Engineering topics
Bills, Bruce G.
Publications and source records attributed to Bills, Bruce G..
Explorations of Psyche and Callisto Enabled by Ion Propulsion
Recent developments in ion propulsion (specifically solar electric propulsion - SEP) have the potential for dramatically reducing the transportation cost of planetary missions. We examine two representative cases, where these new developments enable missions which, until recently, would have required resouces well beyond those allocated to the Discovery program. The two cases of interest address differentiation of asteroids and large icy satellites
Long Period Variations in Tidal and Librational Forcing of Europa
The gravitational field of Jupiter exerts a profound influence on the energy balance, thermal evolution, and stress regime of Europa. It widely appreciated that dissipation associated with the spheroidal tidal deformation is a major source of heat. Another possibly important source of dissipation is the toroidal deformation field associated with forced librations. Both tidal and librational deformations depend on the distance and direction Jupiter, as seen from Europa. These quantities vary with time as a result of the finite values of orbital eccentricity and spin pole obliquity, though the obliquity effects have been ignored in most previous studies. Variations in eccentricity and obliquity of the Galilean satellites occur on a very wide range of time scales, as angular momentum is exchanged among the orbital and rotational components of the coupled system. The orbital periods are only a few days in length, and the secular changes in orbital period associated with tidal and librational dissipation have characteristic time scales of 10-9 years or longer. On intermediate time scales, the satellites perturb each other, and the Sun and Saturn make additional contributions. The present values of satellite orbital inclinations and obliquities are not particularly representative their respective longer term variations. As a result, the tidal stress and dissipation regimes at present may not provide adequate explanation of the sources of surface features seen on the satellites.
How Does Titan Retain a Finite Orbital Eccentricity?
There is appreciable evidence for a significant hydrocarbon ocean on the surface of Titan. However, it has long been appreciated that tidal dissipation within a putative hydrocarbon ocean on Titan easily yields an orbital eccentricity damping time e which is short compared to the age of the solar system. Unless Titan s present eccentricity (e = 0.0288) were acquired recently, it requires that either: the ocean has a configuration which limits dissipation, or some mechanism exists which effectively maintains the eccentricity against dissipative damping. We argue for the latter. Specifically, the proximity of Jupiter and Saturn to a 5:2 mean motion resonance may provide a sufficient excitation source, and thereby effectively remove dynamical constraints on the dissipation and configuration of the Titan ocean.
Topography of the Flattest Surface on Earth: using ICESAT, GPS, and MISR to Measure Salt Surface Topography on Salar de Uyuni, Bolivia
Salt flats are aptly named: they are composed largely of salt, and are maintained as nearly equipotential surfaces via frequent flooding. The salar de Uyuni, on the Altiplano in southwestern Bolivia, is the largest salt flat on Earth, with an area of 9,800 sq km. Except for a few bedrock islands, it has less than 40 cm of relief. The upper-most salt unit averages 5 m thick and contains 50 cu km of nearly pure halite. It includes most of the salt that was in solution in paleolake Minchin, which attained a maximum area of 60,000 sq km and a maximum depth of 150 m, roughly 15 kyr ago. Despite approx. 10 m of differential isostatic rebound since deposition, the salar surface has been actively maintained as an extraordinarily flat and smooth surface by annual flooding during the rainy season. We have used the strong optical absorption properties of water in the visible band to map spatial variations in water depth during a time when the salar was flooded. As water depth increases, the initially pure white surface appears both darker and bluer. We utilized MISR images taken during the interval from April to November 2001. The red and infra-red bands (672 and 867 nm wavelength) were most useful since the water depth is small and the absorption at those wavelengths is quite strong. Nadir pointed MISR images have 275 m spatial resolution. To aid in our evaluation of water depth variations over the saiar surface, we utilized two sources of direct topographic measurements: several ICESAT altimetry tracks cross the area, and a 40x50 km GPS grid was surveyed to calibrate ICESAT. A difficulty in using these data types is that both give salt surface elevations relative to the ellipsoid, whereas the water surface will, in the absence of wind or tidal disturbances, follow an equipotential surface. Geoid height is not known to the required accuracy of a few cm in the central Andes. As a result, before comparing optical absorption from MISR to salt surface topography from GPS or ICESAT, we removed the longest wavelengths from both.
A Solar System Survey of Forced Librations in Longitude
Forced librations are periodic rotational rate variations due to gravitational interactions with an orbital partner. We have developed an analytic theory capable of calculating expected amplitudes of forced librations for nonresonant rotators as well as for bodies existing in a spin-orbit resonance. The theory has been applied to 34 solar system bodies, including terrestrial planets, planetary satellites, and the asteroid Eros. Parameters governing libration amplitude are the body s orbital eccentricity, moment difference, and the ratio of its spin rate to its orbital rate. In each case the largest libration amplitude is associated with the forcing frequency 2 (p - 1) n, where n is the orbital mean motion and p is the spin/orbit rate ratio. This dominant frequency is simply semidiurnal as seen from the position of the torquing body. The maximum libration angular amplitude is 1.3 x 10(exp -2) radians for Thebe, and the maximum mean equatorial displacement is 1.4 km for Mimas.
Spatial and Temporal Patterns of Tidal Dissipation in Synchronous Satellites
Tidal heating is an important energy source for several solar system bodies, and there is a wide-spread perception that the pattern of surface heat flow is diagnostic of internal structure. We wish to clarify that situation. Our analysis depends upon two important assumptions: First, that heat transport is dominated by conduction. Second, that the body can be modeled by a sequence of spherically symmetric layers, each with a linear visco-elastic rheology. Under these assumptions, surface heat flow patterns in tidally dominated satellites will reflect radially integrated dissipation patterns. For synchronously rotating satellites with zero obliquity, this pattern depends quite strongly on orbital eccentricity but relatively little on purely radial variations in internal structure. The total amount of heat generated within the body does depend sensitively on internal structure, but the spatial pattern is rather insensitive to structure, especially at low orbital eccentricities.
The State and Future of Mars Polar Science and Exploration
As the planet's principal cold traps, the martian polar regions have accumulated extensive mantles of ice and dust that cover individual areas of approx. 10(exp 6)sq km and total as much as 3-4 km thick. From the scarcity of superposed craters on their surface, these layered deposits are thought to he comparatively young-preserving a record of the seasonal and climatic cycling of atmospheric CO2, H2O, and dust over the past approx. 10(exp 5)-10(exp 8) years. For this reason, the martian polar deposits may serve as a Rosetta Stone for understanding the geologic and climatic history of the planet-documenting variations in insolation (due to quasiperiodic oscillations in the planet's obliquity and orbital elements), volatile mass balance, atmospheric composition, dust storm activity, volcanic eruptions, large impacts, catastrophic floods, solar luminosity, supernovae, and perhaps even a record of microbial life. Beyond their scientific value, the polar regions may soon prove important for another reason-providing a valuable and accessible reservoir of water to support the long-term human exploration of Mars. In this paper we assess the current state of Mars polar research, identify the key questions that motivate the exploration of the polar regions, discuss the extent to which current missions will address these questions, and speculate about what additional capabilities and investigations may be required to address the issues that remain outstanding.
Climate-Rotation Feedback on Mars
A new model is presented for the coupled evolution of climate and rotation, as applied to Mars. It has long been appreciated that changes in the orbital and rotational geometry of Mars will influence the seasonal and latitudinal pattern of insolation, and this will likely dominate climatic fluctuations on time scales of 10(exp 5) to 10(exp 7) years. Equally important, but less widely appreciated, is the influence climatic change can have on rotational dynamics. The primary means by which climate influences rotation is via its influence on transport of mass (volatiles and dust) into and out of the polar regions. Many important issues remain unresolved: What are the ages of the polar caps? What climatic periods are recorded in the polar layered deposits? What is the long term obliquity history? Additional information is contained in the original extended abstract.
Climate-Rotation Feedback on Mars
A new model is presented for the coupled evolution of climate and rotation, as applied to Mars. It has long been appreciated that changes in the orbital and rotational geometry of Mars will influence the seasonal and latitudinal pattern of insolation [1-5], and this will likely dominate climatic fluctuations on time scales of 10(exp 5) to 10(exp 7) years [6-9]. Equally important, but less widely appreciated, is the influence climatic change can have on rotational dynamics. The primary means by which climate influences rotation is via its influence on transport of mass (volatiles and dust) into and out of the polar regions. Many important issues remain unresolved: What are the ages of the polar caps? What climatic periods are recorded in the polar layered deposits? What is the long term obliquity history?
Lunar and Solar Torques on the Oceanic Tides
A general framework for calculating lunar and solar torques on the oceanic tides is developed in terms of harmonic constituents. Axial torques and their associated angular momentum and earth-rotation variations are deduced from recent satellite-altimeter and satellite-tracking tide solutions. Torques on the prograde components of the tide produce the familiar secular braking of the rotation rate. The estimated secular acceleration is approximately -1300 sec/century(sup 2) (less 4% after including atmospheric tides); the implied rate of change in the length of day is 2.28 milliseconds/century. Torques on the retrograde components of the tide produce periodic rotation variations at twice the tidal frequency. Interaction torques, e.g. solar torques on lunar tides, generate a large suite of rotation-rate variations at sums and differences of the original tidal frequencies. These are estimated for periods from 18.6 years to quarter-diurnal. At subdaily periods the angular momentum variations are 5 to 6 orders of magnitude smaller than the variations caused by ocean tidal currents.
