The dynamical environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.     

Olivine or impact melt: Nature of the “Orange” material on Vesta from Dawn

NASA’s Dawn mission observed a great variety of colored terrains on asteroid (4) Vesta during its survey with the Framing Camera (FC). Here we present a detailed study of the orange material on Vesta, which was first observed in color ratio images obtained by the FC and presents a red spectral slope. The orange material deposits can be classified into three types: (a) diffuse ejecta deposited by recent medium-size impact craters (such as Oppia), (b) lobate patches with well-defined edges (nicknamed “pumpkin patches”), and (c) ejecta rays from fresh-looking impact craters. The location of the orange diffuse ejecta from Oppia corresponds to the olivine spot nicknamed “Leslie feature” first identified by Gaffey (Gaffey, M.J. [1997]. Icarus 127, 130–157) from ground-based spectral observations. The distribution of the orange material in the FC mosaic is concentrated on the equatorial region and almost exclusively outside the Rheasilvia basin. Our in-depth analysis of the composition of this material uses complementary observations from FC, the visible and infrared spectrometer (VIR), and the Gamma Ray and Neutron Detector (GRaND). Several possible options for the composition of the orange material are investigated including, cumulate eucrite layer exposed during impact, metal delivered by impactor, olivine–orthopyroxene mixture and impact melt. Based on our analysis, the orange material on Vesta is unlikely to be metal or olivine (originally proposed by Gaffey (Gaffey, M.J. [1997]. Icarus 127, 130–157)). Analysis of the elemental composition of Oppia ejecta blanket with GRaND suggests that its orange material has ∼25% cumulate eucrite component in a howarditic mixture, whereas two other craters with orange material in their ejecta, Octavia and Arruntia, show no sign of cumulate eucrites. Morphology and topography of the orange material in Oppia and Octavia ejecta and orange patches suggests an impact melt origin. A majority of the orange patches appear to be related to the formation of the Rheasilvia basin. Combining the interpretations from the topography, geomorphology, color and spectral parameters, and elemental abundances, the most probable analog for the orange material on Vesta is impact melt.     

Quantified mineralogical evidence for a common origin of 1929 Kollaa with 4 Vesta and the HED meteorites

In this paper, we present the first correlation of derived mineral abundances of V-class Asteroid 1929 Kollaa, 4 Vesta, and the HED meteorites. We demonstrate that 1929 Kollaa has a basaltic composition consistent with an origin within the crustal layer of 4 Vesta, and show a plausible genetic connection between Kollaa and the cumulate eucrite meteorites. These data support the proposed delivery mechanism of HED meteorites to the Earth from Vesta, and provide the first mineralogical constraint derived from the observation of a small V-class, Vesta family asteroid on the crustal thickness of 4 Vesta.     

Mineralogical characterization of some basaltic asteroids in the neighborhood of (4) Vesta: first results

We present reflectance spectra of 19 V-type asteroids obtained at the 3.6 m Telescopio Nazionale Galileo covering 0.8 to 2.5 μm. For 8 of these asteroids we obtained also visible spectra in the same observational run. The range from 0.8 to 2.5 μm, encompassing the 1 and 2 μm pyroxene features, allows a precise mineralogical characterization of these asteroids. The obtained data suggests the possible coexistence of distinct mineralogical groups among the V-type asteroids, either probing different layers of (4) Vesta or coming from different bodies. No clear correlation was found between mineralogies and the objects being, or not, member of the Vesta dynamical family.     

Compositional heterogeneity of Asteroid 4 Vesta’s southern hemisphere: Implications for the Dawn mission

High signal-to-noise, rotationally-resolved spectra of Asteroid 4 Vesta’s southern hemisphere from the 2007 opposition were used to constrain its compositional and mineralogical variations. The spectra were rotationally-phased using closely timed HST observations of Vesta by Li et al. (Li, J.-Y., McFadden, L.A., Thomas, P.C., Mutchler, M.J., Parker, J.Wm., Young, E.F., Russell, C.T., Sykes, M.V., Schmidt, B.E. [2010]. Icarus 208, 238–251). The average surface of Vesta’s southern hemisphere is analogous to a howardite or polymict eucrite assemblage similar to the northern hemisphere, although the band parameters are distinctly shifted towards the diogenite zone on the Band–Band plot. A few distinct compositional units were detected and they might be related to albedo features detected by Hubble Space Telescope (Li et al., 2010). We have identified two compositionally distinct regions overlaying the background surface. The first unit is a polymict eucrite and/or low-Ca eucrite compositional unit at 143° longitude that border the eucrite zone on the Band–Band plot and the second is a diogenite unit at 159°. While we did not detect any distinct olivine units as suggested by Gaffey (Gaffey, M.J. [1997]. Icarus 127, 130–157), we cannot rule out the possibility of smaller olivine-rich units that are below the detection limit of the instrumentation we used. Based on the analysis and the limitations of the data, we do not suggest that Vesta’s surface is olivine-free. Mean pyroxene chemistry estimates for both hemispheres broadly agree with one another (to within one-sigma) with the northern hemisphere ferrosilite (Fs) and wollastonite (Wo) values being slightly higher than southern hemisphere.     

On the coupling of lunisolar resonances for Earth satellite orbits

The resonance C1 occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion. This resonance is one of the critical inclination family with I 46°. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance C1. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g+h and h,+2 , seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincaré maps.     

Geochemistry of 4 Vesta based on HED meteorites: Prospective study for interpretation of gamma ray and neutron spectra for the Dawn mission

Abstract— Asteroid 4 Vesta, believed to be the parent body of the howardite, eucrite, and diogenite (HED) meteorites, will be investigated by the Dawn orbiting spacecraft. Dawn carries a gamma ray and neutron detector (GRaND) that will measure and map some major‐ and trace‐element abundances. Drawing on HED geochemistry, we propose a mixing model that uses element ratios appropriate for the interpretation of GRaND data. Because the spatial resolution of GRaND is relatively coarse, the analyzed chemical compositions on the surface of Vesta will likely reflect mixing of three endmember components: diogenite, cumulate eucrite, and basaltic eucrite. Reliability of the mixing model is statistically investigated based on published whole‐rock data for HED meteorites. We demonstrate that the mixing model can accurately estimate the abundances of all the GRaND‐analyzed major elements, as well as of minor elements (Na, Cr, and Mn) not analyzed by this instrument. We also show how a similar mixing model can determine the modal abundance of olivine, and we compare estimated and normative olivine data for olivine‐bearing diogenites. By linking the compositions of well‐analyzed HED meteorites with elemental mapping data from GRaND, this study may help constrain the geological context for HED meteorites and provide new insight into the magmatic evolution of Vesta.     

Rotational evolution of exoplanets under the action of gravitational and magnetic perturbations

We investigate the evolution of the rotational axes of exoplanets under the action of gravitational and magnetic perturbations. The planet is assumed to be dynamically symmetrical and to be magnetised along its dynamical-symmetry axis. By qualitative methods of the bifurcation theory of multiparametric PDEs, we have derived a gallery of 69 phase portraits. The portraits illustrate evolutionary trajectories of the angular momentum of a planet for a variety of the initial conditions, for different values of the ratio between parameters describing gravitational and magnetic perturbations, and for different rates of the orbital evolution. We provide examples of the phase portraits, that reveal the differences in topology and the evolutionary track of in the vicinity of an equilibrium state. We determine the bifurcation properties, i.e., the way of reorganisation of phase trajectories in the vicinities of equilibria; and we point out the combinations of parameters’ values that permit ip-overs from a prograde to a retrograde spin mode.     

Analytical and numerical results on the stability of a planetary precessional model

A model for planetary precession is investigated using analytical and numerical techniques. A Hamiltonian function governing the model is derived in terms of action-angle Andoyer-Déprit variables under the assumption of equatorial symmetry. As a first approximation a simplified Hamiltonian with zero-eccentricity is considered and stability estimates are derived using KAM theory. A validation of the analytical results is performed computing Poincaré surfaces of section for the circular and elliptical model. We also investigate the role of the eccentricity and its connection with the appearance of resonances. Special attention is devoted to the particular case of the Earth–Moon system. This revised version was published online in July 2006 with corrections to the Cover Date.     

