Real-Time Flux Density Measurements of the 2011 Draconid Meteor Outburst

During the 2011 outburst of the Draconid meteor shower, members of the Video Meteor Network of the International Meteor Organization provided, for the first time, fully automated flux density measurements in the optical domain. The data set revealed a primary maximum at 20:09 UT ± 5 min on 8 October 2011 (195.036° solar longitude) with an equivalent meteoroid flux density of (118 ± 10) × 10^?3/km²/h at a meteor limiting magnitude of +6.5, which is thought to be caused by the 1900 dust trail. We also find that the outburst had a full width at half maximum of 80 min, a mean radiant position of α = 262.2°, δ = +56.2° (±1.3°) and geocentric velocity of v_geo = 17.4 km/s (±0.5 km/s). Finally, our data set appears to be consistent with a small sub-maximum at 19:34 UT ±7 min (195.036° solar longitude) which has earlier been reported by radio observations and may be attributed to the 1907 dust trail. We plan to implement automated real-time flux density measurements for all known meteor showers on a regular basis soon.     

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus’ equilateral equilibrium points is investigated with respect to the inclination of the asteroid’s orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L ₄ and L ₅, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 × 10⁹ years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 ≤ a ≤ 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids’ orbit was varied in the range 0° < i < 60° and the semimajor axes were fixed. It turned out that only four ‘windows’ of stable orbits survive: these are the orbits for the initial inclinations 0° < i < 7°, 9° < i < 13°, 31° < i < 36° and 38° < i < 50°. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.     

Atmospheric trajectory and orbit of the Omolon meteorite

Abstract— The Omolon meteorite fell on 1981 May 15 at 17:10 U.T. to a point with the coordinates φ = 64°01′08″ N, λ = 161°48′30″ E. This is the fifth pallasite that was observed at the moment of its fall and the largest of the pallasites known worldwide (250 kg). The history of the observation, search, and finding of the meteorite is briefly described. From the size of the meteorite and the funnel that it produced, the velocity of its encounter with the ground is estimated by aerodynamic formulas to be 220 m/s. An attempt at estimating the meteorite's initial velocity and mass from its terminal values (which yielded the mass range of 390–490 kg that corresponds to the velocity range of 12–15 km/s) was successful for the mass but unsuccessful for the velocity and the incidence angle, because the problem was ill posed. The position of the radiant is determined from the available observations to be α = 176.4°, δ = +24.1° (Leo). The radiant was situated at an elongation of 29° from the antapex, which means that this was an overtaking meteorite and its entry velocity did not exceed 16 km/s. Three variants of the calculation of the orbital elements—for an entry velocity of 12, 14, and 16 km/s—are presented. In all the three cases, the meteoroid's orbit is close to the orbits of Apollo asteroids and to the orbits of iron meteoroids observed as fireballs with bright iron lines in their spectra. The Omolon meteorite was probably a fragment of an Apollo M-type asteroid. This study is the first attempt at calculating the orbit of a pallasite.     

Hercules and Wolf 630 stellar streams and galactic bar kinematics

We have identified the four most significant features in the UV velocity distribution of solarneighborhood stars: H1, H2 in the Hercules stream and W1, W2 in the Wolf 630 stream. We have formulated the problemof determining several characteristics of the centralGalactic bar independently from each of the identified features by assuming that the Hercules and Wolf 630 streams are of a bar-induced dynamical nature. The problem has been solved by constructing 2: 1 resonant orbits in the rotating bar frame for each star in these streams. Analysis of the resonant orbits found has shown that the bar pattern speed is 45–55 km s^?1 kpc^?1, while the bar angle lies within the range 40°?60°. The results obtained are consistent with the view that the Hercules andWolf 630 streams could be formed by a long-term influence of the Galactic bar leading to a characteristic bimodal splitting of the UV velocity plane.     

Analysis of a Low Density Meteoroid with Enhanced Sodium

We present an analysis of sporadic meteor number 07406018, observed by image intensified video cameras at two stations, which showed a pronounced deceleration along its trajectory. We have applied the erosion model to analyze simultaneously the deceleration and light curve. We have found that the meteoroid had a low density of about 500 kg m⁻³, consistent with its cometary orbit. The meteoroid structure was, nevertheless, markedly different from the Draconid meteoroids, studied recently with the same model. The size of the constituent grains was larger and the erosion energy was higher than in Draconids. The meteor spectrum was also different from Draconid spectra and showed very bright Na lines. The meteoroid composition was probably different from normal cometary composition.     

