Fractal Analyses of Small Scale Features on Eros
We will discuss the fractal nature of surface structures on asteroid 433 Eros. Additional information is contained in the original extended abstract.
Cheng, A. F.↗
Engineering topics
Smith, D. E.
Publications and source records attributed to Smith, D. E..
Estimating the Libration of Mercury by Remote Sensing of Gravity and Altimetry
One of the most intriguing scientific questions about Mercury is whether the planet possesses a liquid core. One way that this can be ascertained is through the measurement of the longitudinal libration of Mercury about its rotation axis. The MESSENGER (Mercury Surface, Space, Environment, Geochemistry, and Ranging) mission to Mercury will attempt this measurement by deriving the rotation of the planet from remotely sensed observations of the Mercury gravity field and the planet's shape. For a fully fluid core the libration is expected to be an approximately 350-m-amplitude oscillation (at the equator) about the mean rotation of the planet. Thus, the shape of the planet undergoes a librational oscillation in the same way that features on the surface participate in the motion. In this sense altimetric topography can be considered analogous to imaging, with the important exception that for altimetry, the long wavelengths corresponding to low degrees and orders in a spherical harmonic expansion, can be precisely determined from orbital measurements. The rotation of the planet thus introduces a time dependence of the topographic image in an inertial (i.e. fixed) reference frame and the libration is a variation in the planetary rotation rate, manifest as an oscillation of the topographic image. Similarly, gravity measures the distribution of mass within a planet and as such can be viewed as providing a vertically integrated 'image' of the internal density structure. For a librating planet the gravitational field will also reveal a variation in the rotation rate, manifest as an oscillation of the field with respect to an inertial reference frame. While the long-wavelength gravity field contains contributions from the radial distribution of mass with depth, the long wavelength terms are most sensitive to the mass distribution of the deep interior. Thus, both the topography and the gravity independently can be used to determine the (irregular) rotation of a planet, although the topographical method measures the rotation of the crust while the gravity measures the rotation of the distributed mass, and these are not necessarily identical. For example, for a planet that contains a fluid outer core that is effectively decoupled from the mantle the gravity field will not librate in the manner of a solid body. The libration obtained from the variable rotation of the gravity field will represent a combination of contributions due to a librating mantle and a differentially rotating fluid core. Differential rotation of the Earth's inner core had been theoretically predicted from three dimensional geodynamical models and subsequently reported from seismic observations. A difference between the libration of the lithosphere as determined from altimetry and the deep interior as determined from gravity, if it could be detected, might provide further insight into the nature of core-mantle coupling. Additional information is contained in the original extended abstract.
Smith, D. E.↗
A Procedure for Determining the Nature of Mercury's Core
We review past assertions that the determinations of the four parameters, C(20), C(22), theta, phi, are sufficient to determine the size and state of Mercury's core. C(20) and C(22) are gravitational harmonics, theta is Mercury's obliquity and phi is the amplitude of the forced, 88 day period libration in longitude. The upcoming MESSENGER orbiter mission to Mercury with onboard instrumentation capable of measuring these four parameters, and the possibility of precision measurements of Mercury's spin geometry with radar interferometry techniques make a reexamination of this proposal particularly relevant. The two necessary conditions on the core-mantle interaction for the experiment to work are: 1. The core must not follow the 88 day physical librations of the mantle. 2. The core must follow the mantle on the time scale of the 250,000 year precession of the spin in Cassini state 1. We shall assume these two conditions are satisfied to develop the method and later establish the constraints on the core viscosity for which they are satisfied. Proposed mechanisms of core mantle coupling other than a viscous coupling do not frustrate the first condition. The physical libration of the mantle about the mean resonant angular velocity arises from the periodically reversing torque on the permanent deformation as Mercury rotates relative to the Sun. Additional information is contained in the original extended abstract.
Peale, S. J.↗
Crustal Structure of Mars from Mars Global Surveyor Topography and Gravity
In this analysis we invert global models of Mars' topography from Mars Orbiter Laser Altimeter (MOLA) and gravity from Doppler tracking obtained during the mapping mission of Mars Global Surveyor (MGS). We analyze the distribution of Martian crust and discuss implications for Mars' thermal history.
Zuber, M. T.↗
Seasonal Record of Cloud Activity Observed by MOLA
After a quarter billion laser shots, Mars Orbiter Laser Altimeter (MOLA) has now recorded more atmospheric observations alone than all previous planetary lidar missions have returned in total.
Neumann, G. A.↗
The Density Structure of the Martian Thermosphere from MGS Drag Measurements During SPO
We present measurements of the density of the Martian atmosphere made from the observed orbital decay of MGS during SPO.