Lunar and Solar Torques on the Oceanic Tides
Brosche and Seiler recently suggested that direct lunar and solar tidal torques on the oceanic tides play a significant role in the earth's short-period angular momentum balance ("short-period" here meaning daily and sub-daily). We reexamine that suggestion here, concentrating on axial torques and hence on variations in rotation rate. Only those spherical harmonic components of the ocean tide having the same degree and order as the tidal potential induce nonzero torques. Prograde components (those moving in the same direction as the tide-generating body) produce the familiar secular braking of the earth's rotation. Retrograde components, however, produce rapid variations in UTI at twice the tidal frequency. There also exist interaction torques between tidal constituents, e.g. solar torques on lunar tides. They generate UTI variations at frequencies equal to the sums and differences of the original tidal frequencies. We give estimates of the torques and angular momentum variations for each of the important regimes, secular to quarter-diurnal. For the M(sub 2) potential acting on the M(sub 2) ocean tide, we find an associated angular momentum variation of amplitude 3 x 10(exp 19) N m. This is 5 to 6 orders of magnitude smaller than the angular momentum variations associated with tidal currents. We conclude that these torques do not play a significant role in the short-period angular momentum balance.
Climate Rotation Feedback on Mars
It has long been appreciated that changes in the orbital and rotational geometry of Mars will influence the seasonal and latitudinal pattern of insolation [1-5], and this will likely dominate climatic fluctuations on time scales of 101 to 107 years (6-9]. Equally important, but less widely appreciated, is the influence climatic change can have on rotational dynamics. The primary means by which climate influences rotation is via its influence on transport of mass (volatiles and dust) into and out of the polar regions. Both the rate and direction of Mars rotation can be changed by these mass fluxes, but only the directional changes are climatically relevant.
An Inversion of Gravity and Topography for Mantle and Crustal Structure on Mars
Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree less than or equal to 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees greater than or equal to 4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the model's input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantle's viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature.
Viscosity estimates for the crust and upper mantle from patterns of lacustrine shoreline deformation in the Eastern Great Basin
The deformed shorelines of Lake Bonneville constitute a classic source of information on lithospheric elastic thickness and upper mantle viscosity. We describe and apply a new model to a recently augmented data set. New data better constrain both the complex spatio-temporal pattern of the lake load and the crustal deformation response to that load. The history of lake level fluctuations has been significantly refined and somewhat modified. This is due to both more radiocarbon dates from within the Bonneville basin and to an improved calibration of the radiocarbon timescale itself. The data which constrain the crustal deformation pattern consist of ages and shoreline elevations from several hundred points which sample three major levels of Lake Bonneville and corresponding elevations from the high stands of three smaller lakes situated to the west of Lake Bonneville. The geometry of the Earth model incorporates an arbitrary number of layers overlying a half-space, and the rheology of each level can accommodate an arbitrary number of Maxwell viscoelastic elements in parallel. The inverse modeling comprises three complementary approaches: for the simplest configurations, we performed a direct search of the parameter space and delineated the irregular boundary of the subspace of acceptable models. For more complex configurations, we constrained the elastic parameters to their seismically determined values and then solved for viscosity versus depth profiles by either expressing the log(viscosity) versus log(depth) profile as a series of specially constructed orhtogonal polynomials, or by allowing each of 8-10 layers (plus the half-space) to have an independently determined viscosity. We found that the data do not strongly support (nor can they conclusively exclude) a more complex rheology than simple Maxwell viscoelasticity. The orthogonal polynomial solution exhibits an essentially monotonic decrease in viscosity with depth.
Hydro-isostatic deflection and tectonic tilting in the central Andes: Initial results of a GPS survey of Lake Minchin shorelines
Sufficiently large lake loads provide a means of probing rheological stratification of the crust and upper mantle. Lake Minchin was the largest of the late Pleistocene pluvial lakes in the central Andes. Prominent shorelines, which formed during temporary still-stands in the climatically driven lake level history, preserve records of lateral variations in subsequent net vertical motions. At its maximum extent the lake was 140 m deep and spanned 400 km N-S and 200 km E-R. The load of surficial water contained in Lake Minchin was sufficient to depress the crust and underlying mantle by 20-40 m, depending on the subjacent rheology. Any other differential vertical motions will also be recorded as departures from horizontality of the shorelines. We recently conducted a survey of shoreline elevations of Lake Minchin with the express intent of monitoring the hydro-isostatic deflection and tectonic tilting. Using real-time differential Global Positioning System (GPS), we measured topographic profiles across suites of shorelines at 15 widely separated locations throughout the basin. Horizontal and vertical accuracies attained are roughly 30 and 70 cm, respectively. Geomorphic evidence suggests that the highest shoreline was occupied only briefly (probably less than 200 years) and radiocarbon dates on gastropod shells found in association with the shore deposits constrain the age to roughly 17 kyr. The basin-side pattern of elevations of the highest shoreline is composed of two distinct signals: (27 +/- 1) m of hydro-isostatic deflection due to the lake load, and a planar tilt with east and north components of (6.8 +/- 0.4) 10(exp -5) and 9-5.3 +/- 0.3) 10(exp -5). This rate of tilting is too high to be plausibly attributed to steady tectonism, and presumably reflects some unresolved combination of tectonism plus the effects of oceanic and lacustrine loads on a laterally heterogeneous substrate. The history of lake level fluctuations is still inadequately known to allow detailed inferences of crust and mantle rheology. However, it is already clear that the effective elastic plate thickness is closer to 40 km than the 60-70 km crustal thickness in the central Andes and the effective viscosity is less than 5 10(exp 20) Pa s.