Small observatories for the UV

We describe concepts for small space telescopes that are able to provide significant UV science and can be realized with small (but realistic) budgets. The concepts are based on nano-satellites carrying small optics, with no redundancy, without producing intermediate models prior to flight model, and using COTS (custom off-the-shelf) components. We describe a few concepts of deployable optics that could provide large collecting areas and high angular resolution while packaged in the small volume of a nano-satellite. We point out areas where technological development is still required.     

Distribution of small channels on the Martian surface

The distribution of small channels on Mars has been mapped from Mariner 9 images, at the 1:5 000 000 scale, by the author. The small channels referred to here are small valleys ranging in width from the resolution limit of the Mariner 9 wide-angle images (～1 km) to about 10 km. The greatest density of small band occurs in dark cratered terrain. This dark zone forms a broad subequatorial band around the planet. The observed distribution may be the result of decreased small-channel visibility in bright areas due to obscuration by a high albedo dust or sediment mantle. Crater densities within two small-channel segments show crater size-frequency distributions consistent with those of the oldest of the heavily cratered plains units. Such crater densities coupled with the almost exclusive occurrence of small channels in old cratered terrain and the generally degraded appearance of small channels in the high-resolution images (～100 m) imply a major episode of small-channel formation early in Martian geologic history.     

Families of periodic planetary-type orbits in the three-body problem and their stability

Several families of the planar general three-body problem for fixed values of the three masses are found, in a rotating frame of reference, where the mass of two of the bodies is small compared to the mass of the third body. These families were obtained by the continuation of a degenerate family of periodic orbits of three bodies where two of the bodies have zero masses and describe circular orbits around a third body with finite mass, in the same direction.The above families represent planetary systems with the body with the large mass representing the Sun and the two small bodies representing two planets or comets. One section of a family is shown to represent the Jupiter family of comets and also a model for the Sun-Jupiter-Saturn system is found.The stability analysis revealed that stability exists for small masses and small eccentricities of the two planets. Planetary systems with relatively large masses and eccentricities are proved to be unstable. In particular, the Jupiter family of comets, for small masses of the two small bodies, and the Sun-Jupiter-Saturn system are proved to be stable. Also, it was shown that resonances are not necessarily associated with instabilities.     

Shape of small solar system bodies

The morphometric parameters are examined for the shape of fragments of ordinary chondrites, iron meteorites, S- and C-class stony asteroids, metallic asteroids, and icy small bodies of the Solar System. All small Solar System bodies are shown to have, depending on their composition and, hence, physical and mechanical properties, a specific shape that is unique to a given composition. C-class asteroids, the strength of which is almost three times less than that of S asteroids, differ from the latter in their less elongated shape. No systematic change is observed in the morphometric parameters (increased roundness or sphericity) of small bodies of differing compositions depending on their mass, which suggests that the hypothesis of creep in small Solar System bodies is unlikely to be true. The absence of creep confirms that, regardless of their composition, all small Solar System bodies are solid elastic bodies having an ultimate strength (tensile strength and compressive strength) and a yield strength.     

Dynamical capture in the Pluto–Charon system

This paper explores the possibility that the progenitors of the small satellites of Pluto got captured in the Pluto?CCharon system from the massive heliocentric planetesimal disk in which Pluto was originally embedded into. We find that, if the dynamical excitation of the disk is small, temporary capture in the Pluto?CCharon system can occur with non- negligible probability, due to the dynamical perturbations exerted by the binary nature of the Pluto?CCharon pair. However, the captured objects remain on very elliptic orbits and the typical capture time is only ~ 100?years. In order to explain the origin of the small satellites of Pluto, we conjecture that some of these objects got disrupted during their Pluto-bound phase by a collision with a planetesimal of the disk. This could have generated a debris disk, which damped under internal collisional evolution, until turning itself into an accretional disk that could form small satellites on circular orbits, co-planar with Charon. Unfortunately, we find that objects large enough to carry a sufficient amount of mass to generate the small satellites of Pluto have collisional lifetimes orders of magnitude longer than the capture time. Thus, this scenario cannot explain the origin of the small satellites of Pluto, which remains elusive.     

Microstrip antenna array for the onboard radio system of small spacecraft

The article presents the results of the development of a directional microstrip antenna array with small mass-dimensional characteristics as a directional antenna of the transmitting channel of a small spacecraft.     

Second-order matching in the restricted three-body problem (smallμ)

Elliptic orbits around the large primary are matched to hyperbolas, osculating at closest approach, around the small primary of the circular restricted three-body problem. The distance of closest approach to the small primary is assumed to be of the same order as the mass-ratio μ of small to large primary. The dependence of the hyperbola on initial conditions for the elliptic orbit is carried to second order jointly in μ and in the variations of the initial conditions, which are three-dimensional rather than two-dimensional.     