Tracadas, P. W.↗
The gravity field of Mars: results from Mars Global Surveyor
Observations of the gravity field of Mars reveal a planet that has responded differently in its northern and southern hemispheres to major impacts and volcanic processes. The rough, elevated southern hemisphere has a relatively featureless gravitational signature indicating a state of near-isostatic compensation, whereas the smooth, low northern plains display a wider range of gravitational anomalies that indicates a thinner but stronger surface layer than in the south. The northern hemisphere shows evidence for buried impact basins, although none large enough to explain the hemispheric elevation difference. The gravitational potential signature of Tharsis is approximately axisymmetric and contains the Tharsis Montes but not the Olympus Mons or Alba Patera volcanoes. The gravity signature of Valles Marineris extends into Chryse and provides an estimate of material removed by early fluvial activity.
long duration↗
MOLA: The Future of Mars Global Cartography
The MGS Orbiter is carrying the high-precision Mars Orbiter Laser Altimeter (MOLA) which, when combined with precision reconstructed orbital data and telemetered attitude data, provides a tie between inertial space and Mars-fixed coordinates to an accuracy of 100 m in latitude / longitude and 10 m in radius (1 sigma), orders of magnitude more accurate than previous global geodetic/ cartographic control data. Over the 2 year MGS mission lifetime, it is expected that over 30,000 MOLA Global Cartographic Control Points will be produced to form the basis for new and re-derived map and geodetic products, key to the analysis of existing and evolving MGS data as well as future Mars exploration. Additional information is contained in the original extended abstract.
Duxbury, T. C.↗
The Removal of Periodic Gravitational Perturbations from Mars Global Surveyor's Science Phasing Orbits Applied to the Study of the Martian Exosphere
The martian exosphere and upper atmosphere exert measurable drag on the Mars Global Surveyor (MGS) spacecraft. Using the Goddard Space Flight Center's GEODYN orbit determination software, the science phasing orbits (SPO) were analyzed to determine the atmospheric drag and hence, measure the average density near the orbits' perifocus (170-180 km altitude above high northern latitudes). Future work will include the gravity calibration and mapping periods as well. Additional information is contained in the original extended abstract.
Tracadas, P. W.↗
Preliminary Correlations of Gravity and Topography from Mars Global Surveyor
The Mars Global Surveyor (MGS) spacecraft is currently in a 400-km altitude polar mapping orbit and scheduled to begin global mapping of Mars in March of 1999. Doppler tracking data collected in this Gravity Calibration Orbit prior to the nominal mapping mission combined with observations from the MGS Science Phasing Orbit in Spring - Summer 1999 and the Viking and mariner 9 orbiters has led to preliminary high resolution gravity fields. Spherical harmonic expansions have been performed to degree and order 70 and are characterized by the first high spatial resolution coverage of high latitudes. Topographic mapping by the Mars Orbiter Laser Altimeter on MGS is providing measurements of the height of the martian surface with sub-meter vertical resolution and 5-30 m absolute accuracy. Data obtained during the circular mapping phase are expected to provide the first high resolution measurements of surface heights in the southern hemisphere. The combination of gravity and topography measurements provides information on the structure of the planetary interior, i.e. the rigidity and distribution of internal density. The observations can also be used to address the mechanisms of support of surface topography. Preliminary results of correlations of gravity and topography at long planetary wavelengths will be presented and the implications for internal structure will be addressed.
Zuber, M. T.↗
The global topography of Mars and implications for surface evolution
Elevations measured by the Mars Orbiter Laser Altimeter have yielded a high-accuracy global map of the topography of Mars. Dominant features include the low northern hemisphere, the Tharsis province, and the Hellas impact basin. The northern hemisphere depression is primarily a long-wavelength effect that has been shaped by an internal mechanism. The topography of Tharsis consists of two broad rises. Material excavated from Hellas contributes to the high elevation of the southern hemisphere and to the scarp along the hemispheric boundary. The present topography has three major drainage centers, with the northern lowlands being the largest. The two polar cap volumes yield an upper limit of the present surface water inventory of 3.2 to 4.7 million cubic kilometers.
Water↗
Regional Elevations in the Southern Hemisphere of Mars From the Mars Orbiter Laser Altimeter
The Mars Orbiter Laser Altimeter (MOLA) is an instrument on the Mars Global Surveyor (MGS) spacecraft that is currently providing the first high vertical and spatial resolution topographic measurements of surface elevations on Mars. The shot size in the mapping orbit is about 100 m and the shot-to-shot spacing is 330 m. The instrument has a vertical precision of 37.5 cm and a vertical accuracy that depends on the radial accuracy of the MGS orbit that is currently in the range 5-30 km. The initial focus on observations in the nominal mapping mission will be on the southern hemisphere, which was not sampled during the MGS aerobraking hiatus and Science Phasing orbits. During the first several weeks of global mapping there will be emphasis on producing a digital terrain model (DTM) of the Mars '98 landing site.
