The Pribram,Lost City,Innisfree, and Neuschwanstein falls: An analysis of the atmospheric trajectories

To date, several meteorites have been found for which their flight in the atmosphere was recorded by special fireball camera networks. Because of this, a thorough analysis of the instrumentally registered falls is of current importance. For such fireballs, not only the high-quality photo images of the motion in the atmosphere exist, but also the density and the shape of the meteor body fragments reached the Earth’s surface are known for sure. In the present study, for the Innisfree, Lost City, and Pribram fireballs, new models of the entry to the atmosphere have been built. The values of the ballistic coefficient and the mass-loss parameter providing the best approximation for the observations of the luminous trajectory segment with the analytical solution of the meteor physics equations have been obtained. From recent results of the numerical experiments on the supersonic airflow of bodies of various shapes, the preatmospheric masses of the fireballs, as well as the dynamic estimates of the mass at the other trajectory points, were obtained. In particular, the terminal mass of the fireballs in the lower segment of the analyzed trajectories is in good agreement with the total mass of the meteorite material recovered in all of the cases considered. Moreover, to calculate the acceleration of the meteor bodies, a new analytical formula has been suggested, which allows the obtained theoretical time dependencies of the velocity and altitude to be compared with the observational data.     

Meteor Outburst Profiles and Cometary Ejection Models

The spatial structure of meteor streams, and the activity profiles of their corresponding meteor showers, depend firstly on the distribution of meteoroid orbits soon after ejection from the parent comet nucleus, and secondly on the subsequent dynamical evolution. The latter increases in importance as more time elapses. For younger structures within streams, notably the dust trails that cause sharp meteor outbursts, it is the cometary ejection model (meteoroid production rate as a function of time through the several months of the comet’s perihelion return, and velocity distribution of the meteoroids released) that primarily determines the shape and width of the trail structure. This paper describes how a trail cross section can be calculated once an ejection model has been assumed. Such calculations, if made for a range of ejection model parameters and compared with observed parameters of storms and outbursts, can be used to constrain quantitatively the process of meteoroid ejection from the nucleus, including the mass distribution of ejected meteoroids.     

Frequency of hyperbolic and interstellar meteoroids

Hyperbolic meteor orbits from the catalog of 64,650 meteors observed by the multistation video meteor network located in Japan (SonotaCo 2009) have been investigated with the aim of determining the relation between the frequency of hyperbolic and interstellar meteors. The proportion of hyperbolic meteors in the data decreased significantly (from 11.58% to 3.28%) after a selection of quality orbits, which shows its dependence on the quality of observations. Initially, the hyperbolic orbits were searched for meteors unbound due to planetary perturbation. It was determined that 22 meteors from the 7489 hyperbolic orbits in the catalog (and 2 from the selection of the orbits with the highest quality) had had a close encounter with a planet, none of which, however, produced essential changes in their orbits. Similarly, the fraction of hyperbolic orbits in the data, which could be hyperbolic by reason of a meteor's interstellar origin, was determined to be at most 3.9 × 10^?2. From the statistical point of view, the vast majority of hyperbolic meteors in the database have definitely been caused by inaccuracy in the velocity determination. This fact does not necessarily assume great measurement errors, since, especially near the parabolic limit, a small error in the value of the heliocentric velocity of a meteor can create an artificial hyperbolic orbit that does not really exist. The results show that the remaining 96% of meteoroids with apparent hyperbolic orbits belong to the solar system meteoroid population. This is also supported by their high abundance (about 50%) among the meteor showers.     

The Phase Space Structure Around L4 in the Restricted Three-Body Problem

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.     

