Some of the problems related to Near Earth Objects (NEOs), like orbit determination and ephemeris computation, are not new, and had to be dealt with since the beginning of NEO astronomy. The latter practically started with the discovery of Comet D/1770 L1 Lexell, that passed very close to the Earth in 1770; studies of the chaotic dynamics of this exceptional object continued well into the XIXth century. At the end of the XXth century there has been a renewal of interest in NEOs, as attested by IAU Symposium 236.

George Wetherill and I worked together as scientific collaborators when I was a postdoctoral fellow in 1977-1978 at the Department of Terrestrial Magnetism (DTM) of the Carnegie Institution of Washington (CIW) in Washington, D.C. We worked on problems of meteoroids interacting in Earth's atmosphere along with Richard McCrosky at Harvard College Observatory and Zdeněk Ceplecha at the Ondřejov Observatory in Czechoslovakia and also with Sundar Rajan who had already arrived at DTM from the University of California at Berkeley before me.

The Minimum Orbit Intersection Distance (MOID) between two confocal Keplerian orbits is a useful tool to know if two celestial bodies can collide or undergo a very close approach. We describe some results and open problems on the number of local minimum points of the distance between two points on the two orbits and the position of such points with respect to the mutual nodes. The errors affecting the observations of an asteroid result in uncertainty in its orbit determination and, consequently, uncertainty in the MOID. The latter is always positive and is not regular where it vanishes; this prevents us from considering it as a Gaussian random variable, and from computing its covariance by standard tools. In a recent work we have introduced a regularization of the maps giving the local minimum values of the distance between two orbits. It uses a signed value of the distance, with the sign given to the MOID according to a simple orientation property. The uncertainty of the regularized MOID has been computed for a large database of orbits. In this way we have searched for Virtual PHAs, i.e. asteroids which can belong to the category of PHAs (Potentially Hazardous Asteroids) if the errors in the orbit determination are taken into account. Among the Virtual PHAs we have found objects that are not even NEA, according to their nominal orbit.

In theoretical as well as practical issues of the asteroidal hazard problem, it is important to be able to assess the degree of predictability of the orbital motion of asteroids. Some asteroids move in a virtually predictable way, others do not. The characteristic time of predictability of any motion is nothing but the Lyapunov time (the reciprocal of the maximum Lyapunov exponent) of the motion. In this report, a method of analytical estimation of the maximum Lyapunov exponents of the orbital motion of asteroids is described in application for two settings of the problem. Namely, the following two types of the motion are considered: (1) the motion close to the ordinary or three-body mean motion resonances with planets, and (2) the motion in highly eccentric orbits subject to moderately close encounters with planets. Whatever different these settings may look, the analytical treatment is universal: it is performed within a single framework of the general separatrix map theory. (Recall that the separatrix maps describe the motion near the separatrices of a nonlinear resonance.) The analytical estimates of the Lyapunov times are compared to known numerical ones, i.e., to known estimates obtained by means of numerical integration of the orbits.

The dynamical interrelation between resonant trans-Neptunian objects and short-period comets is studied. Initial orbits of resonant objects are based on computations in the model of the outward transport of objects during Neptune's migration in the early history of the outer Solar system. The dynamical evolution of this population is investigated for 4.5 Gyr, using a symplectic integrator. Our calculations show that resonant trans-Neptunian objects give a substantial contribution to the planetary region. We have estimated that the relative fraction of objects captured per year from the 2/3 resonance to Jupiter-family orbits with perihelion distances q<2.5 AU is 0.4×10−10 near the present epoch.

The orbital evolution of comets with high values of the Tisserand constant is studied for a time interval of 800 years. Scenarios of dynamical evolution are obtained for 85 comets. Particular features of the orbital evolution of the comets of this class are singled out. The orbits of all comets are tangent to the orbit of Jupiter and have a steadily low inclination. For 80% of comets, the evolution scenario includes a timespan in which the comets move in low-eccentricity orbits. The possibility is analyzed of a change in the Tisserand constant and of a transition of the comet to be controlled by other giant planets.

The dynamical evolution of 2⋅105 hypothetical Oort cloud comets by the action of planetary, galactic and stellar perturbations during 2⋅109 years is studied numerically. The evolution of comet orbits from the outer (104 AU <a<5⋅104 AU, a is semimajor axes) and the inner Oort cloud (5⋅103 AU <a<104 AU) to near-Earth space is investigated separately. The distribution of the perihelion (q) passage frequency in the planetary region is obtained calculating the numbers of comets in every interval of Δ q per year. The flux of long-period (LP) comets (orbital periods P>200 yr) with perihelion distances q<1.5 AU brighter than visual absolute magnitude H10=7 is ∼ 1.5 comets per year, and ∼18 comets with H10<10.9. The ratio of all LP comets with q<1.5 AU to ‘new’ comets is ∼5. The frequency of passages of LP comets from the inner Oort cloud through region q<1.5 AU is ∼3.5⋅10−13 yr−1, that is roughly one order of magnitude less than frequency of passages of LP comets from the outer cloud (∼5.28⋅10−12 yr−1). We show that the flux of ‘new’ comets with 15<q<31 AU is higher than with q<15 AU, by a factor ∼1.7 for comets from the outer Oort cloud and, by a factor ∼7 for comets from the inner cloud. The perihelia of comets from the outer cloud previously passed through the planetary region are predominated in the Saturn-Uranus region. The majority of inner cloud comets come in the outer solar system (q>15 AU), and a small fraction (∼0.01) of them can reach orbits with q<1.5 AU. The frequency of transfer of comets from the inner cloud (a<104 AU) to the outer Oort cloud (a>104 AU), from where they are injected to the region q<1.5 AU, is ∼6⋅10−14 yr−1.

We studied the orbital evolution of objects with initial orbits close to those of Jupiter-family comets (JFCs), Halley-type comets (HTCs), and long-period comets, and the probabilities of their collisions with the planets. In our runs the probability of a collision of one object with the Earth could be greater than the sum of probabilities for thousands of other objects. Even without the contribution of such a few objects, the probability of a collision of a former JFC with the Earth during the dynamical lifetime of the comet was greater than 4×10−6. This probability is enough for delivery of all the water to Earth's oceans during the formation of the giant planets. The ratios of probabilities of collisions of JFCs and HTCs with Venus and Mars to the mass of the planet usually were not smaller than that with Earth. Among 30,000 considered objects with initial orbits close to those of JFCs, a few objects got Earth-crossing orbits with semimajor axes a<2 AU and aphelion distances Q<4.2 AU, or even got inner-Earth (Q<0.983 AU), Aten, or typical asteroidal orbits, and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myr). From a dynamical point of view, the fraction of extinct comets among near-Earth objects can exceed several tens of percent, but, probably, many extinct comets disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes.

The Taiwan-America Occultation Survey (TAOS) aims to determine the number of small icy bodies in the outer reach of the Solar System by means of stellar occultation. An array of 4 robotic small (D=0.5 m), wide-field (f/1.9) telescopes have been installed at Lulin Observatory in Taiwan to simultaneously monitor some thousand of stars for such rare occultation events. Because a typical occultation event by a TNO a few km across will last for only a fraction of a second, fast photometry is necessary. A special CCD readout scheme has been devised to allow for stellar photometry taken a few times per second. Effective analysis pipelines have been developed to process stellar light curves and to correlate any possible flux changes among all telescopes. A few billion photometric measurements have been collected since the routine survey began in early 2005. Our preliminary result of a very low detection rate suggests a deficit of small TNOs down to a few km size, consistent with the extrapolation of some recent studies of larger (30–100 km) TNOs.

The distribution of Near-Earth Objects, in particular Near-Earth asteroids is examined using maximum likelihood methods. These are analysed with respect magnitudes, taxonomic classes and to their orbital distances. Comparisons are made with the distributions of main-belt asteroids and short-period comets.

We investigate the secular resonances for massless small bodies and Earth-like planets in several planetary systems. We further compare the results with those of Solar System. For example, in the GJ 876 planetary system, we show that the secular resonances ν1 and ν2 (respectively, resulting from the inner and outer giant planets) can excite the eccentricities of the Earth-like planets with orbits 0.21≤ a <0.50 AU and eject them out of the system in a short timescale. However, in a dynamical sense, the potential zones for the existence of Earth-like planets are in the area 0.50≤ a ≤1.00 AU, and there exist all stable orbits last up to 105 yr with low eccentricities. For other systems, e.g., 47 UMa, we also show that the Habitable Zones for Earth-like planets are related to both secular resonances and mean motion resonances in the systems.

Many of our annual showers do not have active parent comets. In recent years, minor planets have been identified that move among the meteoroids streams. Some streams, such as the Quadrantids, Geminids, and Sextantids, are in such unusual orbits that the probability of a chance association is only of order 1 in 106. The streams identify those objects as dormant comet nuclei. Other streams, such as the Phoenicids and α-Capricornids are associated with minor planets that were found to be weakly active at their last perihelion passage. All the streams investigated so far are young, less than 2,000 years old, and can not have been created in the classical sense of meteoroids being ejected from the comet nucleus by water vapor drag. Instead, these (mostly) dormant comets lost fragments at some point in the past, which crumbled into meteoroid streams. Scars of such events are now identified on the surface of active Jupiter family comets 9P/Tempel 1 and 81P/Wild 2. Thus, the meteor showers on Earth bear witness to what is the dominant mass-loss mechanism of comets in the inner solar system, a process that can account for much of the zodiacal cloud dust and the zodiacal dust bands.

