Dah-Ning Yuan

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.

Improved methods for observing Earth's time variable mass distribution with GRACE using spherical cap mascons

We discuss several classes of improvements to gravity solutions from the Gravity Recovery and Climate Experiment (GRACE) mission. These include both improvements in background geophysical models and orbital parameterization leading to the unconstrained spherical harmonic solution JPL RL05, and an alternate JPL RL05M mass concentration (mascon) solution benefitting from those same improvements but derived in surface spherical cap mascons. The mascon basis functions allow for convenient application of a priori information derived from near-global geophysical models to prevent striping in the solutions. The resulting mass flux solutions are shown to suffer less from leakage errors than harmonic solutions, and do not necessitate empirical filters to remove north-south stripes, lowering the dependence on using scale factors (the global mean scale factor decreases by 0.17) to gain accurate mass estimates. Ocean bottom pressure (OBP) time series derived from the mascon solutions are shown to have greater correlation with in situ data than do spherical harmonic solutions (increase in correlation coefficient of 0.08 globally), particularly in low-latitude regions with small signal power (increase in correlation coefficient of 0.35 regionally), in addition to reducing the error RMS with respect to the in situ data (reduction of 0.37 cm globally, and as much as 1 cm regionally). Greenland and Antarctica mass balance estimates derived from the mascon solutions agree within formal uncertainties with previously published results. Computing basin averages for hydrology applications shows general agreement between harmonic and mascon solutions for large basins; however, mascon solutions typically have greater resolution for smaller spatial regions, in particular when studying secular signals.

Gravity field of Mars: A 75th Degree and Order Model

Radiometric tracking data collected by NASAs Deep Space Network (DSN) for Mariner 9, Viking 1 and 2 orbiters, and Mars Global Surveyor (MGS) have been analyzed to determine the gravity field of Mars. The gravity solution (MGS75D) is a complete spherical harmonics model to degree and order 75. Also parts of the solution are the gravitational constants of Mars, Phobos, and Deimos. The significant improvement in the MGS75D Mars gravity model is mainly a consequence of globally distributed data set collected from the MGS mapping orbits, the use of optimal weighting and constrained least squares solution techniques, and improved force and measurement models in the orbit determination process. The gravity anomaly map reveals significantly more detail and larger amplitudes than any previous Mars gravity map over the major impact and volcanic areas on Mars. Olympus Mons remains the largest known gravity anomaly in our solar system and Isidis Planitia, the highest-amplitude mascon. There are mascons in the Hellas, Argyre, and Utopia basins. Valles Marineris has distinctive negative anomalies, and all volcanic features are positive. Gravity anomalies over several craters have also been resolved. The overall correlation of the MGS75D gravity anomaly map with topography derived from the Mars Orbiter Laser Altimeter (MOLA) is very high, while the polar regions display relatively poor correlation.

High‐resolution lunar gravity fields from the GRAIL Primary and Extended Missions

The resolution and accuracy of the lunar spherical harmonic gravity field have been dramatically improved as a result of the Gravity Recovery and Interior Laboratory (GRAIL) mission. From the Primary Mission, previous harmonic gravity fields resulted in an average n = 420 surface resolution and a Bouguer spectrum to n = 330. The GRAIL Extended Mission improves the resolution due to a lower average 23 km altitude orbit. As a result, new harmonic degree 900 gravity fields (GL0900C and GL0900D) show nearly a factor of 2 improvement with an average surface resolution n = 870 and the Bouguer spectrum extended to n = 550. Since the minimum spacecraft altitude varies spatially between 3 km and 23 km, the surface resolution is variable from near n = 680 for the central farside to near n = 900 for the polar regions. These gravity fields with 0.8 million parameters are by far the highest-degree fields of any planet ever estimated with a fully dynamic least squares technique using spacecraft tracking data.

Spacecraft Thermal and Optical Modeling Impacts on Estimation of the GRAIL Lunar Gravity Field

We summarize work performed involving thermo-optical modeling of the two Gravity Recovery And Interior Laboratory (GRAIL) spacecraft. We derived several reconciled spacecraft thermo-optical models having varying detail. We used the simplest in calculating SRP acceleration, and used the most detailed to calculate acceleration due to thermal re-radiation. For the latter, we used both the output of pre-launch finite-element-based thermal simulations and downlinked temperature sensor telemetry. The estimation process to recover the lunar gravity field utilizes both a nominal thermal re-radiation accleration history and an apriori error model derived from that plus an off-nominal history, which bounds parameter uncertainties as informed by sensitivity studies.