Black hole at the center of the globular cluster M15: Estimation of the mass and specific angular momentum

Using the technique of determining the sum of the masses of double stars, we have estimated the mass of the central object in the globular cluster M15. The radial velocities of stars at distances up to 1″ from the cluster center have been used. The parameters of circular orbits and the space velocities of 11 selected field stars relative to the cluster center have been determined from the calculated velocity dispersions with respect to the mean radial velocity. Based on the mean space velocity V, 14 km s^?1, and using the energy integral, we have estimated the mass of the central object to be within the range (1?9) × 10³ M _⊙. We have estimated the kinetic power of the outflow of matter from the region surrounding the black hole in M15 and the specific angular momentum of the black hole.     

2-Gyr Simulation of the Oort-cloud Formation II. A Close View of the Inner Oort cloud after the First Two Giga-years

We simulate the formation of the Oort cloud (OC) till the age of 2 Gyr starting from an initial disc of planetesimals made by 10 038 test particles. The results on the outer part of the distant comet reservoir are reported by Neslu?an et al. (this issue). Here we deal with the evolution of the population and structure at 2 Gyr of the complementary inner part of the Oort cloud. The dynamical evolution of the massless test particles was followed via the numerical integration of their orbits. We considered the perturbations produced by four giant planets assuming they have their current orbits and masses, as well as the perturbations caused by the Galactic tide and passing stars. The efficiency of the formation of inner OC is found to be very low: only about 1.1% of all considered particles ended in this part of the OC. At 2 Gyr, the dynamics of the inner cloud is mainly governed by the dominant z-term of the Galactic tide. The number density of the bodies is proportional to the heliocentric distance, r, as r ^?3.53. The directional distribution of orbits is still strongly inhomogeneous. There are large empty regions in the space angles around the Galactic Equator points with the galactic longitude 90 and 270° (non-rotating frame), or there are only few bodies having the ecliptical latitude higher than +60° or lower than 60°. A strong concentration of objects at the Ecliptic is apparent up to ≈1,000 AU, with a possible—but still not proved—extension to ≈1,500 AU. Beyond r ≈ 6,000 AU, bodies directly above and below the Sun, with respect to the Ecliptic, are absent.     

Periodic orbits in the general three-body problem and the relationship between them

We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ₁ and φ₂, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ₁, φ₂∈(0, π) at steps of δk=0.01; δφ₁=δφ₂=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ₁, φ₂). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup.     

The stability of vertical motion in the N-body circular Sitnikov problem

We present results about the stability of vertical motion and its bifurcations into families of 3-dimensional (3D) periodic orbits in the Sitnikov restricted N-body problem. In particular, we consider ν = N ? 1 equal mass primary bodies which rotate on a circle, while the Nth body (of negligible mass) moves perpendicularly to the plane of the primaries. Thus, we extend previous work on the 4-body Sitnikov problem to the N-body case, with N = 5, 9, 15, 25 and beyond. We find, for all cases we have considered with N ≥ 4, that the Sitnikov family has only one stability interval (on the z-axis), unlike the N = 3 case where there is an infinity of such intervals. We also show that for N = 5, 9, 15, 25 there are, respectively, 14, 16, 18, 20 critical Sitnikov periodic orbits from which 3D families (no longer rectilinear) bifurcate. We have also studied the physically interesting question of the extent of bounded dynamics away from the z-axis, taking initial conditions on x, y planes, at constant z(0) = z ₀ values, where z ₀ lies within the interval of stable rectilinear motions. We performed a similar study of the dynamics near some members of 3D families of periodic solutions and found, on suitably chosen Poincaré surfaces of section, “islands” of ordered motion, while away from them most orbits become chaotic and eventually escape to infinity. Finally, we solve the equations of motion of a small mass in the presence of a uniform rotating ring. Studying the stability of the vertical orbits in that case, we again discover a single stability interval, which, as N grows, tends to coincide with the stability interval of the N-body problem, when the values of the density and radius of the ring equal those of the corresponding system of N ? 1 primary masses.     

Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

A rare reflection effect eclipsing sdB+dM binary: 2M 1533+3759

In this paper, we report a rare reflection effect eclipsing sdB+dM binary, 2M?1533+3759. It is the seventh eclipsing sdB+dM binary that has been discovered to date. This system has an orbital period of 0.16177042 day and a velocity semi-amplitude of 71.1 km?s^?1. Using a grid of zero-metallicity NLTE model atmospheres, we derived T _eff=29250 K, log?g=5.58 and [He/H]=?2.37 from spectra taken near the reflection effection minimum. Lightcurve modeling resulted in a system mass ratio of 0.301 and an orbital inclination angle of 86.6°. The derived primary mass for 2M?1533+3759, 0.376±0.055 M _⊙, is significantly lower than the canonical mass (0.48 M _⊙) found for most previously investigated sdB stars. This implies an initial progenitor mass >1.8 M _⊙, at least a main sequence A star and perhaps even one massive enough to undergo non-degenerate helium ignition.     

Spectral,Photometric, and Dynamic Analysis of Eight Draconid Meteors

A Draconid meteor shower outburst was observed from on board two scientific aircraft deployed above Northern Europe on 8th October 2011. The activity profile was measured using a set of photographic and video cameras. The main peak of the activity occurred around 20:15 ± 0:0.5 UT which is consistent with the model prediction as well as with the IMO network visual observations. The corrected hourly rates reached a value of almost 350. The brighter meteors peaked about 15–20 min earlier than the dimmer ones. This difference can be explained by different directions of the ejection of the meteoroids from the parent comet. One of the instruments was even able to detect meteors connected with the material ejected from the parent comet before 1900 and thus confirmed the prediction of the model, although it was based on uncertain pre-1900 cometary data. Another small peak of the activity, which was caused by material ejected during the 1926 perihelion passage of the parent comet, was detected around 21:10 UT. The mass distribution index determined using the narrow field-of-view video camera was 2.0 ± 0.1. This work shows that the observation of meteor outbursts can constrain the orbital elements, outgassing activity and existence of jets at the surface of a comet.     

Eccentricity Generation in Hierarchical Triple Systems with Non-coplanar and Initially Circular Orbits

In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well-separated components, based on an expansion of the rate of change of the Runge-Lenz vector. Now, the same technique is extended to non-coplanar orbits. However, it can only be applied to systems with I ₀ < 39.23° or I ₀ > 140.77°, where I is the inclination of the two orbits, because of complications arising from the so-called ‘Kozai effect’. The theoretical model is tested against results from numerical integrations of the full equations of motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Atmospheric parameters of the B-supergiant HD 198478 from the UV spectra

We determined atmospheric parameters of the Galactic early B-supergiant HD 198478 (55 Cyg) from the UV silicon lines taken from the high-resolution 1150–1980 Å IUE spectra. TLUSTY numerical code was used to model the stellar atmosphere and to determine the temperature and surface gravity assuming a non-LTE plane parallel hydrostatic stellar atmosphere with microturbulence. The synthesized spectra were broadened by the IUE instrumental profile, rotational and macroturbulent velocity with ROTIN numerical code. The silicon 1264 Å, 1309 Å, 1312 Å, 1417 Å and 1294–1303 Å multiplet lines of different stages of ionization (Si II and Si III) and Balmer Hδ 4101 Å line were modeled, leading to the temperature, surface gravity, rotational and macroturbulent velocity values. Our results have shown that the line broadening cannot be explained by rotational velocity only, but additional macroturbulent velocity component should be taken into account. HD 198478 shows a significant degeneracy in velocity, which means that the individual contributions of the macroturbulence and rotation in the total velocity broadening cannot be distinguished. Adequate fit of TLUSTY models to the observed non-resonant silicon lines suggests that the non-LTE plane-parallel hydrostatic stellar model without wind contribution can be used to explain such lines. We have obtained similar results using the HST STIS spectra in the same procedure, showing that the IUE spectra, despite their lacking quality compared to the STIS spectra, are reliable enough in determination of the B supergiants’ photospheric parameters.     

