The fate of primordial lunar Trojans

Multiple large impact basins on the lunar nearside formed in a relatively-short interval around 3.8-3.9 Gyr ago, in what is known as the Lunar Cataclysm (LC; also known as Late Heavy Bombardment). It is widely thought that this impact bombardment has affected the whole Solar System or at least all the inner planets. But with non-lunar evidence for the cataclysm being relatively weak, a geocentric cause of the Lunar Cataclysm cannot yet be completely ruled out [Ryder, G., 1990. Eos 71, 313, 322-323]. In principle, late destabilization of an additional Earth satellite could result in its tidal disruption during a close lunar encounter (cf. [Asphaug, E., Agnor, C.B., Williams, Q., 2006. Nature 439, 155-160]). If the lost satellite had D>500 km, the resulting debris can form multiple impact basins in a relatively short time, possibly explaining the LC. Canup et al. [Canup, R.M., Levison, H.F., Stewart, G.R., 1999. Astron. J. 117, 603-620] have shown that any additional satellites of Earth formed together with (and external to) the Moon would be unable to survive the rapid initial tidally-driven expansion of lunar orbit. Here we explore the fate of objects trapped in the lunar Trojan points, and find that small lunar Trojans can survive the Moon's orbital evolution until they and the Moon reach 38 Earth radii, at which point they are destabilized by a strong solar resonance. However, the dynamics of Trojans containing enough mass to cause the LC (diameters >150 km) is more complex; we find that such objects do not survive the passage through a weaker solar resonance at 27 Earth radii. This distance was very likely reached by the Moon long before the LC, which seems to rule out the disruption of lunar Trojans as a cause of the LC.     

On the asteroid belt's orbital and size distribution

For absolute magnitudes greater than the current completeness limit of H-magnitude ∼15 the main asteroid belt's size distribution is imperfectly known. We have acquired good-quality orbital and absolute H-magnitude determinations for a sample of small main-belt asteroids in order to study the orbital and size distribution beyond H=15, down to sub-kilometer sizes (H>18). Based on six observing nights over a 11-night baseline we have detected, measured photometry for, and linked observations of 1087 asteroids which have one-week time baselines or more. The linkages allow the computation of full heliocentric orbits (as opposed to statistical distances determined by some past surveys). Judged by known asteroids in the field the typical uncertainty in the (a/e/i) orbital elements is less than 0.03 AU/0.03/0.5°. The distances to the objects are sufficiently well known that photometric uncertainties (of 0.3 magnitudes or better) dominate the error budget of their derived H-magnitudes. The detected asteroids range from HR=12-22 and provide a set of objects down to sizes below 1 km in diameter. We find an on-sky surface density of 210 asteroids per square degree in the ecliptic with opposition magnitudes brighter than mR=23, with the cumulative number of asteroids increasing by a factor of 10^0.27/mag from mR=18 down to the mR?23.5 limit of our survey. In terms of absolute H magnitudes, we find that beyond H=15 the belt exhibits a constant power-law slope with the number increasing proportional to ¹⁰0.30H from H?15 to 18, after which incompleteness begins in the survey. Examining only the subset of detections inside 2.5 AU, we find weak evidence for a mildly shallower slope for H=15-19.5. We provide the information necessary such that anyone wishing to model the main asteroid belt can compare a detailed model to our detected sample.     

Evaluation of on-line DEMs for flood inundation modeling

Recent and highly accurate topographic data should be used for flood inundation modeling, but this is not always feasible given time and budget constraints so the utility of several on-line digital elevation models (DEMs) is examined with a set of steady and unsteady test problems. DEMs are used to parameterize a 2D hydrodynamic flood simulation algorithm and predictions are compared with published flood maps and observed flood conditions. DEMs based on airborne light detection and ranging (LiDAR) are preferred because of horizontal resolution, vertical accuracy (∼0.1 m) and the ability to separate bare-earth from built structures and vegetation. DEMs based on airborne interferometric synthetic aperture radar (IfSAR) have good horizontal resolution but gridded elevations reflect built structures and vegetation and therefore further processing may be required to permit flood modeling. IfSAR and shuttle radar topography mission (SRTM) DEMs suffer from radar speckle, or noise, so flood plains may appear with non-physical relief and predicted flood zones may include non-physical pools. DEMs based on national elevation data (NED) are remarkably smooth in comparison to IfSAR and SRTM but using NED, flood predictions overestimate flood extent in comparison to all other DEMs including LiDAR, the most accurate. This study highlights utility in SRTM as a global source of terrain data for flood modeling.     