Smith, D. E.↗
Orbit Determination for Mars Global Surveyor During Mapping
The Mars Global Surveyor (MGS) spacecraft reached a low-altitude circular orbit on February 4, 1999, after the termination of the second phase of aerobraking. The MGS spacecraft carries the Mars Orbiter Laser Altimeter (MOLA) whose primary goal is to derive a global, geodetically referenced 0.2 deg x 0.2 deg topographic grid of Mars with a vertical accuracy of better than 30 meters. During the interim science orbits in the' Hiatus mission phase (October - November 1997), and the Science Phasing Orbits (March - April, 1998, and June - July 1998) 208 passes of altimeter data were collected by the MOLA instrument. On March 1, 1999 the first ten orbits of MOLA altimeter data from the near-circular orbit were successfully returned from MGS by the Deep Space Network (DSN). Data will be collected from MOLA throughout the Mapping phase of the MCS mission, or for at least one Mars year (687 days). Whereas the interim orbits of Hiatus and SPO were highly eccentric, and altimeter data were only collected near periapsis when the spacecraft was below 785 km, the Mapping orbit of MGS is near circular, and altimeter data will be collected continuously at a rate of 10 Hz. The proper analysis of the altimeter data requires that the orbit of the MGS spacecraft be known to an accuracy comparable to that of the quality of the altimeter data. The altimeter has an ultimate precision of 30 cm on mostly flat surfaces, so ideally the orbits of the MGS spacecraft should be known to this level. This is a stringent requirement, and more realistic goals of orbit error for MGS are ten to thirty meters. In this paper we will discuss the force and measurement modelling required to achieve this objective. Issues in force modelling include the proper modelling of the gravity field of Mars, and the modelling of non-conservatives forces, including the development of a 'macro-model', in a similar fashion to TOPEX/POSEIDON and TDRSS. During Cruise and Aerobraking, the high gain antenna (HGA) was stowed on the +X face of the spacecraft. On March 29, 1999 the HGA will be deployed on a meter long boom which will remain Earth-pointing while the instrument panel (including the MOLA instrument) remains pointed at nadir. The tracking data must be corrected for the regular motion of the high gain antenna with respect to the center of mass, and the success of the MGS determination during Mapping will depend on correctly accounting for this offset in the measurement model.
Lemoine, F. G.↗
Observations of the north polar region of Mars from the Mars orbiter laser altimeter
Elevations from the Mars Orbiter Laser Altimeter (MOLA) have been used to construct a precise topographic map of the martian north polar region. The northern ice cap has a maximum elevation of 3 kilometers above its surroundings but lies within a 5-kilometer-deep hemispheric depression that is contiguous with the area into which most outflow channels emptied. Polar cap topography displays evidence of modification by ablation, flow, and wind and is consistent with a primarily H2O composition. Correlation of topography with images suggests that the cap was more spatially extensive in the past. The cap volume of 1.2 x 10(6) to 1.7 x 10(6) cubic kilometers is about half that of the Greenland ice cap. Clouds observed over the polar cap are likely composed of CO2 that condensed out of the atmosphere during northern hemisphere winter. Many clouds exhibit dynamical structure likely caused by the interaction of propagating wave fronts with surface topography.
Flight Experiment↗
Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter
The first 18 tracks of laser altimeter data across the northern hemisphere of Mars from the Mars Global Surveyor spacecraft show that the planet at latitudes north of 50 degrees is exceptionally flat; slopes and surface roughness increase toward the equator. The polar layered terrain appears to be a thick ice-rich formation with a non-equilibrium planform indicative of ablation near the periphery. Slope relations suggest that the northern Tharsis province was uplifted in the past. A profile across Ares Vallis channel suggests that the discharge through the channel was much greater than previously estimated. The martian atmosphere shows significant 1-micrometer atmospheric opacities, particularly in low-lying areas such as Valles Marineris.
unmanned↗
An Overview of Observations of Mars' North Polar Region From the Mars Global Surveyor Laser Altimeter
Since its arrival at Mars on September l5, 1997, the Mars Global Surveyor (MGS) has been in a near-polar elliptical orbit, with the orbital eccentricity decreasing during orbital periapse passes where the spacecraft aerobrakes through the martian atmosphere. The Mars Orbiter Laser Altimeter (MOLA), an instrument on the MGS, has the ability to range to the martian surface during nonaerobraking passes. MOLA can operate whenever the range from the spacecraft to the surface is less than 786 km, with the limit determined by the number of bits encoded for the range measurement During the capture orbit, aerobraking hiatus, and science phasing orbit (SPO) mission phases, MOLA acquired approximately 200 profiles across the northern hemisphere of Mars and provided more than 2,000,000 measurements of the radius of the planet. These observations cover the region from the north pole to about 10 degrees S latitude with a precision of a few tens of centimeters and an accuracy (at present) of about 30 in. Absolute accuracy of the elevations is limited by the knowledge of the MGS orbits; these should improve later in the mission due to a more optimal tracking geometry, an improved gravitational field, and the use of the high-gain antenna once the spacecraft achieves its approximately 400-km-altitude circular mapping orbit. MOLA measurements so far show a planet with a low, flat high-latitude region in the north and a higher, topographically rougher terrain nearer the equator. The north polar cap stands approximately 2-3 km above the surrounding terrain and displays deep chasms and complex structure. MOLA measurements of elevation, 1064-nm reflectivity, and backscattered pulse width indicate that the layered terrains are composed mainly of ice.
Smith, D. E.↗
Lunar Basins: New Evidence from Gravity for Impact-Formed Mascons
The prominent gravity highs (mascons) associated with uncompensated mass anomalies in lunar mare basins are a dramatic expression of the present-day rigidity of the lunar lithosphere. First discovered in Lunar Orbiter tracking data, these about 350-mGal gravity highs have been redetermined from the analysis of Clementine and historical tracking. These highs coincide with topographic lows, indicating nonisostatic support. One of the rediscoveries of this analysis is the encirclement of the highs by substantial negative anomalies over topographic highs. Recent gravity fields are providing the increased resolution necessary to determine the causes of this unique mascon signature. The compensation of the basin anomalies remains controversial. The mascon highs have long been interpreted as the result of mare loading, subsequent to the decay of residual stresses resulting from the impact. Substantially more mare fill is required to produce mascon highs than has been inferred on geological grounds, and the amount of near-surface mass deficit required to produce a gravity most exceeds bounds inferred from terrestrial examples. This problem is most acute for the youngest basin, Orientale. Recent gravity fields from Lunar Prospector have suggested mascon highs associated with nonmare basins such as Mendel-Rydberg, or minimally filled basins like Humboldtianum, further calling this explanation into question. We suggest that the mascon gravity signal is produced by a combination of crustal thickness changes, manifested by central mantle uplift, outward displacement of crust, and downward flexure of the lithosphere under mare loading. The mantle uplift is superisostatic, maintained by residual stresses resulting from the process of impact cratering and modification. In particular, the process of crater collapse and mantle rebound terminates abruptly, leaving the mantle plug in a non-equilibrium state, surrounded by a ring of thickened crust. Viscous relaxation over geological timescales has erased some but not all of the signature of the impact process. Mantle uplift inferred from gravity modeling is inversely correlated with age. While the oldest basins such as South Pole Aitken are mainly compensated isotatically, the younger basins appear to have been in a state of superisostatic loading prior to mare emplacement. If this is true, this places an important constraint on the impact process at basin scales. The idea that rebound of the transient crater via acoustic fluidization may freeze substantial stresses imcomplete to this day, may be tested by examining the gravity signatures of major basins on terrestrial bodies. The moon provides the clearest resolved examples to date, but uncertainty in gravity knowledge remains problematic.
Neumann, Gregory A.↗
Inferences About the Early Moon From Gravity and Topography
Recent spacecraft missions to the Moon have significantly improved our knowledge of the lunar gravity and topography fields, and have raised some new and old questions about the early lunar history. It has frequently been assumed that the shape of the Moon today reflects an earlier equilibrium state and that the Moon has retained some internal strength. Recent analysis indicating a superisostatic state of some lunar basins lends support to this hypothesis. On its simplest level, the present shape of the Moon is slightly flattened by 2.2 +/- 0.2 km while its gravity field, represented by an equipotential surface, is flattened only about 0.5 km. The hydrostatic component to the flattening arising from the Moon's present day rotation contributes only 7 m. This difference between the topographic shape of the MOon and the shape of its gravitational equipotential has frequently been explained as the "memory" of an earlier moon that was rotating faster and had a correspondingly larger hydrostatic flattening. To obtain this amount of hydrostatic flattening from rotation alone, and accounting for the contribution of the present-day gravity field, the Moon's rotation rate would need to be about 15x greater than at present, leading ot a period of < 2 days. Maintaining its synchronous rotation with Earth would require a radius for the Moon's orbit of approximately 9 Earth Radii. Unfortunately, our confidence in the observed lunar flattening is not as great as we would like. The uncertainty of .02 km may not properly reflect the limitations of the Clementine dataset, which did not sample poleward of latitudes 81 N and 79 S. Also, the large variation of topography +/- 8 km seen on the MOon dwarfs our estimate fo the flattening. Further the lunar south pole is on the edge of, or possibly inside the massive deep, South Pole-Aitken Basin. Thus, polar radii could be underestimated. This would yield a smaller flattening, which would imply a greater lunar rotation period and orbital radius. However, Basin compensation states and analyses of support and relaxation of topography at long wavelengths point to a lunar shape that has retained a flattening from an earlier faster rotation period.
Smith, D. E.↗