A Model for the Common Origin of Jupiter Family and Halley Type Comets

A numerical simulation of the Oort cloud is used to explain the observed orbital distributions and numbers of Jupiter-family (JF) and Halley-type (HT) short-period (SP) comets. Comets are given initial orbits with perihelion distances between 5 and 36 au, and evolve under planetary, stellar and Galactic perturbations for 4.5 Gyr. This process leads to the formation of an Oort cloud (which we define as the region of semimajor axes a > 1,000 au), and to a flux of cometary bodies from the Oort cloud returning to the planetary region at the present epoch. The results are consistent with the dynamical characteristics of SP comets and other observed cometary populations: the near-parabolic flux, Centaurs, and high-eccentricity trans-Neptunian objects. To achieve this consistency with observations, the model requires that the number of comets versus initial perihelion distance is concentrated towards the outer planetary region. Moreover, the mean physical lifetime of observable comets in the inner planetary region (q < 2.5 au) at the present epoch should be an increasing function of the comets’ initial perihelion distances. Virtually all observed HT comets and nearly half of observed JF comets come from the Oort cloud, and initially (4.5 Gyr ago) from orbits concentrated near the outer planetary region. Comets that have been in the Oort cloud also return to the Centaur (5 < q < 28 au, a < 1,000 au) and near-Neptune high-eccentricity regions. Such objects with perihelia near Neptune are hard to discover, but Centaurs with characteristics predicted by the model (e.g. large semimajor axes, above 60 au, or high inclinations, above 40°) are increasingly being found by observers. The model provides a unified picture for the origin of JF and HT comets. It predicts that the mean physical lifetime of all comets in the region q < 1.5 au is less than ～200 revolutions.     

Numerical experiment applicable to the latest stage of planet growth

A three-dimensional numerical model was developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (～ Moon size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion, and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of R. Greenberg et al. (1978, Icarus, 35, 1–26). In the present work, we consider 25 protoplanets with uniform mass distribution in the range 2 × 10²⁵?4 × 10²⁶ g on heliocentric orbits in the Earth zone. These bodies are initially confined to a small volume of space to permit gravitational perturbations by close approaches and collisions within a finite length of integration time. The dynamical evolution of the swarm is followed for four different sets of initial ranges in semimajor axis, eccentricity, and inclination: Δa=0.01, 0.02, 0.04, 0.08 AU; Δe= 0.005, 0.01, 0.02, 0.04; Δi=0°3, 0°6, 1°2, 2°4. Among other results, it is found that average eccentricities and inclinations evolve toward a steady state such that $\text{i}\text{?}\text{1}\text{2}\text{,}\text{e}$; it is also found that, whatever the initial conditions, the population evolves toward a quasi-equilibrium relative velocity distribution corresponding to a Safronov parameter value $\text{θ?10}$. Moreover, the growth process of the growing planet presents very similar behavior in the four cases considered, except for the time scale of evolution, which increases with the initial range of orbital elements. Earlier works of this kind have been presented by L.P. Cox and J.S. Lewis (1980, Icarus, 44, 706–721) and by G.N. Wetherill (1980b, In Geol. Soc. Canad. Spec. Publ., p. 20), although a number of differences exist between the three approaches.     

Radiants of the Leonids 1999 and 2001 Obtained by Lltv Systems Using Automatic Software Tools

Both amateur and professional meteor groups are more frequently using Low-Light level TV (LLTV) systems to record meteors. Double-station observations can yield orbit data. However, data analysis normally is still done by hand and thus time consuming. This paper addresses the question of whether available automated tools can be used to determine reasonably accurate orbits with minimum human intervention. The European Space Agency performed several observing campaigns to observe the Leonid meteor stream. In November 1999, the ESA meteor group was stationed at two locations in Southern Spain, in November 2001 at two stations close to Broome in North-Western Australia. Double-station observations with LLTV systems were conducted. The data was recorded on S-VHS video tapes. The tapes were processed using automatic detection software from which meteor heights, velocities and radiants were computed. This paper shows the results for the two maximum nights. The radiants determined in 1999 show a very large scatter due to unfortunate observing geometry and inaccurate position determination since one of the cameras was moving because of the wind. The 2001 data is excellent and the radiant was determined to be at RA = 153.96°±0.3° and Dec = 21.09°±0.2°. The error bars for individual meteor radiants are about 0.2° to 0.4°. This demonstrates that is indeed possible to determine good radiant positions using totally automated tools. Orbits, on the other hand, are not well defined due to the fact that the velocity of individual meteors shows large errors. Reasons for this are described.     