The Changes of the Orbital Elements and Estimation of the Initial Velocities of Stream Meteoroids Ejected from Comets and Asteroids

The values of the initial velocity of the meteoroids ejected from the parent bodies are small and as a result, the most of the young meteoroid streams have similar orbits to their parent bodies. Assuming that the members of the observed meteor stream evolved under the influence of gravitational perturbations mostly, Pittich [1991, Proceedings of the Conference on Dynamic of Small Bodies of the Solar System, Polish-Slovak Conference, Warsaw, October 25–28, 1988, pp. 55-61], Williams [1996, Earth, Moon, Planets 72, 321–326; 2001, Proceedings of the Meteoroids 2001 conference, Kiruna, Sweden, August 6–10, 2001, pp. 33–42] estimated the ejection velocities of the stream meteoroids. Equation relating the ejection velocity Δυ and the change Δa of the semi-major axis, Williams (2001), was applied with two slightly different variations. In the first one (M1) as Δa the difference between the mean orbit of the stream and the orbit of the parent body was substituted, in the second one (M2), as Δa the dispersion of semi-major axes around the mean orbit of the stream was used. The results obtained by these two methods are not free from discrepancies, partly explained by the particular orbital structure of the stream. Kresak [1992, Contrib. Astron. Obs. Skalnate Pleso 22, 123–130] strongly criticized the attempts to determine the initial velocities of the stream using the statistics of the meteor orbits. He argued that this is essentially impossible, because the dispersion of the initial velocities are masked by much larger measuring errors and by the accumulated effects of planetary perturbations. In our paper, we study the reliability of M1 and M2 methods. We made a numerical experiment consisting of formation of several meteor streams and their dynamical evolution over 5000 years. We ejected meteoroids particles from the comets: 1P/Halley, 2P/Encke, 55P/Tempel-Tuttle, 109P/Swift-Tuttle and from minor planets (3200) Phaethon and 2002 SY₅₀. During the integration, the ejection velocities were estimated using both M1 and M2 methods. The results show that the velocities obtained by M1 method are unstable: too high or too low, when compared with the known ejection velocities at the time of the stream formation. On the other hand, the velocities obtained using M2 method are too small, mostly. In principle, M2 estimates the dispersion of the distribution of the ejection velocities around the mean value, not the mean value itself. Applying more accurate Equation relating Δυ and Δa we decreased the bias of the results, but not their variation observed during the evolution of the streams and the parent bodies. We have found that the variability of the estimated ejection velocities was caused mainly by the gravitational changes of the semi-major axis and eccentricity of the parent body. In brief, we have found that the reliability of the results obtained by M1 or M2 method are low, and have to be used with great care.     

The IMO Virtual Meteor Observatory (VMO): Architectural Design

This paper describes the progress on the Virtual Meteor Observatory (VMO), a database which is being developed at ESA/RSSD to store video meteor observations and their derived orbits. The VMO was triggered by a discussion which took place at the first Meteor Orbit Determination (MOD) workshop in Roden, The Netherlands, in September 2006. Representatives of 15 groups working on the determination of meteor orbits and working with the resulting orbits discussed the design and implementation of a database which would combine different meteor orbit datasets. From this the concept of the VMO was born, which will, in the long run, allow accessing meteor observations via the internet. In the beginning, it will focus on meteor orbit data obtained with video systems. This paper presents the architectural design of the database as it has been defined in the meantime.     

The origin of the June Bootid outburst in 1998 and determination of cometary ejection velocities

Numerical integrations are used to show that the main contribution to the outburst observed in the June Bootid meteor shower in 1998 was a subset of meteoroids released from the parent comet, 7P/Pons–Winnecke, at its 1825 return. A substantial part of the June Bootid stream is in 2:1 resonance with Jupiter. This inhibits chaotic motion, allowing structures in the stream to remain compact enough over centuries that meteor outbursts can still be produced. Circumstances of ejection in 1825 are calculated that exactly result in orbits capable of producing meteors at the observed time in 1998. Required ejection velocities are  10–20 m s^-1  .     

