The Crust of the Moon as Seen by GRAIL Wieczorek, Mark A.; Neumann, Gregory A.; Nimmo, Francis ...
Science,
02/2013, Volume:
339, Issue:
6120
Journal Article
Peer reviewed
Open access
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.
•Vesta spherical harmonic gravity field to degree 20 (42-km resolution).•Vesta pole determination error<0.0001 deg.•Detection of combined Vesta pole precession and nutation.•Vesta ephemeris ...improvement to 10-m in Earth-Vesta direction.
The Vesta gravity field and related physical parameters have been precisely measured using 10-months of radiometric Doppler and range data and optical landmark tracking from the Dawn spacecraft. The gravity field, orientation parameters, landmark locations, and Vesta’s orbit are jointly estimated. The resulting spherical harmonic gravity field has a half-wavelength resolution of 42km (degree 20). The gravitational mass uncertainty is nearly 1 part in 106. The inertial spin pole location is determined to better than 0.0001° and the uncertainty in the rotation period has been reduced by nearly a factor of 100. The combined precession and nutation of the pole of Vesta has been detected with angular rates about 70% of expected values, but not well enough to constrain the moment of inertia. The optical landmark position estimates reduce the uncertainty in the center-of-mass and center-of-figure offset to 10m. The Vesta ephemeris uncertainty during the Dawn stay was reduced from 20km to better than 10m in the Earth–Vesta direction.
The Mercury gravity field, spin-pole axis, rotation period, Love number, and ephemeris have been determined using the complete four years of MESSENGER tracking data from March 2011 to April 2015. The ...pole location and obliquity (1.99 ± 0.12 arcmin) is consistent with previous determinations. Since MESSENGER was in a highly elliptical orbit with periapsis in the far northern hemisphere, the gravity resolution over the surface of Mercury varies greatly from harmonic degree n = 12 at the south pole to n = 154 in a small region near the north pole which was covered with exceptionally low periapsis data near the end of mission. The gravity field MESS160A is determined to n = 160 and shows notable improvement in the correlation with topography. Three different constraint methods are used to generate the gravity field. The nominal method is a Kaula power law of 5 × 10−5/n2 to constraint the coefficients. One alternate constraint uses surface acceleration measurements, which only constrains the unobserved portion of the gravity field. The other constraint method sets the gravity uncertainties using the harmonic spectrum of the gravity derived from topography. The Mercury tidal Love number solution k2 = 0.53 ± 0.03 is larger than previous results but within suggested error bounds. In addition, the technique for estimating the Mercury ephemeris is discussed.
•Mercury gravity field has a maximum resolution of n = 154 or 50 km.•Mercury tidal response Love number estimate is k2 = 0.53.•Localized studies show larger admittance and smoother GTR results.•The orbit of Mercury is converged with an iterative process with the gravity field.
The solar tidal deformation of Mars, measured by its k2potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k2of$0.153 \pm 0.017$is large ...enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J3, given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.
Ceres’ gravity field and rotational parameters have been precisely measured using 1.5 years of radiometric Doppler and range data and optical landmark tracking from the Dawn spacecraft in orbit about ...the dwarf planet. As was the case with Dawn at Vesta, the gravity field, orientation parameters, landmark locations, and Ceres’ orbit are jointly estimated in a global solution. Even though Dawn's radio science investigation at Ceres was complicated by additional thrusting for attitude control, the resulting spherical harmonic gravity field has a half-wavelength resolution of up to 82 km (degree 18) near the equator, which is similar harmonic resolution to that of Vesta. The gravity field is consistent with Airy isostatic compensation, and this model assumption limits Ceres’ crustal density to be between 1200 and 1600 kg/m3 for two-layer and three-layer models with mean crustal thickness between 27 and 43 km. The compensation depth is determined using admittance between gravity and gravity from topography and is superior to admittance between gravity and topography. The gravitational mass of Ceres is determined to better than 0.002% (GMCeres = 62.62736 ± 0.00040 km3/s2), the spin pole location is improved by 10× over previous results with right ascension (α = 291.427°) and declination (δ = 66.760°) uncertainty less than 0.001°, and the rotation rate is improved by ∼100× over previous determinations from Hubble Space Telescope (HST) images. Ceres’ heliocentric orbit has also been improved, with about 17 months of precision range measurements reducing ephemeris uncertainties to about 10 m during the Dawn timeframe.
Dawn at Vesta: Testing the Protoplanetary Paradigm Russell, C. T.; Raymond, C. A.; Coradini, A. ...
Science (American Association for the Advancement of Science),
05/2012, Volume:
336, Issue:
6082
Journal Article
Peer reviewed
The Dawn spacecraft targeted 4 Vesta, believed to be a remnant intact protoplanet from the earliest epoch of solar system formation, based on analyses of howardite-eucrite-diogenite (HED) meteorites ...that indicate a differentiated parent body. Dawn observations reveal a giant basin at Vesta's south pole, whose excavation was sufficient to produce Vesta-family asteroids (Vestoids) and HED meteorites. The spatially resolved mineralogy of the surface reflects the composition of the HED meteorites, confirming the formation of Vesta's crust by melting of a chondritic parent body. Vesta's mass, volume, and gravitational field are consistent with a core having an average radius of 107 to 113 kilometers, indicating sufficient internal melting to segregate iron. Dawn's results confirm predictions that Vesta differentiated and support its identification as the parent body of the HEDs.
