Charging and motion of dust grains near the terminator of the moon

We discuss the formation of strong local electric fields near minicraters or hills in the vicinity of the terminator. Electrons, having large thermal velocity compared to the solar wind speed can easily penetrate into the shadowed part of a minicrater. At the same time only protons with velocities much higher than their thermal speed can reach such regions. This results in the formation of a strong local negative potential whose magnitude depends on the steepness of the shadowed slope of the minicrater. The extremely small conductivity of the lunar regolith at the shadowed side of the crater prevents any significant electric discharge and thus supports the formation of a strong potential difference at scales much smaller than the Debye radius. Our estimates show that the created local electric fields are sufficiently strong enough to elevate dust grains with the sizes of the order of above the surface. The suggested mechanism is efficient only after sunset rather close to the terminator. Far away from the terminator at the dark side the fluxes of charged particles hitting the surface are so small that the process of dust elevation becomes too weak.     

Peculiarities of the motion of asteroid 99942 Apophis

The Apophis asteroid attracted the attention of scientists immediately after its discovery in 2004, because the initially determined orbit of this asteroid assumes a possible collision with Earth in April 2029. The size of Apophis is about several hundred meters, and its collision with Earth might result in a large regional or even global catastrophe. At present, the trajectory of Apophis has been calculated more accurately, and a collision in 2029 has ruled out; the asteroid will pass Earth at a distance of about 37 000 km from its center. However, close approaches or collisions are possible after 2029, including the most probable in 2036. The risk of collision in 2036 is well known and actively examined by the scientists. In this study, we consider the peculiarities of the asteroid motion associated with its approach in 2029 and with a possible close approach in 2036. The trajectories scatter during the approaches and the loss of accuracy is associated with these scatterings. As a result, the trajectory of Apophis may become nondeterministic after 2036; that is, it cannot now be determined unambiguously. Although such events are very unlikely, it is interesting to examine a variety of alternative variants of Apophis’ close approaches and collisions with Earth immediately after 2036. The effects of small variations in the asteroid velocity at different moments in time after its impact with a certain mass are discussed.     