We have examined the behavior of a number of bolides in Earth's atmosphere from the standpoint of recent entry modeling techniques. The entry modeling has been carried out including a triggered progressive fragmentation model (TPFM) which maintains a maximum drag orientation for the fragments in either the collective or a non-collective wake limit during entry (ReVelle 2004). Specifically in this paper, we have proposed a new method of estimating the terminal bolide mass and have compared it against the corresponding single-body mass loss prediction. A new expression for the terminal mass is proposed that corrects the mass of the body for the changing mass to area ratio during the fragmentation process. As a result of this new work we have found two very interesting features that correspond very closely to those found from a direct analysis of the observational data. These include an instantaneous mass that closely resembles that directly observed and an ablation coefficient behavior that also strongly resembles meteor observations (such as those found recently by Ceplecha & ReVelle 2005). During fragmentation, the apparent ablation coefficient has now been shown to decrease dramatically approaching the intrinsic ablation coefficient proposed by Ceplecha & ReVelle (2005). In our modeling we have assumed a breakup into equal size fragments that are consistently and progressively multiples of two of the original unbroken leading piece. Had we assumed a multitude of many much smaller pieces that made up the totality of the original body, our predicted ablation coefficient would indeed have approached the very small intrinsic ablation parameter values predicted by Ceplecha and ReVelle. This is especially evident in the case of Sumava, but is also true in a number of other cases as well. The bolides whose properties have been modeled using our detailed entry code including a prediction of the panchromatic luminosity consist of the 1965 Revelstoke meteorite fall (Folinsbee 1967; Carr 1970; Shoemaker 1983), the 1974 Sumava fireball and the 1991 Benesov fireball as presented in Borovička & Spurný (1996) and in Borovička et al. (1998), the Tagish Lake meteorite fall of January 8, 2000 (Brown et al. 2002), the March 9, 2002 Park Forest meteorite fall (Brown et al. 2004), the June 6, 2002 Mediterranean (Crete) bolide as presented in Brown et al. (2002) and finally the September 4, 2004 Antarctic bolide respectively (Klekociuk et al. 2005). A self-consistent assessment of the detailed properties of each of the fireballs was made using all available information for each event. In the future, more reliable estimates of all of the necessary source parameters (including their overall degree of bulk porosity) will be made if all channels of information are reliably retrieved for bolide events (channels such as acoustic-gravity waves and specifically its infrasound emission, seismic waves, satellite optical and IR data, ground-based spectroscopy, ground-based photometry and radiometry, VLF radiation, meteorite fragment recovery, etc.).

Meteoroids observed to disintegrate in the terrestrial atmosphere can be directly linked to their parent bodies in case that they belong to certain meteor showers. We present a list of two dozens of parent bodies reliably associated with well recognized meteor showers. Among the parent bodies are long period comets, Halley-type comets, Jupiter family comets, comets of the inner solar system (such as 2P/Encke) and asteroids. Physical and chemical properties of meteoroids coming from various parents are compared on the basis of meteor heights, decelerations, light curves and spectra. Jupiter family comets produce meteoroids with the lowest strength, namely porous aggregates of dust grains with bulk densities of about 0.3 g cm−3 or less. Halley type material is somewhat stronger and the material related to comet Encke is even stronger. In addition, small strong constituents, perhaps similar to carbonaceous chondrites, can be encountered within the normal cometary material. The strength of cometary material is also enhanced by long-term exposure to cosmic rays and by solar heating in the vicinity to the Sun (r<0.2 AU). Both these processes lead to the loss of volatile sodium. Southern δ-Aquariids, Geminids and partly also Quadrantids were influenced by solar radiation. We argue that these showers, the asteroids associated with them ((3200) Phaethon and 2003 EH1), and the whole interplanetary complexes they belong to are of cometary origin. The argument is supported by lower than chondritic Fe/Mg ratio found in Geminids as well as in Halley type comets. The typical property of stony meteoroids of asteroidal origin is the presence of internal cracks which cause that the incoming meteoroids are much weaker than the recovered meteorites.

In the last several years the manually operated fish-eye cameras in the Czech part of the European fireball Network (EN) have been gradually replaced with new generation cameras, the modern and sophisticated completely autonomous fireball observatories (AFO), which were recently developed in the Czech Republic. The main motivation for construction of this new observing system was to continue in regular fireball observations and to make these observations more complex and efficient. In this paper we briefly describe basic design and work of this new instrument and its deployment at the Czech stations of the EN. The current dislocation of the individual stations and their equipment is also discussed. Along with this new modern instrument we developed also new software for measurement of photographic negatives which makes this time consuming work more efficient and easier. The AFOs provide us with data on fireballs far richer and more interesting than those we were able to get in the past. This is illustrated by the cases of two recently observed fireballs which were recorded by the AFOs. We describe the high precision of all the measureded values as well as the very detailed information about light curves in both cases.