•Processed ∼38,000 images acquired by the Dawn spacecraft to determine Ceres’ shape.•High-resolution global shape of Ceres was determined using stereophotoclinometry.•Highly accurate spin-pole axis ...and rotation rate of Ceres were determined.•The average height error of the final global Ceres topography model is about 10 m.•About 89% of the Ceres topography model has the total height error below 20 m.
We present a high-resolution global shape model of Ceres determined using the stereophotoclinometry technique developed at the Jet Propulsion Laboratory by processing Dawn's Framing Camera data acquired during Approach to post-Low Altitude Mapping Orbit (LAMO) phases of the mission. A total of about 38,000 images were processed with pixel resolutions ranging from 35.6 km/pixel to 35 m/pixel and the final global shape model was produced with 100-m grid spacing. The final SPC-derived topography was computed relative to the (482 km, 482 km, 446 km) mean ellipsoid, which ranges from −7.3 km to 9.5 km. For the purpose of validation, we performed various error analyses to assess and quantify realistic uncertainties in the derived topography, such as dividing the data into different subsets and re-computing the entire topography. Based on these studies, we show that the average total height error of the final global topography model is 10.2 m and 88.9% of the surface has the total height error below 20 m. We also provide improved estimates of several physical parameters of Ceres. The resulting GM estimate is (62.62905 ± 0.00035) km3/s2, or the mass value of (938.392 ± 0.005) × 1018 kg. The volume estimate is (434.13 ± 0.50) × 106 km3 with a volumetric mean radius of 469.72 km. Combined with the mass estimate, the resulting bulk density is (2161.6 ± 2.5) kg/m3. Other improved parameters include the pole right ascension, α0 = (291.42763 ± 0.0002)°, pole declination, δ0 = (66.76033 ± 0.0002)°, and prime meridian and rotation rate of (W0 = 170.309 ± 0.011)° and (dW/dt = 952.1532635 ± 0.000002) deg/day, respectively. Also, for geophysical and geological studies, we provide spherical harmonic coefficients and a gravitational slope map derived from the global shape model.
•A 20th degree ellipsoidal harmonic gravity field of Vesta is determined.•Gravity anomalies are mapped to the Brillouin ellipsoid of Vesta (304×289×247-km).•Average crustal thicknesses of 55.5km and ...22.4km are subsequently explored.•The Bouguer gravity anomaly is minimized for the crustal density of 2970kg/m3.•Both gravity and geochemical models of Vesta give an excellent level of mutual consistency.
A 20th degree ellipsoidal harmonic gravity field of Vesta is determined by processing radiometric Doppler and range data from the Dawn mission. The gravity field shows sensitivity up to degree 18 and the coefficients are globally determined on average to degree 15. Gravity anomalies are mapped to the Brillouin ellipsoid (304×289×247-km), which is a substantially closer fit to the surface than the reference ellipsoid (290×290×265-km) used to map the conventional spherical harmonic series, especially near the poles. Two models of internal structure are subsequently explored, in which density variations are permitted in the uppermost layer (i.e., crust) in order to explain Vesta’s local gravitational signature. These models include the case of a two-layer model with an average crustal thickness of 55.5km and a three-layer model with an average crustal thickness of 22.4km. For both two-layer and three-layer scenarios, the Bouguer gravity anomaly is minimized for a crustal density of 2970kg/m3. The remaining Bouguer anomalies can be explained by lateral crustal density variation of 2310–3440kg/m3 and 2660–3240kg/m3 for the 22.4km and 55.5km crustal thickness models, respectively. The general trend of the estimated lateral crustal densities for the two cases is very similar, with a wider range for the 22.4km case due to a thinner crust. This indicates that a thick crust (e.g., 55.5km) would be more favorable for minimizing the range of lateral crustal density variations. Consideration of independent geochemical and petrological constraints suggests that a three-layer model is a more appropriate representation of Vesta’s internal structure, despite the fact that two-layer models provide a satisfactory fit to gravity data alone. In detail, it is found that densities derived from gravity data assuming three-layer models and those derived from the howardite–eucrite–diogenite meteorites and estimates of plausible bulk-Vesta composition show an excellent level of mutual consistency.
With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes ...the measurement of the seasonal changes in the gravity coefficients (e.g.,
J
¯
2
,
J
¯
3
,
C
¯
21
,
S
¯
21
,
C
¯
31
,
S
¯
31
) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of
C
¯
21
and
S
¯
21
. A strong annual signature is observed in
C
¯
21
, and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data Yoder et al., 2003. Science 300, 299–303, giving a combined solution of
k
2
=
0.152
±
0.009
using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos
GM
=
(
7.16
±
0.005
)
×
10
−4
km
3
/
s
2
and Deimos
GM
=
(
0.98
±
0.07
)
×
10
−4
km
3
/
s
2
. Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.
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