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David E Smith

Publications and source records attributed to David E Smith.

16 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Gravity Degree-Depth Relationship Using Point Mass Spherical Harmonics

Relationships between the degree of a spherical harmonic model of the gravitational field of a body and the depth of a source expressed as a density contrast can be used to study the structure of features. Here, we show that the gravitational acceleration per spherical harmonic degree of a constant density source has an extremum that depends on the depth of the source. Using the spherical harmonics expansion for a point mass source, we use this to derive a degree-depth relationship. Our relationship resembles an earlier one derived by Bowin (1983), with substantial differences at the lower degrees. We also find that a recent relationship derived by Deng et al. (2022) over-estimates the source depth. The relationship that we derive relates spherical harmonic degree n to depth d for a planet of radius R according to d = (1 - e -1/n+1 )R, which simplifies to d = R/(n + 1) for high degrees. We support our new relationship with synthetic models of a density contrast in a planet. We also show how the differences between our relationship and that of Bowin (1983) affect band-filtered gravity, for example when inspecting the upper 100 km of the Moon. Using point masses in our modeling results in an approximate relationship where in reality sources can be deeper than estimated, since any source contributes to all spherical harmonic degrees. The use of the contribution per individual degree however provides an intuitive relationship between spherical harmonic degree and depth that can be used to place relative bounds on source depths or to determine the bounds on spherical harmonic expansions when band-filtering gravity field models.

Geopotential theory↗
NASA NTRS2022

Geodetic Investigations of the Mission Concept MAGIC to Reveal Callisto’s Internal Structure

Geodetic and geophysical investigations of the Galilean moon Callisto address fundamental questions regarding the formation and evolution of the Jovian system. Callisto's evolution and internal structure appear to significantly differ from the other Jovian satellites. Similarly-sized Ganymede is a highly evolved ice-rock moon with a differentiated interior, intrinsic magnetic field, and abundant surface evidence of internal activity. In contrast, Callisto's surface is ancient, and Galileo spacecraft data suggest its interior is only incompletely differentiated, despite the presumed presence of a sub-surface ocean. These properties make Callisto uniquely able to constrain the timing and nature of the Jovian system formation. The Magnetics, Altimetry, Gravity, and Imaging of Callisto (MAGIC) mission concept is conceived to fully characterize the properties of this enigmatic moon from its deep interior to the icy shell. Three main instruments are included as a scientific payload. Highly accurate measurements of Callisto's topography, magnetic field, and morphology are obtained by the onboard laser altimeter, magnetometer, and camera, respectively. The telecommunication system supports an additional gravity and radio science investigation. Long- and short-wavelength gravity anomalies afford powerful constraints on internal differentiation and the properties of the hydrosphere (water and ice). Comprehensive numerical simulations and covariance analyses of MAGIC mission scenarios presented in this paper show that the gravitational degree-2 normalized coefficients and the pole obliquity enable the determination of the moment of inertia with an accuracy better than 0.015%. The combination of gravity and altimetry measurements acquired by MAGIC are essential to the characterization of Callisto's interior if – as is likely – the degree-2 gravity includes non-hydrostatic terms. MAGIC's radio science data yield the estimation of Callisto's gravity field with spatial resolutions of <100 km. The combination of gravitational and deformation tides that are retrieved by the radio science and altimetry investigations, respectively, leads to the recovery of the rigid ice shell thickness to within ∼3 km. Together these datasets would resolve ambiguities inherent in Galileo flyby data, revealing Callisto's interior structure as well as the existence and properties of its postulated internal ocean.

Antonio Genova↗
NASA NTRS2020

Improved LOLA Elevation Maps for South Pole Landing Sites: Error Estimates and Their Impact on Illumination Conditions

We present new high-resolution topographic models of 4 high-priority lunar south pole landing sites based exclusively on the laser altimetry data acquired by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter. By iteratively adjusting the LOLA tracks to the LOLA-based digital elevation model (LDEM) in a self-consistent fashion, we reduce the orbital geolocation errors by over a factor of 10 such that the new ground track geolocation uncertainty is ~10–20 ​cm horizontally and ~2–4 ​cm vertically over each 16 ​× ​16 km region. These new and improved 5 ​m/pix LDEMs will be useful to constrain higher-resolution topographic models derived from imagery, which are not as well controlled geodetically and which can be hindered by shadows. We developed a method to estimate surface height uncertainty in the new LDEMs, which accounts for the reduced orbital errors and interpolation errors by assuming a fractal behavior for the short-scale topography. The LDEM surface height and slope uncertainties have typical RMS values of ~0.30–0.50 ​m and ~1.5–2.5°, respectively. Finally, we examine how height uncertainties propagate to variations in horizon elevation and thus the predicted illumination conditions at these polar latitudes, and we show how this error characterization can inform landing site studies.