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.     

A Small Pore Observed with a 1.6 m Telescope

A small pore was observed with the New Solar Telescope of 1.6 m aperture at Big Bear Solar Observatory. At a wavelength of 705.68 nm, a diffraction limit of 0.09″ was reached and approximately 700 small structures were analyzed. The achieved high resolution has revealed details about the dynamics of small structures in and around the pore. The small structures either reside in the pore, enter the pore from the vicinity, or dip in and out of the pore. Their sizes are similar, ≈?0.2″, but their observed oscillations do not show power peaks at the same periods. Horizontal plasma flows were suppressed in the pore by 38 % for average velocities, and 65 % for maximum velocities, compared to the quiet Sun.     

High-velocity stars from decay of small stellar systems

In this paper we present numerical results on the decay of small stellar systems under different initial conditions (multiplicity 3 ≤  N  ≤ 10, and various mass spectra, initial velocities and initial configurations). The numerical treatment uses the CHAIN1 code (Mikkola &38; Aarseth). Particular attention is paid to the distribution of high-velocity escapers: we define these as stars with velocity above 30 km s⁻¹. These numerical experiments confirm that small N -body systems are dynamically unstable and produce cascades of escapers in the process of their decay. It is shown that the fraction of stars that escape from small dense stellar systems with an escape velocity greater than 30 km s⁻¹ is ∼1 per cent for all systems treated here. This relatively small fraction must be considered in relation to the rate of star formation in the Galaxy in small groups: this could explain some moderately high-velocity stars observed in the Galactic disc and possibly some young stars with relatively high metallicity in the thick disc.     

Combined effect of YORP and collisions on the rotation rate of small Main Belt asteroids

The rotation rate distribution of small Main Belt asteroids is dominated by YORP and collisions. These mechanism act differently depending on the size of the bodies and give rise to non-linear effects when they both operate. Using a Monte Carlo method we model the formation of a steady state population of small asteroids under the influence of both mechanisms and the rotation rate distribution is compared to the observed one as derived from Pravec et al. (Pravec, P. et al. [2008]. Icarus 197, 497-504). A better match to observations is obtained with respect to the case in which only YORP is considered. In particular, an excess of slow rotators is produced in the model with both collisions and YORP because bodies driven to slow rotation by YORP have a random walk-like evolution of the spin induced by repeated collisions with small projectiles. This is a dynamical evolution different from tumbling and it lasts until a large impact takes the body to a faster rotation rate. According to our model, the rotational fission of small asteroids is a very frequent event and might explain objects like P/2010 A2 and its associated tail of millimeter-sized dust particles. The mass loss during fission of small asteroids might significantly influence the overall collisional evolution of the belt. Fission can in fact be considered as an additional erosion mechanism, besides cratering and fragmentation, acting only at small diameters.     

Radiation absorption effects on the transient free-convection currents of a laminar boundary-layer

The influence of radiation absorption on the free-convection currents on a vertical porous flat plate has been considered. A steady transverse magnetic field has been assumed, while the absorption is the result of the presence of a strong radiation-absorbing second material, in a small concentration within the main fluid. The analytical solution is in terms of the very small Eckert number, which expresses the viscous dissipation term. The solution shows small influence on the general velocity and temperature profile, but a strong one in the skin friction and the heat flux.     

On the problem of designing small spacecraft with electric propulsion power plants for studying minor bodies of the Solar System

Aspects of the design of small spacecraft with electric propulsion power plants for investigating minor bodies in the Solar System are examined. The results of design and ballistic analysis of transfer into an orbit of terrestrial asteroids using electric propulsion thrusters are given. The possible concept design of the spacecraft is determined and the structure of a small spacecraft with an electric propulsion power plant is presented. Parameters of the electric propulsion power plant of a small spacecraft for a flight to the minor bodies of the Solar System are estimated.     

Optical properties of particulates

Optical properties of small particles of olivine (less than 0.1 μ) have been studied in the ultraviolet as an example of an insulating solid. Very little structure survives in the ultraviolet extinction curves for such small particles. By contrast ‘surface modes’, observed for graphite small particles in the ultraviolet and for olivine particles in the infrared, produce dominant and persistent structure in extinction. The general trend of optical properties of graphite is surprisingly similar to the behavior required to explain all features of the interstellar extinction and albedo curves from near visible to 1000 Å. Measured extinction of small olivine particles in the infrared agrees with calculations based on newly measured optical constants, but dominant sharp structure in the 10μ region still presents a bit of a problem in explaining ‘silicate’ features in astronomical data.     