Physical properties of asteroid dust bands and their sources

Disruptive collisions in the main belt can liberate fragments from parent bodies ranging in size from several micrometers to tens of kilometers in diameter. These debris bodies group at initially similar orbital locations. Most asteroid-sized fragments remain at these locations and are presently observed as asteroid families. Small debris particles are quickly removed by Poynting-Robertson drag or comminution but their populations are replenished in the source locations by collisional cascade. Observations from the Infrared Astronomical Satellite (IRAS) showed that particles from particular families have thermal radiation signatures that appear as band pairs of infrared emission at roughly constant latitudes both above and below the Solar System plane. Here we apply a new physical model capable of linking the IRAS dust bands to families with characteristic inclinations. We use our results to constrain the physical properties of IRAS dust bands and their source families. Our results indicate that two prominent IRAS bands at inclinations ≈2.1° and ≈9.3° are byproducts of recent asteroid disruption events. The former is associated with a disruption of a ≈30-km asteroid occurring 5.8 Myr ago; this event gave birth to the Karin family. The latter came from the breakup of a large >100-km-diameter asteroid 8.3 Myr ago that produced the Veritas family. Using an N-body code, we tracked the dynamical evolution of ≈10⁶ particles, 1 μm to 1 cm in diameter, from both families. We then used these results in a Monte Carlo code to determine how small particles from each population undergo collisional evolution. By computing the thermal emission of particles, we were able to compare our results with IRAS observations. Our best-fit model results suggest the Karin and Veritas family particles contribute by 5-9% in 10-60-μm wavelengths to the zodiacal cloud's brightness within 50° latitudes around the ecliptic, and by 9-15% within 10° latitudes. The high brightness of the zodiacal cloud at large latitudes suggests that it is mainly produced by particles with higher inclinations than what would be expected for asteroidal particles produced by sources in the main belt. From these results, we infer that asteroidal dust represents a smaller fraction of the zodiacal cloud than previously thought. We estimate that the total mass accreted by the Earth in Karin and Veritas particles with diameters 20-400 μm is ≈15,000-20,000 tons per year (assuming 2 g cm⁻³ particles density). This is ≈30-50% of the terrestrial accretion rate of cosmic material measured by the Long Duration Exposure Facility. We hypothesize that up to ≈50% of our collected interplanetary dust particles and micrometeorites may be made up of particle species from the Veritas and Karin families. The Karin family IDPs should be about as abundant as Veritas family IDPs though this ratio may change if the contribution of third, near-ecliptic source is significant. Other sources of dust and/or large impact speeds must be invoked to explain the remaining ≈50-70%. The disproportional contribution of Karin/Veritas particles to the zodiacal cloud (only 5-9%) and to the terrestrial accretion rate (30-50%) suggests that the effects of gravitational focusing by the Earth enhance the accretion rate of Karin/Veritas particles relative to those in the background zodiacal cloud. From this result and from the latitudinal brightness of the zodiacal cloud, we infer that the zodiacal cloud emission may be dominated by high-speed cometary particles, while the terrestrial impactor flux contains a major contribution from asteroidal sources. Collisions and Poynting-Robertson drift produce the size-frequency distribution (SFD) of Karin and Veritas particles that becomes increasingly steeper closer to the Sun. At 1 AU, the SFD is relatively shallow for small particle diameters D (differential slope exponent of particles with D?100 μm is ≈2.2-2.5) and steep for D?100 μm. Most of the mass at 1 AU, as well as most of the cross-sectional area, is contributed by particles with D≈100-200 μm. Similar result has been found previously for the SFD of the zodiacal cloud particles at 1 AU. The fact that the SFD of Karin/Veritas particles is similar to that of the zodiacal cloud suggests that similar processes shaped these particle populations. We estimate that there are ≈5×¹⁰²⁴ Karin and ≈10²⁵ Veritas family particles with D>30 μm in the Solar System today. The IRAS observation of the dust bands may be satisfactorily modeled using ‘averaged’ SFDs that are constant with semimajor axis. These SFDs are best described by a broken power-law function with differential power index α≈2.1-2.4 for D?100 μm and by α?3.5 for 100 μm?D?1 cm. The total cross-sectional surface area of Veritas particles is a factor of ≈2 larger than the surface area of the particles producing the inner dust bands. The total volumes in Karin and Veritas family particles with 1 μm<D<1 cm correspond to D=11 km and D=14 km asteroids with equivalent masses ≈1.5×¹⁰¹⁸ g and ≈3.0×¹⁰¹⁸ g, respectively (assuming 2 g cm⁻³ bulk density). If the size-frequency and radial distribution of particles in the zodiacal cloud were similar to those in the asteroid dust bands, we estimate that the zodiacal cloud represents ∼3×¹⁰¹⁹ g of material (in particles with 1 μm<D<1 cm) at ±10° around the ecliptic and perhaps as much as ∼¹⁰²⁰ g in total. The later number corresponds to about a 23-km-radius sphere with 2 g cm⁻³ density.     

About averaging procedures in the problem of asteroid motion

A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements.     

Orbits and manifolds near the equilibrium points around a rotating asteroid

We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless test particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four relevant cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than 4, and we find at least one family of periodic orbits near the resonant equilibrium points. As an application of the theory developed here, we study relevant orbits for the asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia and 6489 Golevka.     

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

In asteroid rendezvous missions, the dynamical environment near an asteroid's surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes,which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped nearEarth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.     

On quasi-satellite periodic motion in asteroid and planetary dynamics

Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family f, which consists of 1:1 resonant retrograde orbits. In our study, we determine the critical orbits of family f that are continued both in the elliptic and in the spatial models and compute the corresponding families that are generated and consist the backbone of the quasi-satellite regime in the restricted model. Then, we show the continuation of these families in the general three-body problem, we verify and explain previous computations and show the existence of a new family of spatial orbits. The linear stability of periodic orbits is also studied. Stable periodic orbits unravel regimes of regular motion in phase space where 1:1 resonant angles librate. Such regimes, which exist even for high eccentricities and inclinations, may consist dynamical regions where long-lived asteroids or co-orbital exoplanets can be found.     

Singularly weighted symplectic forms and applications to asteroid motion

New techniques to study Hamiltonian systems with Hamiltonian forcing are proposed. They are based on singularly weighted symplectic forms and transformations which preserve these forms. Applications pertaining to asteroid motion are outlined. These involve the presence of both Jupiter and Saturn.     

The surface of asteroid 951 Gaspra

I present new maps, photomosaics and geological interpretations of asteroid 951 Gaspra. Facets and limb concavities suggest a long history of large impacts producing 5 to 7 km diameter craters. Craters 1 to 4 km in diameter date the last facet-forming impact, though it is not clear which facet this formed. These craters are more numerous than previously thought because much of the area seen at high resolution seems to be depleted in these larger craters. Craters in that area probably date the last body-jolting impact. Linear features, probably the surface expressions of deep fractures, form at least two groups with different trends and probably different ages. Previously noted fresh and spectrally distinct materials are concentrated on ridges. One or two dark markings occur on a steep slope seen at high sun. Smooth materials, probably consisting of thicker or more mobile regolith than elsewhere, occur on steep slopes, usually on rotational leading surfaces.     

Linking meteorites to their asteroid parent bodies: The capabilities of dust analyzer instruments during asteroid flybys

Linking meteorites to their asteroid parent bodies remains an outstanding issue. Space-based dust characterization using impact ionization mass spectrometry is a proven technique for the compositional analysis of individual cosmic dust grains. Here we investigate the feasibility of determining asteroid compositions via cation mass spectrometric analyses of their dust ejecta clouds during low (7–9 km s⁻¹) velocity spacecraft flybys. At these speeds, the dust grain mass spectra are dominated by easily ionized elements and molecular species. Using known bulk mineral volume abundances, we show that it is feasible to discriminate the common meteorite classes of carbonaceous chondrites, ordinary chondrites, and howardite–eucrite–diogenite achondrites, as well as their subtypes, relying solely on the detection of elements with ionization efficiencies of ≤700 or ≤800 kJ mol⁻¹, applicable to low (~7 km s⁻¹) and intermediate (~9 km s⁻¹) flyby speed scenarios, respectively. Including the detection of water ion groups enables greater discrimination between certain meteorite types, and flyby speeds ≥10 km s⁻¹ enhance the diagnostic capabilities of this technique still further. Although additional terrestrial calibration is required, this technique may allow more unequivocal asteroid-meteorite connections to be determined by spacecraft flybys, emphasizing the utility of dust instruments on future asteroid missions.     

Nano dust impacts on spacecraft and boom antenna charging

High rate sampling detectors measuring the potential difference between the main body and boom antennas of interplanetary spacecraft have been shown to be efficient means to measure the voltage pulses induced by nano dust impacts on the spacecraft body itself (see Meyer-Vernet et al. in Sol. Phys. 256:463, 2009). However, rough estimates of the free charge liberated in post impact expanding plasma cloud indicate that the cloud’s own internal electrostatic field is too weak to account for measured pulses as the ones from the TDS instrument on the STEREO spacecraft frequently exceeding 0.1 V/m. In this paper we argue that the detected pulses are not a direct measure of the potential structure of the plasma cloud, but are rather the consequence of a transitional interruption of the photoelectron return current towards the portion of the antenna located within the expanding cloud.     

Water combinations on the surface of the asteroid 4 Vesta

The spectral-frequency method (Busarev et al., 2007b) allowed us to obtain data on 16 sizes of hydrosilicate spots on the surface of the asteroid 4 Vesta. Large sizes (800 and 750 km) show clusters of small hydrosilicate spots near a well-known crater. Small spots of 50–13 km cover more than 50% of the surface. The predominant number of small-sized spots suggests their recent origin. Our data confirm the presence of water combinations on the surface of 4 Vesta and allow us to draw a conclusion on their recent appearance in collisions of this asteroid with primitive bodies arriving from the zone of Jupiter.     

Investigation of the electrostatic charging of dust particles in a Paul-trap

Dust particles (glass, tungsten, and nickel) with sizes ranging from 0.25 to 3m were levitated in a Paul-trap and charged by ions or electrons. For ions the particle potential is limited at field strength of about 1×10⁹ V m^–1 by a temperature-dependent discharge mechanism. The particles interaction with 2 to 20 keV electrons always leads to positive surface potentials which can be explained in terms of a decreased absorption of electrons by small particles. Micrometer sized agglomerates were used for the investigation of the electrostatic fragmentation. Fragmentation takes place in a twofold manner: small surface flufl can be removed or the parent particle can be disrupted into smaller agglomerates.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Electrostatic forces and shadow effects in planetary dust rings

The vertical dust distribution of dust clouds around planets, resulting from electrostatic forces, is calculated as a function of dust and plasma parameters. Photoelectric charging is included and differences between clouds on the illuminated side and in the shadow zone are examined. We compute ring structures for conditions which may apply in the spoke-forming regions and study at what dust and plasma conditions the shadow has a significant effect on the vertical dust cloud structure.     

Factors affecting the motion of interplanetary dust particles

In this paper the dynamics of individual dust particles and the effects on their motion caused by insolation and consequent evaporation is considered. Evaporation rates and the radii of dust-free zones have been computed using thermodynamic data from various sources. Some doubt is thrown on the validity of the process of matching observed thermal emission peaks with theoretical evaporation zone radii.     

Hydromagnetic flow near an oscillating porous limiting surface

Unsteady hydromagnetic flow near a harmonically oscillating limiting surface (e.g., of a star) is considered in presence of a transverse magnetic field. Exact solutions, for a periodic boundary layer without a mean steady flow,are obtained when the magnetic Prandtl number is unity and there is a normal velocity of injection imposed at the wall. The results are also presented for the case when the wall is subjected to a normal velocity of suction instead of injection. It is observed that two distinct boundary (or hydromagnetic boundary) layers exist and tend to coalesce into a single layer when the magnetic field parameter approaches zero. The thicknesses of these boundary layers are significantly affected by the injection/suction velocity and the applied magnetic field.     

The Electrostatic Lunar Dust Analyzer (ELDA) for the detection and trajectory measurement of slow-moving dust particles from the lunar surface

Micron and submicron-sized dust particles can be lifted from the lunar surface due to continual micrometeoroid bombardment and electrostatic charging. The characteristics of these dust populations are of scientific interest and engineering importance for the design of future equipment to operate on the lunar surface. The mobilized grains are expected to have a low velocity, which makes their detection difficult by traditional methods that are based on momentum transfer or impact energy. We describe a newly developed instrument concept, the Electrostatic Lunar Dust Analyzer (ELDA), which utilizes the charge on the dust for detection and analysis. ELDA consists of an array of wire electrodes combined with an electrostatic deflection field region, and measures the mass, charge, and velocity vector of individual dust grains. The first basic prototype of the ELDA instrument has been constructed, tested and characterized in the laboratory. The instrument is set up to measure over a velocity range 1–100 m/s and is sensitive to particles from an approximate mass range from 2×10⁻¹⁶ to 10⁻¹¹ kg, depending on the charge state and velocity.     

A multi-year survey of dynamics near the surface in the northern hemisphere of Mars: Short-period baroclinic waves and dust storms

Baroclinic waves figure prominently in the dynamics of the northern hemisphere of Mars, and extensive observations by the Viking Landers and two atmospheric sounders on Mars Global Surveyor have revealed many of their basic properties. However, previous investigations considered these data sets individually, so that their cumulative value is not fully appreciated. We have re-examined these data to extract new information about the dynamics near the surface at mid-to-high northern latitudes. By applying the same method of spectral analysis to each type of observation, we derive a uniform, multi-year characterization of basic elements of martian weather. This survey documents the time evolution of baroclinic waves among modes with different periods and zonal wave numbers. We devote particular attention to a recurring “wave-3 mode”, which is distinguished by its capacity to initiate regional dust storms in the topographic basins of the northern hemisphere. Our results include a detailed case study that shows how the intermittence of this mode and the strong zonal modulation of its amplitude influence the timing and location of these distinctive “flushing” dust storms. More generally, we find that the properties of the wave-3 mode are largely the same whenever it appears and that its intermittence plays an important role in the annual dust cycle.