Orbital Distribution Arbitrarily Close to the Homothetic Equilateral Triple Collision in the Free‐Fall Three‐Body Problem with Equal Masses

The existence of escape and nonescape orbits arbitrarily close to the homothetic equilateral triplecollision orbit is considered analytically in the threebody problem with zero initial velocities and equal masses. It is proved that escape orbits in the initial condition space are distributed around three kinds of isosceles orbits. It is also proved that nonescape orbits are distributed in between the escape orbits where different particles escape. In order to show this, it is proved that the homotheticequilateral orbit is isolated from other triplecollision orbits as far as the collision at the first triple encounter is concerned. Moreover, the escape criterion is formulated in the planarisosceles problem and translated into the words of regularizing variables. The result obtained by us explains the orbital structure numerically.     

Orbital structure of the meteor complex according to radar observations in Kazan. 1. Apparent distributions of aphelia

The results of an analysis of the orbital structure of the meteor complex accessible for radar observations at northern midlatitudes are reported. Experimentally, the study is based on the long-term monitoring of the influx of meteor matter into the Earth’s atmosphere performed with the meteor radar of Kazan State University starting from 1986. The study uses a discrete quasi-tomographic method to measure the radiants and velocities of meteor showers based on goniometric data of the meteor radar and diffraction measurements of meteor velocities. The discretization of the detection environment—in particular, in terms of velocity—is shown to result in no substantial loss of measurement accuracy. The error of the measured velocity of the shower does not exceed 1.5 km/s for a standard deviation of a single velocity measurement equal to 3 km/s. Microshower representation is used with microshowers either representing the correlated part of the sporadic complex or being partial streams of major and minor showers, or fragments of the dust environment of minor bodies passing by Earth or falling onto it. The data of measurements made over the entire annual cycle are used to construct combined maps of the distribution of the observed 2263 microshowers (a total of 22 604 orbits) by their inclination, aphelion distance, and longitudes of the ascending nodes of their orbits. The observing conditions are shown to have a significant effect on the parameters of the distribution of aphelion distances for different months, and the corresponding distributions for prograde and retrograde orbits are shown to differ fundamentally. A specific feature of such distribution maps is that they allow uniform representation of both meteor showers and irregularities of the sporadic complex.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

The Canadian Meteor Orbit Radar Meteor Stream Catalogue

The Canadian Meteor Orbit Radar is a multi-frequency backscatter radar which has been in routine operation since 1999, with an orbit measurement capability since 2002. In total, CMOR has measured over 2 million orbits of meteoroids with masses greater than 10 μg, while recording more than 18 million meteor echoes in total. We have applied a two stage comparative technique for identifying meteor streams in this dataset by making use of clustering in radiants and velocities without employing orbital element comparisons directly. From the large dataset of single station echoes, combined radiant activity maps have been constructed by binning and then stacking each years data per degree of solar longitude. Using the single-station mapping technique described in Jones and Jones (Mon Not R Astron Soc 367:1050–1056, 2006) we have identified probable streams from these single station observations. Additionally, using individual radiant and velocity data from the multi-station velocity determination routines, we have utilized a wavelet search algorithm in radiant and velocity space to construct a list of probable streams. These two lists were then compared and only streams detected by both techniques, on multiple frequencies and in multiple years were assigned stream status. From this analysis we have identified 45 annual minor and major streams with high reliability.     

A new octuple Earth-crossing meteoroid stream

It was shown that the orbit of Virginid meteors is an octuple Earth-crosser so that the stream can produce eight related meteor showers. Of these eight theoretical showers five are identified in the catalogues; one of these is the Cygnids.     

Is 2329 Orthos a dead comet?

Probably most meteor showers have a cometary origin. Investigation of Near-Earth asteroids' orbital evolution to determine whether they have related meteor showers is necessary to determine which asteroids evolved from comets. The results of calculations show that asteroid Orthos' orbit is an octuple Earth-crosser. Therefore, if Orthos has an old meteoroid stream it may produce eight meteor showers observable on the Earth. The existence of four Orthos' Northern meteor showers is confirmed by our search in the published catalogues of meteor radiants and orbits or in the archives of the IAU Meteor Data Center (Lund, Sweden).     