Martian cratering 11. Utilizing decameter scale crater populations to study Martian history

New information has been obtained in recent years regarding formation rates and the production size‐frequency distribution (PSFD) of decameter‐scale primary Martian craters formed during recent orbiter missions. Here we compare the PSFD of the currently forming small primaries (P) with new data on the PSFD of the total small crater population that includes primaries and field secondaries (P + fS), which represents an average over longer time periods. The two data sets, if used in a combined manner, have extraordinary potential for clarifying not only the evolutionary history and resurfacing episodes of small Martian geological formations (as small as one or few km²) but also possible episodes of recent climatic change. In response to recent discussions of statistical methodologies, we point out that crater counts do not produce idealized statistics, and that inherent uncertainties limit improvements that can be made by more sophisticated statistical analyses. We propose three mutually supportive procedures for interpreting crater counts of small craters in this context. Applications of these procedures support suggestions that topographic features in upper meters of mid‐latitude ice‐rich areas date only from the last few periods of extreme Martian obliquity, and associated predicted climate excursions.     

Small hypervelocity particles captured in aerogel collectors: Location,extraction, handling and storage

Abstract— It has now been about a decade since the first demonstrations that hypervelocity particles could be captured, partially intact, in aerogel collectors. But the initial promise of a bonanza of partially‐intact extraterrestrial particles, collected in space, has yet to materialize. One of the difficulties that investigators have encountered is that the location, extraction, handling and analysis of very small (10 μm and less) grains, which constitute the vast majority of the captured particles, is challenging and burdensome. Furthermore, current extraction techniques tend to be destructive over large areas of the collectors. Here we describe our efforts to alleviate some of these difficulties. We have learned how to rapidly and efficiently locate captured particles in aerogel collectors, using an automated microscopic scanning system originally developed for experimental nuclear astrophysics. We have learned how to precisely excavate small access tunnels and trenches using an automated micromanipulator and glass microneedles as tools. These excavations are only destructive to the collector in a very small area—this feature may be particularly important for excavations in the precious Stardust collectors. Using actuatable silicon microtweezers, we have learned how to extract and store “naked” particles—essentially free of aerogel—as small as 3 μm in size. We have also developed a technique for extracting particles, along with their terminal tracks, still embedded in small cubical aerogel blocks. We have developed a novel method for storing very small particles in etched nuclear tracks. We have applied these techniques to the extraction and storage of grains captured in aerogel collectors (Particle Impact Experiment, Orbital Debris Collector Experiment, Comet‐99) in low Earth orbit.     

The strength of regolith and rubble pile asteroids

We explore the hypothesis that, due to small van der Waals forces between constituent grains, small rubble pile asteroids have a small but nonzero cohesive strength. The nature of this model predicts that the cohesive strength should be constant independent of asteroid size, which creates a scale dependence with relative strength increasing as size decreases. This model counters classical theory that rubble pile asteroids should behave as scale‐independent cohesionless collections of rocks. We explore a simple model for asteroid strength that is based on these weak forces, validate it through granular mechanics simulations and comparisons with properties of lunar regolith, and then explore its implications and ability to explain and predict observed properties of small asteroids in the NEA and Main Belt populations, and in particular of asteroid 2008 TC₃. One conclusion is that the population of rapidly rotating asteroids could consist of both distributions of smaller grains (i.e., rubble piles) and of monolithic boulders.     

用切比雪夫曲线拟合导航卫星广播星历

提出用一种基于切比雪夫曲线多项式拟合的方法,来拟合导航卫星广播星历。该方法对解决 GEO导航卫星的小倾角、小偏心率问题特别有效,并具有精度高、使用方便等特点。     

Dynamical evolution of weakly disturbed two-planetary system on cosmogonic time scales: The Sun-Jupiter-Saturn system

In the present paper, we used the Hori-Deprit method to construct the averaged Hamiltonian of the two-planetary problem accurate to the second order of a small parameter, the generating function of the transform, the change of variables formulas, and the right-hand sides of the equations in average elements. The evolution of the two-planet Sun-Jupiter-Saturn system was investigated by numerical integration over 10 billion years. The motion of the planets has an almost periodic character. The eccentricities and inclinations of Jupiter’s and Saturn’s orbits remain small but different from zero. The short-term disturbances remain small over the entire period considered in the study.     

Series expansions for encounter-type solutions of Hill's problem

Hill's problem is defined as the limiting case of the planar three-body problem when two of the masses are very small. This paper describes analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem.