Near-Sun asteroids

As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.     

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.     

Capture of comets from the Oort cloud into Halley-type and Jupiter-family orbits

This paper analyzes the capture of comets into Halley-type and Jupiter-family orbits from the nearparabolic flux of the Oort cloud. Two types of capture into Halley-type orbits are found. The first type is the evolution of near-parabolic orbits into short-period orbits (with heliocentric orbital periods P < 200 years) as a result of close encounters with giant planets. This process is followed by a very slow drift of cometary orbits into the inner part of the Solar System. Only those comets may pass from short-period orbits into Halley-type and Jupiter-family orbits, which move in orbits with perihelion distances q < 13 au. In the second type of capture, the perihelion distances of cometary orbits become rather small (< 1.5 au) during the first stage of dynamic evolution under the action of perturbations from the Galaxy, and then their semimajor axes decrease as a result of diffusion. The capture takes place, on average, in 500 revolutions of the comet about the Sun, whereas in the first case, the comet is captured, on average, after 12500 revolutions. The region of initial orbital perihelion distances q > 4 au is found to be at least as important a source of Halley-type comets as the region of perihelion distances q < 4 au. More than half of the Halley-type comets are captured from the nearly parabolic flux with q > 4 au. The analysis of the dynamic evolution of objects moving in short-period orbits shows that the distribution of Centaurs orbits agrees well with the observed distribution corrected for observational selection effects. Hence, the hypothesis associating the origin of Centaurs with the Edgeworth-Kuiper belt and the trans-Neptunian region exclusively should be rejected.     

Secular Dynamics of Asteroids in the Inner Solar System

In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets. The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap. Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asteroids in the Eccentrids meteor system

Among 11 673 of near-Earth objects (NEOs), 52 asteroids are identified, which, together with the Eccentrids meteor system, comprise a single population of small bodies of the Solar System with the smallest orbits of high eccentricity. Some features of this unique system of bodies are discussed in this paper. The distribution of perihelion longitudes is studied for the given group of asteroids and compared to that of the Aten asteroids, which are the most similar to the Eccentrids. The dependence is obtained of the character of perihelion longitude distribution on the eccentricities of the NEO orbits. Eight asteroid stream of the Eccentrids are found. The Eccentrids asteroids approaching the Earth’s orbit along its whole length in their aphelia can pose a certain hazard for the Earth.     

On the Origin of the Last Meteorite Parent Bodies

The existence of gaps in the perihelion distribution of the orbits of multikilometer-sized asteroids that approach the orbits of terrestrial-group planets is confirmed. This property of the orbits of large asteroids suggests the existence among them of a family of last meteorite parent bodies. Astrophysical data were considered for S-asteroids of the Main Belt and those that approach terrestrial planets. The u–x color index, which is related to the position of the absorption band at 950 nm in the asteroid spectra, was chosen for a qualitative comparison of the surface composition of these asteroids (identical or differing composition). The u – x color-index distributions were analyzed statistically according to the perihelion (q) and mean heliocentric distances (a) of the S-asteroids. It is shown that these distributions are -shaped, peaking at q 1.8 AU and a 2.2 AU. The wings of the distributions can be approximated by linear regressions. A comparison of the u – x color-index mean values for S-asteroids in the regions of the Earth and Mars and of the Main Belt prompts the conclusion that the last meteorite parent bodies in the vicinity of the orbits of the Earth and Mars come primarily from various regions of the asteroid Main Belt.     

Dynamical behaviour of Earth orbit crossing asteroids

Computing the maximum and minimum values of the eccentricities and inclinations as functions of the arguments of perihelion for about 7000 numbered asteroids by adopting a simple model it is found that 80 have the minimum perihelion distances less than 1.04 AU. Still, it is proved that 20% of them have no chance of colliding with the Earth, whereas 30 of them have relatively high collision probability as they have orbits similar to those of typical short-period comets.     