TV cameras equipped with image intensifiers are suitable and often used instruments for observing faint meteors. Our regular double-station observations with image intensifiers Dedal (type Dedal 41) started in 1998. Since 2006 we perform observations using new Mullard XX1332 intensifiers. In this paper we present an overview of the eight years of Dedal era. The amount of observing hours, number of meteors, statistics how many meteors were recognized using the automatic system MetRec or found manually, etc. are presented for each year. We also briefly overview the science results from these observations.

The existence of an observed meteor shower associated with some Near-Earth Asteroid (NEA) is one of the few useful criteria that can be used to indicate that such an object could be a candidate for being regarded as an extinct or dormant cometary nucleus. In order to identify possible new NEA-meteor showers associations, the secular variations of the orbital elements of the NEA 2000 PG3, with comet-like albedo (0.02), and moving on a comet-like orbit, was investigated under the gravitational action of the Sun and six planets (Mercury to Saturn) over one cycle of variation of the argument of perihelion. The theoretical geocentric radiants and velocities of four possible meteor showers associated with this object are determined. Using published data, the theoretically predicted showers were identified with the night-time September Northern and Southern δ-Piscids fireball showers and several fireballs, and with the day-time meteor associations γ-Arietids and α-Piscids. The character of the orbit and low albedo of 2000 PG3, and the existence of observed meteor showers associated with 2000 PG3 provide evidence supporting the conjecture that this object may be of cometary nature.

Radar is a uniquely powerful source of information about near-Earth asteroid (NEA) physical properties and orbits. This review consists largely of edited excerpts from Ostro and Giorgini (2004).

The physical properties of NEOs and other asteroids are mostly obtained with photometry. The resulting models describe the shapes, spin states, scattering properties and surface structure of the targets, and are the solutions of inverse problems involving comprehensive mathematical analysis. We review what can and cannot be obtained from photometric (and complementary) data, and how all this is done in practice. The role of photometry will become completely dominating with the advent of large-scale surveys capable of producing calibrated brightness data. Due to their quickly changing geometries with respect to the Earth, NEOs are the population that can be mapped the fastest.

Of the nearly 3900 near-Earth asteroids (NEAs) known as of June 2006, 325 have estimated rotation periods, with most of those determined by lightcurve analysis led by a few dedicated programs. NEAs with diameters down to 10 meters have been sampled. Observed spin distribution shows a major changing point around diameter of 200 meters. Larger NEAs show a barrier against spins faster than 11 d−1 (period about 2.2 h) that shifts to slower rates (longer periods) with increasing lightcurve amplitude (i.e., with increasing equatorial elongation). The spin barrier is interpreted as a critical spin rate for bodies in a gravity regime; NEAs larger than 200 meters are predominantly bodies with tensile strength too low to withstand a centrifugal acceleration for rotation faster than the critical spin rate. The cohesionless spin barrier disappears at sizes less than 200 meters where most objects rotate too fast to be held together by self-gravitation only, so a cohesion is implied in the smaller NEAs.

The distribution of NEA spin rates in the cohesionless size range (D0.2 km) is highly non-Maxwellian, suggesting that mechanisms other than just collisions have been at work. There is a pile up just in front of the barrier, at periods 2–3 h. It may be related to a spin up mechanism crowding asteroids to the barrier. An excess of slow rotators is observed at periods longer than 30 hours. A spin-down mechanism has no obvious lower limit on spin rate; periods as long as tens of days have been observed.

Most NEAs appear to be in their basic spin states with rotation around principal axis with maximum moment of inertia. Tumbling objects (i.e., bodies in excited, non-principal axis rotation) are present and actually predominate among slow rotators with estimated damping timescales longer than the age of the solar system. A few tumblers observed among fast rotating coherent objects appear to be either more rigid or younger than the larger (cohesionless) tumblers.

An abundant population of binary systems has been found among NEAs. The fraction of binaries among NEAs larger than 0.3 km has been estimated to be 15 ± 4%. Primaries of binary systems concentrate at fast spin rates (periods 2–3 h) and low amplitudes, i.e., they lie just below the cohesionless spin barrier. The total angular momentum content in binary systems suggests that they formed from parent bodies spinning at the critical rate. The fact that a very similar population of binaries has been found among small main belt asteroids suggests a binary formation mechanism that may not be related to close encounters with the terrestrial planets.