Accurate integration of geostationary orbits with Burdet's focal elements

The theory of Burdet's focal elements is outlined. The differential equations are presented, and the initial value problem is described together with the transformation to rectangular coordinates and classical elements. The focal elements are well defined for zero eccentricity and inclination. They can be adopted for the computation of elliptic, parabolic and hyperbolic motion. For the numerical integration of near-geostationary orbits a comparison of the efficiency is made between focal elements, KS theory and rectangular coordinates. For this class of orbits, a higher accuracy has been obtained by integrating elements than integrating rectangular coordinates.     

Statistical model of meteor streams III. Stream search among 19303 radio meteors

Using a computerized technique of stream search, based on the statistical model of meteor streams, we have detected 72 additional streams in a sample of 19303 radio meteor orbits. The streams are found to have a tendency to cluster, partly along the ecliptic and partly in high-inclination orbits. Also noticed are specific relations among the detected streams, such as stream pairs, stream branches, and twin showers. A very probable association of a prominent stream, the a Capricornids, with the minor planet Adonis has been established, and possible associations of several streams with comets and minor planets of the Apollo and Albert types are also discussed. Identification of the detected radio streams with previously known streams is presented, and plans for future work are briefly outlined.     

TV Observation of the Daytime Meteor Shower; The Arietids

We have carried out multi-station TV observations since 1994 in order to determine the orbit of the Arietid daytime meteor stream. In 1999, one possible Arietid meteor was recorded by our simultaneous observations and its orbit was determined. In 2003, two Arietid meteors were observed from two stations of our observing site, those orbits were determined precisely, the orbital elements were in good agreement with each other. This is the first time that determination of the precise orbit of the Arietids has been made from optical observations. The orbit of these Arietid meteors, and comparison with the orbit obtained from radar observations are discussed.     

Determination of the orbits of inner Jupiter satellites

Some problems in determining the orbits of inner satellites associated with the complex behavior of the target function, which is strongly ravine and which possesses multiple minima in the case of the satellite orbit is determined based on fragmentary observations distributed over a rather long time interval, are studied. These peculiarities of the inverse problems are considered by the example of the dynamics of the inner Jupiter satellites: Amalthea, Thebe, Adrastea, and Metis. Numerical models of the satellite motions whose parameters were determined based on ground-based observations available at the moment to date have been constructed. A composite approach has been proposed for the effective search for minima of the target function. The approach allows one to obtain the respective evaluations of the orbital parameters only for several tens of iterations even in the case of very rough initial approximations. If two groups of observations are available (Adrastea), a formal minimization of the target function is shown to give a solution set, which is the best solution from the point of view of representation of the orbital motion, which is impossible to choose. Other estimates are given characterizing the specific nature of the inverse problems.     

Radar Campaign to Determine the Dependence of Initial Radii of Meteor Plasma Trains on Trajectory and Orbit

Experimental and theoretical work on the transverse dimensions of meteoric plasma trains have not converged to provide generally accepted values especially uncertain is the dependence of the train radii on meteor speeds. The roles of the meteoroid structure, fragmentation and plasma processes such as ion–electron instabilities need establishing. Knowledge of the quantitative spatial distribution of plasma in meteor trains is essential for a correct interpretation of fluxes and orbital characteristics. A current project is described which employs the AMOR 26 MHz radar facility in conjunction with a frequency managed radar operating at longer wavelengths designed to measure the ionization train radii, heights, atmospheric speeds and orbits of individual meteors.     

Hierarchy of periodic solutions families of spatial Hill’s problem

Many modern space projects require the knowledge of orbits with certain properties. Most of these projects assume the motion of a space vehicle in the neighborhood of a celestial body, which in turn moves in the field of the Sun or another massive celestial body. A good approximation of this situation is Hill’s problem. This paper is devoted to the investigation of the families of spatial periodic solutions to the three-dimensional Hill’s problem. This problem is nonintegrable; therefore, periodic solutions are studied numerically. The Poincare theory of periodic solutions of the second kind is applied; either planar or vertical impact orbits are used as generating solutions.