Michael K Barker↗
NASA NTRS2018

Trilogy, A Planetary Geodesy Mission Concept for Measuring the Expansion of the Solar System

The scale of the solar system is slowly changing, likely increasing as a result of solar mass loss, with additional change possible if there is a secular variation of the gravitational constant, G. The measurement of the change of scale could provide insight into the past and the future of the solar system, and in addition a better understanding of planetary motion and fundamental physics. Estimates for the expansion of the scale of the solar system are of order 1.5 cm year(exp -1) AU(exp -1), which over several years is an observable quantity with present-day laser ranging systems. This estimate suggests that laser measurements between planets could provide an accurate estimate of the solar system expansion rate. We examine distance measurements between three bodies in the inner solar system -- Earth's Moon, Mars and Venus -- and outline a mission concept for making the measurements. The concept involves placing spacecraft that carry laser ranging transponders in orbit around each body and measuring the distances between the three spacecraft over a period of several years. The analysis of these range measurements would allow the co-estimation of the spacecraft orbit, planetary ephemerides, other geophysical parameters related to the constitution and dynamics of the central bodies, and key geodetic parameters related to the solar system expansion, the Sun, and theoretical physics.

David E Smith↗
NASA NTRS2018

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 dataset of range measurements for the determination of Mercury's ephemeris. Here we use these precise data collected over seven 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 eta=(-6.6 plus or minus 7.2)x10(exp -5) By assuming a metric theory of gravitation, we retrieved the Post-Newtonian parameter beta = 1 + (-1.6 plus or minus 1.8)x10(exp -5) and the Sun's gravitational oblateness, J(sub 2 solar)=(2.246 plus or minus 0.022)x10(exp -7). Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, G (raised dot)solar mass/G solar mass =(-6.13 plus or minus 1.47)x10(exp -14), which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain |G(raised dot)|/G to be less than 4 x 10(exp -14) yr(exp -1).

Antonio Genova↗
NASA NTRS2017

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 m) 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 m, 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 m). 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.

Erwan Mazarico↗
NASA NTRS2016

Summary of the Results from the Lunar Orbiter Laser Altimeter after Seven Years in Lunar Orbit

In June 2009 the Lunar Reconnaissance Orbiter (LRO) spacecraft was launched to the Moon. The payload consists of 7 science instruments selected to characterize sites for future robotic and human missions. Among them, the Lunar Orbiter Laser Altimeter (LOLA) was designed to obtain altimetry, surface roughness, and reflectance measurements. The primary phase of lunar exploration lasted one year, following a 3-month commissioning phase. On completion of its exploration objectives, the LRO mission transitioned to a science mission. After 7 years in lunar orbit, the LOLA instrument continues to map the lunar surface. The LOLA dataset is one of the foundational datasets acquired by the various LRO instruments. LOLA provided a high-accuracy global geodetic reference frame to which past, present and future lunar observations can be referenced. It also obtained high-resolution and accurate global topography that were used to determine regions in permanent shadow at the lunar poles. LOLA further contributed to the study of polar volatiles through its unique measurement of surface brightness at zero phase, which revealed anomalies in several polar craters that may indicate the presence of water ice. In this paper, we describe the many LOLA accomplishments to date and its contribution to lunar and planetary science.

LRO↗
NASA NTRS2015

The Low-Degree Shape of Mercury

The shape of Mercury, particularly when combined with its geoid, provides clues to the planet’s internal structure, thermal evolution, and rotational history. Elevation measurements of the northern hemisphere acquired by the Mercury Laser Altimeter on the MESSENGER spacecraft, combined with 378 occultations of radio signals from the spacecraft in the planet’s southern hemisphere, reveal the low-degree shape of Mercury. Mercury’s mean radius is 2439.36±0.02 km, and there is a 0.14-km offset between the planet’s centers of mass and figure. Mercury is oblate, with a polar radius 1.65 km less than the mean equatorial radius. The difference between the semimajor and semiminor equatorial axes is 1.25 km with the long axis oriented 15° west of Mercury’s dynamically defined principal axis. Mercury’s geoid is also oblate and elongated, but it deviates from a sphere by a factor of 10 less than Mercury’s shape, implying compensation of elevation variations on a global scale.

Mercury↗
NASA NTRS2014

Constraints on Vesta's Interior Structure Using Gravity and Shape Models from the Dawn Mission

We use the shape and gravity field of Vesta determined from observations of the Dawn spacecraft to place constraints on the asteroid's interior structure. We compute a three-layer interior structure model by minimizing the power of the residual gravity anomaly. The densities of the mantle and crust are based on constraints derived from the Howardite-Eucrite-Diogenite (HED) meteorites. Vesta's present-day shape is not in hydrostatic equilibrium. The Rheasilvia and Veneneia impact basins have a large effect on Vesta's shape and are the main source of deviation from hydrostatic shape. Constraining a pre-giant-impact rotation rate and orientation of the spin axis from an ellipsoidal fit to the parts of Vesta unaffected by the giant impacts, and using the theory of figure, we can constrain the shape of the core. Our solution for Vesta's crust-mantle interface reveals a belt of thick crust around Rheasilvia and Veneneia. The thinnest crust is in the floor of the two basins and in the Vestalia Terra region. Our solution does not reveal an uplift of the crust-mantle boundary to the surface in the largest basins. This, together with the lack of olivine detected by the Visible and Infrared Spectrometer (VIR) data in Rheasilvia and Veneneia, indicates that Vesta's presumed olivine mantle was either not brought to the surface by these large impacts or was covered by ejecta from subsequent impacts.

Interiors↗
NASA NTRS2012

Bright and Dark Polar Deposits on Mercury: Evidence for Surface Volatiles

Measurements of surface reflectance of permanently shadowed areas near Mercury's north pole reveal regions of anomalously dark and bright deposits at 1064-nanometer wavelength. These reflectance anomalies are concentrated on poleward-facing slopes and are spatially collocated with areas of high radar backscatter postulated to be the result of near-surface water ice. Correlation of observed reflectance with modeled temperatures indicates that the optically bright regions are consistent with surface water ice, whereas dark regions are consistent with a surface layer of complex organic material that likely overlies buried ice and provides thermal insulation. Impacts of comets or volatile-rich asteroids could have provided both dark and bright deposits.

Polar Deposits↗
NASA NTRS2012

Gravity Field and Internal Structure of Mercury From MESSENGER

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/MR(exp 2) = 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 C(sub m)/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.

David E Smith↗
NASA NTRS2012

Topography of the Northern Hemisphere of Mercury From MESSENGER Laser Altimetry

Laser altimetry by the MESSENGER spacecraft has yielded a topographic model of the northern hemisphere of Mercury. The dynamic range of elevations is considerably smaller than those of Mars or the Moon. The most prominent feature is an extensive lowland at high northern latitudes that hosts the volcanic northern plains. Within this lowland is a broad topographic rise that experienced uplift after plains emplacement. The interior of the 1500-km-diameter Caloris impact basin has been modified so that part of the basin floor now stands higher than the rim. The elevated portion of the floor of Caloris appears to be part of a quasi-linear rise that extends for approximately half the planetary circumference at mid-latitudes. Collectively, these features imply that long-wavelength changes to Mercury’s topography occurred after the earliest phases of the planet’s geological history.

Maria T Zuber↗
NASA NTRSDate not supplied

New Topographic Products for the Lunar South Pole from the Lunar Orbiter Laser Altimeter (LOLA)

Due to the Moon’s low obliquity and highly cratered topography, its polar environments host regions of extreme illumination conditions. Multiple lines of evidence indicate the presence of geologically stable ice and other volatiles on or below the surface within polar permanently shadowed regions (PSRs). These regions are valuable targets for science and exploration as they hold clues to the history of water in the inner solar system and may hold sufficient reserves for in-situ resource utilization. Standing high above the PSRs, peaks of long-duration sunlight are oases where landed assets can easily generate power and communicate. For these reasons, the lunar south pole is the target of many upcoming missions including NASA’s Artemis program. The Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter (LRO) provides the global geodetic framework with which past, present, and future missions can accurately geolocate their data. Laser altimeters like LOLA are unaffected by shadows and, therefore, provide the most direct measurements of topography within PSRs. Here we present the latest work to improve LOLA’s polar topographic maps and resulting derived products, such as PSR maps, which are crucial tools for science and exploration of the polar regions

Michael K Barker↗