16 arcmin, in good agreement with analysis of Earth-based radar observations. From our updated rotation period (58.646146 ± 0.000011 days) and Mercury ephemeris, we verified experimentally the planets 3 : 2 spin-orbit resonance to greater accuracy than previously possible. We present a detailed analysis of the HgM005 covariance matrix, and we describe some near-circular frozen orbits around Mercury that could be advantageous for future exploration.

Lunar impact basins revealed by Gravity Recovery and Interior Laboratory measurements

New gravity measurements greatly improve the Moon’s preserved impact basin inventory. 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.

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

On the origin of Orientale basin Orientale basin is a major impact crater on the Moon, which is hard to see from Earth because it is right on the western edge of the lunar nearside. Relatively undisturbed by later events, Orientale serves as a prototype for understanding large impact craters throughout the solar system. Zuber et al. used the Gravity Recovery and Interior Laboratory (GRAIL) mission to map the gravitational field around the crater in great detail by flying the twin spacecraft as little as 2 km above the surface. Johnson et al. performed a sophisticated computer simulation of the impact and its subsequent evolution, designed to match the data from GRAIL. Together, these studies reveal how major impacts affect the lunar surface and will aid our understanding of other impacts on rocky planets and moons. Science, this issue pp. 438 and 441 Detailed maps of the Moon’s gravitational field reveal structure in the Orientale impact crater. 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.

Evidence for a low bulk crustal density for Mars from gravity and topography

Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high-resolution gravity and topography data has yielded a low density for the Moons crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well-chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 ± 209 kg m-3. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth.

Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission

The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter ηu2009=u2009(−6.6u2009±u20097.2)u2009×u200910−5. By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter βu2009=u20091u2009+u2009(−1.6u2009±u20091.8)u2009×u200910−5 and the Sun’s gravitational oblateness,