Artificial Martian frozen orbits and Sun-Synchronous orbits using continuous low-thrust control

This paper analyses three types of artificial orbits around Mars pushed by continuous low-thrust control: artificial frozen orbits, artificial Sun-Synchronous orbits and artificial Sun-Synchronous frozen orbits. These artificial orbits have similar characteristics to natural frozen orbits and Sun-Synchronous orbits, and their orbital parameters can be selected arbitrarily by using continuous low-thrust control. One control strategy to achieve the artificial frozen orbit is using both the transverse and radial continuous low-thrust control, and another to achieve the artificial Sun-Synchronous orbit is using the normal continuous low-thrust control. These continuous low-thrust control strategies consider J ₂, J ₃, and J ₄ perturbations of Mars. It is proved that both control strategies can minimize characteristic velocity. Relevant formulas are derived, and numerical results are presented. Given the same initial orbital parameters, the control acceleration and characteristic velocity taking into account J ₂, J ₃, and J ₄ perturbations are similar to those taking into account J ₂ perturbations for both Mars and the Earth. The control thrust of the orbit around Mars is smaller than that around the Earth. The magnitude of the control acceleration of ASFOM-4 (named as Artificial Sun-Synchronous Frozen Orbit Method 4) is the lowest among these strategies and the characteristic velocity within one orbital period is only 0.5219 m/s for the artificial Sun-Synchronous frozen orbit around Mars. It is evident that the relationship among the control thrusts and the primary orbital parameters of Martian artificial orbits is always similar to that of the Earth. Simulation shows that the control scheme extends the orbital parameters’ selection range of three types of orbits around Mars, compared with the natural frozen orbit and Sun-Synchronous orbit.     

Bulk motions of flat galaxies on 100-Mpc scales from new data

We use a new expanded and partially modified sample of 1501 thin edge-on spiral galaxies from the RFGC catalog to analyze the non-Hubble bulk motions of galaxies on the basis of a generalized multiparameter Tully-Fisher relation. The results obtained have confirmed and refined our previous conclusions (Parnovsky et al. 2001), in particular, the statistical significance of the quadrupole and octupole components of the galaxy bulk velocity field. The quadrupole component, which is probably produced by tidal forces from overdense regions, leads to a difference in the recession velocities of galaxies on scales of 8000–10000 km s^?1 up to 6% of their Hubble velocity. On Local Supercluster scales (3000 km s^?1), its contribution increases to about 20%. Including the octupole components in the model causes the dipole component to decrease to the 1σ level. In contrast, in the dipole model, the galaxy bulk velocity relative to the frame of reference of the cosmic microwave background is 310±75 km s^?1 toward the apex with l=311° and b=12°. We also consider a sample of 1493 galaxies that was drawn using a more stringent galaxy selection criterion. The difference between the results of our data analysis for this sample and for the sample of 1501 galaxies is primarily attributable to a decrease in the dipole velocity component (290±75 km s^?1 toward the apex with l=310° and b=12°) and a decrease in σ by about 2%.     

Peculiarities of Uranus’s satellite system

The absence of Uranus’s equatorial satellites in the region of approximately equal influence of its oblateness and solar perturbations is explained in terms of an improved physical model. This model is more complete than the previously studied case of an integrable averaged problem. The model improvement stems from the fact that the inclination of Uranus’s equator to the ecliptic differs by 90° and that the orbital evolution of Uranus due to secular planetary perturbations is taken into account. The lifetime of Uranus’s hypothetical satellites in orbits with semimajor axes 1.3–7 million km can be estimated by numerically integrating the evolution equations to be ～10⁴ yr. This is the time scale on which the evolution of the orbits leads to their intersection with the orbits of inner satellites.