Radar constraints on asteroid regolith properties using 433 Eros as ground truth

Abstract— Radar data enable us to estimate an asteroid's near‐surface bulk density, thus providing a joint constraint on near‐surface porosity and solid density. We investigate two different approaches to simplifying this joint constraint: estimating solid densities by assuming uniform porosities for all asteroids; and estimating porosities by assuming uniform mineralogy within each taxonomic class. Methods used to estimate asteroids' near‐surface solid densities from radar data have not previously been calibrated via independent estimates. Recent spacecraft results on the chondritic nature of 433 Eros now permit such a check, and also support porosity estimation for S‐class objects. We use radar albedos and polarization ratios estimated for 36 main‐belt asteroids and nine near‐Earth asteroids to estimate near‐surface solid densities using two methods, one of which is similar to the uncalibrated algorithms used in previous studies, the other of which treats Eros as a calibrator. We also derive porosities for the same sample by assigning solid densities for each taxonomic class in advance. Density‐estimation results obtained for Eros itself are consistent with the uncalibrated method being valid in the mean; those derived for the full sample imply that uncalibrated solid densities are, at most, a few tens of percent too large on average. However, some derived densities are extremely low, whereas most porosity estimates are physically plausible. We discuss the relative merits of these two approaches.     

A Non-geographical Application of Spatial Information Systems in Pupillometry

Spatial analysis and spatial information systems have great potential in many non‐geographic domains. This paper presents an example of the utility of spatial analysis in a non‐geographic domain. A technique of pupillometry using digital infrared video loosely coupled with a Spatial Information System and a spreadsheet is developed to accurately quantify pupil dilation magnitude and constriction onset latency for participants of different cognitive ability and under different cognitive loads. Spatio‐temporal pupil dynamics of participants are recorded using digital infrared video. The pupil to iris area ratio is calculated for over 470,000 temporally sequenced de‐interlaced video fields by automatic feature extraction using a combination of threshold analysis, spatial smoothing and areal filtering. Pupil dilation magnitudes and constriction onset latencies are calculated through post‐processing in a spreadsheet. The study identifies inadequacies in current spatial analytical techniques for automatic feature extraction not necessarily evident in geographic applications. Issues impeding the employment of spatial analysis in non‐geographic domains including the lack of a generic spatial referencing system are identified and discussed.     

Intrinsic oxygen fugacity measurements on seven chondrites,a pallasite,and a tektite and the redox state of meteorite parent bodies

Intrinsic oxygen-fugacity (fO₂) measurements were made on five ordinary chondrites, a carbonaceous chondrite, an enstatite chondrite, a pallasite, and a tektite. Results are of the form of linear log $\text{f}\text{O}{}_2\text{?}\text{1}\text{T}$ plots. Except for the enstatite chondrite, measured results agree well with calculated estimates by others.The tektite produced fO₂ values well below the range measured for terrestrial and lunar rocks. The lowpressure atmospheric regime that is reported to follow large terrestrial explosions, coupled with a very high temperature, could produce glass with fO₂ in the range measured.The meteorite Salta (pallasite) has low fO₂ and lies close to Hvittis (E6). Unlike the other samples, results for Salta do not parallel the iron-wüstite buffer, but are close to the fayalite-quartz-iron buffer in slope.Minor reduction by graphite appears to have taken place during metamorphism of ordinary chondrites. fO₂ values of unequilibrated chondrites show large scatter during early heating suggesting that the constituent phases were exposed to a range of fO₂ conditions. The samples equilibrated with respect to fO₂ in relatively short time on heating. Equilibration with respect to fO₂ in ordinary chondrites takes place between grades 3 and 4 of metamorphism. Application of P ? T ? fO₂ relations in the system C-CO-CO₂ indicates that the ordinary chondrites were metamorphosed at pressures of 3–20 bars, as it appears that they lay on the graphite surface.A steep positive thermal gradient in a meteorite parent body lying at the graphite surface will produce thin reduced exterior, an oxidized near-surface layer, and an interior that is increasingly reduced with depth; a shallow thermal gradient will produce the reverse. A body heated by accretion on the outside will have a reduced exterior and oxidized interior. Meteorites from the same parent body clearly are not required to have similar redox states.     

Relaxation Oscillations in Tidally Evolving Satellites

We study the rotational evolution under tidal torques of axisymmetric natural satellites in inclined, precessing orbits. In the spin- and orbit-averaged equations of motion, we find that a global limit cycle exists for parameter values near the stability limit of Cassini state . The limit cycle involves an alternation between states of near-synchronous spin at low obliquity, and strongly subsynchronous spin at an obliquity near 90°. This dynamical feature is characterized as a relaxation oscillation, arising as the system slowly traverses two saddle-node bifurcations in a reduced system. This slow timescale is controlled by ε, the nondimensional tidal dissipation rate. Unfortunately, a straightforward expansion of the governing equations for small ε is shown to be insufficient for understanding the underlying structure of the system. Rather, the dynamical equations of motion possess a singular term, multiplied by ε, which vanishes in the unperturbed system. We thus provide a demonstration that a dissipatively perturbed conservative system can behave qualitatively differently from the unperturbed system. This revised version was published online in July 2006 with corrections to the Cover Date.