Palomar-Leiden minor planets: Proper elements,frequency distributions,belt boundaries,and family memberships

Proper elements have been calculated for 1227 higher accuracy orbits from the Palomar-Leiden Survey of faint minor planets. Tabulations are given for the special orbits: Earth and deep Mars crossers, Trojans, Hildas, and one 2:1 librator. The frequency distributions of the proper semimajor axis, eccentricity, sine inclination, longitudes of perihelion and node plus their rates, and the closest distances of approach to Mars and Jupiter are displayed as histograms and discussed. The distribution of the closest approach distance to Mars drops off sharply near zero while that for Jupiter vanishes near 1.1 AU. Mars and Jupiter have apparently caused these boundaries and the asteroid belt must have been larger early in the history of the solar system. 3.5% of the sample can impact Mars. Most of these potential impactors are shallow crossers which require occasional fortuitous alignments of the secular terms to intersect Mars' orbit so that long lifetimes result and moderate populations remain. As these fortuitous alignments occur with near simultaneity for many, but not all, asteroids the shallow crossers in the observed size range will episodically bombard Mars. Proper elements have been used to recognize families and 49% of the sample of minor planets fall into these families. The proper elements and family assignments are tabulated.     

Secular perturbations of resonant asteroids

Secular perturbations of asteroids are derived for mean motion resonance cases under the assumptions that the disturbing planets are moving along circular orbits on the same plane and that critical arguments are fixed at stable equilibrium points. Under these assumptions the equations of motion are reduced to those of one degree of freedom with the energy integral. Then equi-energycurves on (2g-X) plane (g and X being, respectively, the argument of perihelion and (1–e²)^1/2) are derived for given values of the two constant parameters, the semi-major axis and =(1–e²)^1/2 cos i, and the variations of the eccentricity and the inclination as functions of the argument of perihelion are graphically estimated. In fact this method is applied to numbered asteroids with commensurable mean motions to estimate the ranges of the variations of orbital elements.The same method is also applied to the Pluto-Neptune system and the results are found to agree with those of numerical integrations and show that the argument of perihelion of Pluto librates around 90°.     

Close encounters of nearly parabolic comets and planets

An overview is given of close encounters of nearly parabolic comets (NPCs; with periods of P > 200 years and perihelion distances of q > 0.1 AU; the number of the comets is N = 1041) with planets. The minimum distances Δ_min between the cometary and planetary orbits are calculated to select comets whose Δ_min are less than the radius of the planet’s sphere of influence. Close encounters of these comets with planets are identified by numerical integration of the comets’ equations of motion over an interval of ±50 years from the time of passing the perihelion. Close encounters of NPCs with Jupiter in 1663–2011 are reported for seven comets. An encounter with Saturn is reported for comet 2004 F2 (in 2001).     

The Dynamics of Low-Perihelion Meteoroid Streams

The Canadian Meteor Orbit Radar (CMOR) has collected information on a number of weak meteor showers that have not been well characterized in the literature. A subsample of these showers (1) do not show a strong orbital resemblance to any known comets or asteroids, (2) have highly inclined orbits, (3) are at low perihelion distances ( AU) and (4) are at small semimajor axes (<2 AU). Though one might conclude that the absence of a parent object could be the result of its disruption, it is unclear how this relatively inaccessible (dynamically speaking) region of phase space might have been populated by parents in the first place. It will be shown that the Kozai secular resonance and/or Poynting–Robertson drag can modify meteor stream orbits rapidly (on time scales comparable to a precession cycle) and may be responsible for placing some of these streams into their current locations. These same effects are also argued to act on these streams so as to contribute to the high-ecliptic latitude north and south toroidal sporadic meteor sources. There remain some differences between the simple model results presented here and observations, but there may be no need to invoke a substantial population of high-inclination parents for the observed high-inclination meteoroid streams with small perihelion distances.     

The large-scale structure of the asteroid belt

We examine the distributions of 2888 numbered minor planets over orbital inclination, eccentricity, and semimajor axis, and define 19 zones which we believe adequately to isolate the selection biases in survey programs of the physical properties of minor planets. Six numbered asteroids have exceptional orbits and fall into no zone. We also call attention to rather sharp upper limits, which become increasingly stringent at larger heliocentric distances, on orbital inclinations and eccentricity.     

Asteroids with large secular orbital variations

As the classical linear theory of secular perturbations for asteroids is known not to be adequate for computing the perturbations of asteroids with high eccentricities and/or inclinations, a seminumerical method to calculate the secular perturbations by including higher-degree terms in the disturbing function has been developed. It is here applied to asteroids with small values of $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{cos}\text{i}$, since the secular variations as well as their deviations from the results derived by the classical linear theory are generally large for such asteroids. It is found that the arguments of perihelion for five of the numbered asteroids are librating around 90 or 270°. For asteroids with $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>cos</mtext><mtext>\; i</mtext>}}$ less than 0.85 the results of the secular variations are tabulated. Also the stability of such orbits is discussed by comparing the orbital properties of short-periodic comets with them. Generally speaking, orbits of the asteroids are more stable than those of the short-periodic comets, and asteroids with librating arguments of perihelion are more stable than those with circular coplanar orbits although their orbital elements are changed more by secular perturbations.     

Asteroidal jet streams

Detailed studies of the asteroidal belt are of importance for clarifying whether the asteroids are fragments of an exploded planet or represent an intermediate state in the accretion of planets.A study of the Hirayama family Flora shows that it contains three groups of bodies travelling in almost identical orbits, thus constituting three jet streams.It is shown that the formation of jet streams is difficult to reconcile with the exploded planet view.In order to decide whether the formation of jet streams is a general phenomenon in the asteroidal belt, it is necessary to determine the orbits of a large number of small asteroids.     

From the Oort cloud to observable short-period comets – I. The initial stage of cometary capture

We investigate the first stage of the dynamical evolution of Oort cloud comets entering the planetary region for the first time. To this purpose, we integrate numerically the motions of a large number of fictitious comets pertaining to two samples, both with perihelion distances up to 5.7 au and random inclinations; the first sample is composed of comets whose orbits have at least one node close to 5.2 au, while the second is not subject to this constraint. We examine the orbits when the comets come to aphelion after their first perihelion passage within the planetary region, and find that there is a clear statistical dependence of the energy perturbations on the Tisserand parameter. There appear to be two main processes, of comparable importance, governing the shortening of semimajor axes to values of less than 1000 au, i.e. planetary close encounters, especially with Jupiter, and indirect perturbations due to the shifting of the motion from barycentric to heliocentric and back; the former process mostly affects comets crossing the ecliptic at about 5.2 au, or on low-inclination orbits, while the latter mostly affects comets of small perihelion distance. This last result may help to understand the relative paucity of Halley-type comets with perihelion distances larger than about 1.5 au.     

Planet crossing asteroids and parallel computing: Project spaceguard

The orbits of the asteroids crossing the orbit of the Earth and other planets are chaotic and cannot be computed in a deterministic way for a time span long enough to study the probability of collisions. It is possible to study the statistical behaviour of a large number of such orbits over a long span of time, provided enough computing resources and intelligent post processing software are available. The former, problem can be handled by exploiting the enormous power of parallel computing systems. The orbit of the asteroids can be studied as a restricted (N+M)-body problem which is suitable for the use of parallel processing, by using one processor to compute the orbits of the planets and the others to compute the orbits the asteroids. This scheme has been implemented on LCAP-2, an array of IBM and FPS processors with shared memory designed by E. Clementi (IBM). The parallelisation efficiency has been over 80%, and the overall speed over 90 MegaFLOPS; the orbits of all the asteroids with perihelia lower than the aphelion of Mars (410 objects) have been computed for 200,000, years (Project SPACEGUARD). The most difficult step of the project is the post processing of the very large amount of output data and to gather qualitative information on the behaviour of so many orbits without resorting to the traditional technique, i.e. human examination of output in graphical form. Within Project SPACEGUARD we have developed a qualitative classification of the orbits of the planet crossers. To develop an entirely automated classification of the qualitative orbital behaviour-including crossing behaviour, resonances (mean motion and secular), and protection mechanisms avoiding collisions-is a challenge to be met.     

Mass loss from the region of Mars and the asteroid belt

Models of the solar nebula suggest that the mass of solid matter which condensed in the region of Mars and the asteroids was much greater than the amount now present. Bombardment by a primordial population of asteroidal bodies originating near Jupiter's orbit could preferentially remove matter from this region, without significant effects in the Earth's zone. A “critical velocity” exists, for which they can be ejected from the solar system by Jupiter. The minimum perihelion attainable at this velocity lies between the orbits of Mars and the Earth. The lifetimes of Mars-crossing bodies are limited by collisions with Jupiter; Earth-crossers are ejected on a much shorter time scale. The total bombardment flux was at least two orders of magnitude greater in the zone of Mars than in that of the Earth. The flux at Venus and Mercury from this source was negligible. The cratering rate for Mars may have differed greatly from those of the other terrestrial planets for a significant fraction of the age of the solar system.     

The asteroid ephemerides program at the U.S. Naval Observatory

The U.S. Naval Observatory has begun a program of ephemeris improvement and reference frame determination from the main belt asteroids. The program is, currently, starting out with a limited set of observations of the larger asteroids to determine the equator and equinox corrections for the USNO W1J00 transit circle observations catalog, and, if possible, improve the orbits of these asteroids based on this limited set of observations. For this project, transit circle observations of the Sun and the planets Mercury through Jupiter, are also being used to determine the equator, equinox, and ephemeris corrections, the next goal is to improve the orbits of the larger asteroids in the optical reference frame using observation series that cover a much longer period of time. This will allow the exploration of the differences between the dynamical reference frame based on radar observations of main belt asteroids and its relation with the optical reference frame. Other goals include the exploration of the mass distribution in the main asteroid belt from high precision observations, and the effect of this mass on the ephemerides of the major planets.     

Development of a comet as it pursues its orbit

The properties of cometary dust-swarms in almost parabolic long-period orbits are examined. In general their self-gravitation is stronger than the solar disruptive influence for all except the relatively small part of the orbit within planetary distances during which the sun dominates by so great a factor that the individual particles of the swarm pursue independent orbits apart from the possibility of collisions between them. At aphelion the internal relative speeds of particles are only a few centimetres per second, but at and near perihelion they may rise to the order of a kilometre per second. For purely dynamical reasons the extent of the swarm in directions perpendicular to the orbital motion will strongly diminish as perihelion is approached and correspondingly increase thereafter, while the dimension along the orbit will change in direct proportion to the orbital velocity. Every particle must cross through the median orbital plane near perihelion, and collisions between a proportion of the particles will occur at speeds capable of fragmenting them into myriads of smaller dustparticles, also heating them at and near the colliding elements of their surfaces. Increase of reflected sunlight will result and also release of material in gaseous form by solar plus collisional heating. Sufficiently finely divided dust particles will be driven out of the comet by radiation-pressure to form a dust-tail, while suitable gaseous compounds if present will be driven out to give a gas-tail. For Sungrazing comets, complete gasification must occur at and near perihelion, and very considerable extension along the orbit. Such comets would recondense to small solid particles on receding again from the Sun. The effect of passage of the solar system through interstellar gas-clouds is shown to be capable of substantially affecting the angular momentum of a comet about the Sun, thus accounting for the existence of comets with high values of perihelion-distance. This same process would enable cometary particles to adsorb interstellar gases at their surfaces and regenerate their gas-content. The mass-loss by a comet at each return strongly indicates, that comets cannot have originated at the same time as the planets, a result further supported by the rapid expulsion of entire comets through purely dynamical action of the planets. That the quiescent structure of comets consists of a vast widely spaced swarm of minute dust-particles receives circumstantial support from the highly varied and peculiar properties long since recorded for numerous comets. These properties exhibit such erratic diversity as to make clear that only a theory involving considerable range of essential parameters can be capable of accounting for them adequately.     

Searching for the source of short-period comet nuclei: Choosing between different asteroid groups

This study continues our previous works on searching for the main source of the nuclei of Jupiter family comets (JFCs). Angular orbit element distributions are analyzed for comets and asteroids of different groups. The distributions of JFCs by argument of perihelion ω and longitude of perihelion π are studied. The distributions are shown not to have been formed during the evolution of JFCs in their current orbits. Similar distributions N(ω) and N(π) are not observed in bodies that have come into the JFC orbits from external sources. At the same time, the distributions of JFCs by all angular orbit elements are very similar to those of the Trojans. It is concluded that the latter are likely to be the main source of the JFC nuclei.