A spectroscopic comparison of HED meteorites and V-type asteroids in the inner Main Belt

V-type asteroids in the inner Main Belt (a < 2.5 AU) and the HED meteorites are thought to be genetically related to one another as collisional fragments from the surface of the large basaltic Asteroid 4 Vesta. We investigate this relationship by comparing the near-infrared (0.7-2.5 μm) spectra of 39 V-type asteroids to laboratory spectra of HED meteorites. The central wavelengths and areas spanned by the 1 and 2 μm pyroxene-olivine absorption bands that are characteristic of planetary basalts are measured for both the asteroidal and meteoritic data. The band centers are shown to be well correlated, however the ratio of areas spanned by the 1 and 2 μm absorption bands are much larger for the asteroids than for the meteorites. We argue that this offset in band area ratio is consistent with our currently limited understanding of the effects of space weathering, however we cannot rule out the possibility that this offset is due to compositional differences. Several other possible causes of this offset are discussed.Amongst these inner Main Belt asteroids we do not find evidence for non-Vestoid mineralogies. Instead, these asteroids seem to represent a continuum of compositions, consistent with an origin from a single differentiated parent body. In addition, our analysis shows that V-type asteroids with low inclinations (i < 6°) tend to have band centers slightly shifted towards long wavelengths. This may imply that more than one collision on Vesta’s surface was responsible for producing the observed population of inner belt V-type asteroids. Finally, we offer several predictions that can be tested when the Dawn spacecraft enters into orbit around Vesta in the summer of 2011.     

On the gravitational fields of Pandora and Prometheus

Utilizing topographic models of Saturn's F-ring shepherd satellites Prometheus (S16 1980S27) and Pandora (S15 1980S26), derived by Stooke (1994), and supposing that their mass density is constant, we derived basic geometrical and dynamical characteristics of the moons. They include the volume and mass, the mean radii, the tensor of inertia, and Stokes coefficients of the harmonic expansions of external gravitational potential. The best fitting ellipsoid approximations of the topography were calculated. A simple method of determining the gravitational potential on the surface of an irregular satellite is presented. Examples of equipotential surfaces of the satellites are shown     

A symplectic mapping approach to the study of the stochasticity in asteroidal resonances

In the case of the 2:1 and 3:2 resonances with Jupiter, it has not been yet possible to have a complete identification of all chaotic diffusion processes at work, mainly because the time scale of some of them are of an order still out of the reach of precise integrations. A planar Hadjidemetriou's mapping, using expansions valid for high eccentricities and scaled in order to accelerate the diffusion processes, was derived. The solutions obtained with the mapping show huge eccentricity variations in all orbits starting in the middle of the 2:I resonance, when the main short-period perturbations of Jupiter's orbit are considered. The solutions starting in the middle of the 3:2 resonance do not show any important diffusion.     

Gaussian states in de Sitter spacetime and the evolution of semiclassical density perturbations.

The evolution of Gaussian quantum states in the de Sitter phase of the early universe is investigated. The potential is approximated by that of an inverted oscillator. We study the origin and magnitude of the density perturbations with special emphasis on the nature of the semiclassical limits     

Time dependent monochromatic scattering of radiation in one dimensional media: Analytical and numerical solutions

In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic scattering for sources with an arbitrary spatial distribution and an arbitrary time variation of their power. The Lax-Wendroff method seems to be the most suitable. Because it is assumed that radiation delay is caused by the finite speed of light, the following difficulty arises when the numerical method is used: the region of variation of the variables (position τ and time t) is triangular (the inequality τ ≤ t). This difficulty is overcome by expanding the unknown functions in series in terms of small values of the time and position. By comparing the numerical and exact solutions for a point source with a given time dependence for its power and with pure scattering, the number of steps in the variables required to obtain a desired accuracy is estimated. This numerical method can be used to calculate the intensity and polarization of the radiation from sources in the early universe during epochs close to the recombination epoch. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 109–123 (February 2008).     

On the dynamics in the asteroids belt. Part II: Detailed study of the main resonances

The general theory exposed in the first part of this paper is applied to the following resonances with Jupiter's motion : 3/2, 2/1, 5/2, 3/1, 7/2, 4/1; these are the most relevant resonances for the asteroids. The whole analysis is performed in the framework of the spatial problem of three bodies, both in the circular and in the elliptic case. The results are also compared with the observed distribution of the asteroids.     

The quasar population density as a result of the formation rate and the evolutionary pathes. I. Analytical formulas and numerical simulations

Wir verallgemeinern die Kontinuitätsgleichung von CAVALIERE et al. (1971) für den Fall, daß die Leuchtkraftentwicklung nicht nur von der aktuellen Leuchtkraft abhängt. Wir zeigen, daß einfache Fälle (monomiale Entstehungsraten) integrierbar sind und vergleichen einige interessante Merkmale. Testverfahren und die Einbeziehung der Beobachtung sind in Vorbereitung.     

A numerical and experimental study of the time-evolution of a low Mach number jet

We present a comparison between a plasma-generated 'starting jet' experiment and an axisymmetric numerical simulation of the flow. The experimental flow and the numerical simulation give results that agree both qualitatively and quantitatively, showing that the complex vortical structures arising in the flow are surprisingly well reproduced by the numerical model. This result inspires confidence in the accuracy of astrophysical jet numerical simulations. Also, even though the Mach number of our laboratory jet is somewhat low ( M ∼0.5), the dimensionless parameters of this jet are not very far from those expected for Faranoff–Riley class I radio jets.     

Meteoritic and other constraints on the internal structure and impact history of small asteroids

Studies of the internal structure of asteroids, which are crucial for understanding their impact history and for hazard mitigation, appear to be in conflict for the S-type asteroids, Eros, Gaspra, and Ida. Spacecraft images and geophysical data show that they are fractured, coherent bodies, whereas models of catastrophic asteroidal impacts, family and satellite formation, and studies of asteroid spin rates, and other diverse properties of asteroids and planetary craters suggest that such asteroids are gravitationally bound aggregates of rubble. These conflicting views may be reconciled if 10-50 km S-type asteroids formed as rubble piles, but were later consolidated into coherent bodies. Many meteorites are breccias that testify to a long history of impact fragmentation and consolidation by alteration, metamorphism, igneous and impact processes. Ordinary chondrites, which are the best analogs for S asteroids, are commonly breccias. Some may have formed in cratering events, but many appear to have formed during disruption and reaccretion of their parent asteroids. Some breccias were lithified during metamorphism, and a few were lithified by injected impact melt, but most are regolith and fragmental breccias that were lithified by mild or moderate shock, like their lunar analogs. Shock experiments show that porous chondritic powders can be consolidated during mild shock by small amounts of silicate melt that glues grains together, and by friction and pressure welding of silicate and metallic Fe,Ni grains. We suggest that the same processes that converted impact debris into meteorite breccias also consolidated asteroidal rubble. Internal voids would be partly filled with regolith by impact-induced seismic shaking. Consolidation of this material beneath large craters would lithify asteroidal rubble to form a more coherent body. Fractures on Ida that were created by antipodal impacts and are concentrated in and near large craters, and small positive gravity anomalies associated with the Psyche and Himeros craters on Eros, are consistent with this concept. Spin data suggest that smaller asteroids 0.6-6 km in size are unconsolidated rubble piles. C-type asteroids, which are more porous than S-types, and their analogs, the volatile-rich carbonaceous chondrites, were probably not lithified by shock.     

Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series expansion is discussed in the paper.     

K‐Th‐Ti systematics and new three‐component mixing model of HED meteorites: Prospective study for interpretation of gamma‐ray and neutron spectra for the Dawn mission

Abstract– The Dawn spacecraft carries a gamma‐ray and neutron detector (GRaND), which will measure and map the abundances of selected elements on the surface of asteroid 4 Vesta. We compare the variability of moderately volatile/refractory incompatible element ratios (K/Th and K/Ti) in howardite, eucrite, and diogenite (HED) meteorites with those in other achondrite suites that represent asteroidal crusts, because these ratios may be accurately measured by GRaND and likely reflect initial chemical compositions of the HED parent body. The K/Th and K/Ti variations can differentiate HED meteorites from angrites and some unique eucrite‐like lithologies. The results suggest that K, Th, and Ti abundances determined from GRaND data could not only confirm that Vesta is the parent body of HED meteorites but might also allow recognition of as‐yet unsampled compositional terranes on Vesta. Besides the K‐Th‐Ti systematics study, we propose a new three‐component mixing model for interpretation of GRaND spectra, required because the spatial resolution of GRaND is coarser than the spectral (compositional) heterogeneity of Vesta’s surface. The mixing model uses abundances of K, Ti, Fe, and Mg that will be analyzed more accurately than other prospective GRaND‐analyzed elements. We examine propagated errors due to GRaND analytical uncertainties and intrinsic errors that stem from an assumption introduced into the mixing model. The error investigation suggests that the mixing model can adequately estimate not only the diogenite/eucrite mixing ratio but also the abundances of most major and minor elements within the GRaND propagated errors.