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.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

Admissible orbits in the Oort cloud and velocities on such orbits

In this paper we deal with determinations of: admissible orbits and ranges of orbital velocity in the cloud, extremal velocities at the distance r from the Sun. Moreover, in velocity space we consider the _r region in which there are located tips of velocity vectors for comets moving on admissible orbits.     

Opportunities for the stratospheric collection of dust from short‐period comets

Abstract— We have identified four comets which have produced low‐velocity Earth‐crossing dust streams within the past century: 7P/Pons‐Winnecke, 26P/Grigg‐Skjellerup, 73P/Schwassmann‐Wachmann 3, and 103P/Hartley 2. These comets have had the rare characteristics of low eccentricity, low inclination orbits with nodes very close to 1 AU. Dust from these comets is directly injected into Earth‐crossing orbits by radiation pressure, unlike the great majority of interplanetary dust particles collected in the stratosphere which spend millennia in space prior to Earth‐encounter. Complete dust streams from these comets form within a few decades, and appreciable amounts of dust are accreted by the Earth each year regardless of the positions of the parent comets. Dust from these comets could be collected in the stratosphere and identified by its short space exposure age, as indicated by low abundances of implanted solar‐wind noble gases and/or lack of solar flare tracks. Dust from Grigg‐Skjellerup probably has the highest concentration at Earth orbit. We estimate that the proportion of dust from this comet will reach at least several percent of the background interplanetary dust flux in the >40 μm size range during April 23–24 of 2003.     

Temporary satellite capture of comets by Jupiter

This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart??s sense, not associated with a transition of the small body into Jupiter??s family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets?? orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane (a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill??s sense.     

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.     

DYNAMICAL RELATION OF METEORIDS TO COMETS AND ASTEROIDS

We tested four criteria used for discrimination between asteroidal and cometary type of orbits: Whipple criterion K, Kresak criterion Pe, Tisserand invariant T and aphelion distance Q. To estimate their reliability, all criteria were applied to classify the 2225 orbits of NEAs and 582 orbits of comets, for several epochs spanning the time interval of 40 thousands years. The Q-criterion produced the smallest number of exceptions and has shown the best stability. The biggest number of exceptions and the biggest variations are obtained for the K-criterion. We applied the Q-criterion to classify meteor orbits from the IAU Meteor Data Center and the video meteor orbits available on the Web sites. Among the sporadic radar orbits, as well as among the mean orbits of meteor streams a strong preponderance of asteroid-type orbits was observed. In case of the photographic and video meteors a weak preponderance of cometary and asteroidal orbits was found, respectively.     

Laplace's problem in mathematical aspect

In this paper we consider the mathematical aspect of Laplace's problem pertaining to the occurrence probability of elliptical and hyperbolical orbits for comets. We show that, among other things, if we use arbitrary velocity distributions in Laplace's problem, we may obtain an arbitrarily small probability for elliptical orbits and a probability neighbouring around one for hyperbolic orbits, or conversely. Our theorems hold, even for the variable initial conditions. The aspect presented here permits us to describe easily studies of Laplace's problem.Dedicated to my teacher, Professor W. Orlicz, on the occasion of 80th birthday.     

On the collision probability for comets with the Sun

We consider the collision probability for comets with the Sun under the suppositions of different velocity distributions and various initial conditions. We solve the problem applying Laplace's method and using Schiaparelli's hyperboloid of visibility. The probabilities obtained in this manner are given separately for elliptic and hyperbolic orbits.     

Chaotic motion of comets in near-parabolic orbit: Mapping approaches

There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 10³ – 10⁵ AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters.     

Short-Period Comets with a High Tisserand Constant: III. Kinematics of Low-Velocity Encounters

Within the framework of a pair two-body problem (Sun–Jupiter, Sun–comet), the kinematics of the encounter of a minor body with a planet is investigated. The notion of points of low-velocity tangency of the orbits of the comet and Jupiter, as well as the point of Jovicentric velocity and the low-velocity tangent section of a cometary orbit, is introduced. The conditions and definitions of low-velocity and high-velocity encounters are proposed. The systems of inequalities relating the aand eparameters, which make it possible to single out those comets that are likely to be objects with low-velocity encounters, are presented. The regions of orbits that have low-velocity tangent sections, i.e., regions of low-velocity tangency of orbits, are singled out on the (a, e) plane. These regions agree well with the corresponding parameters of the orbits of real comets whose evolution contains low-velocity encounters with Jupiter.     

New reductions of orbits based upon Chinese ancient cometary records

From 146 B.C. to 1760 A.D., 363 sets of cometary observations for a total 88 different comets were recorded in Chinese Ancient Records of Celestial Phenomena. According to those records, we reduced apparent positions and mean equatorial coordinates (epoch 2000.0) for all more than three times recorded comets. Taking into account the perturbations of all nine planets and using the numerical method of N-body problem, the orbits of correlative comets were calculated. For thirty different comets, new orbits are presented for the first time.     

A former asteroidal planet as the origin of comets

The idea of a missing planet between Mars and Jupiter has been with us since the formulation of the Titius-Bode law. The discovery of the asteroid belt in that location led to speculation about a planetary breakup event. Both ideas remained conjectures until Ovenden's finding in 1972, from which it could be derived that the mass of the missing planet was about 90 Earth masses and that its breakup was astronomically recent. Apparently much of that mass was blown out of the solar system during the disruption of the planet. Because of the action of planetary perturbations, only two types of orbits of surviving fragments could remain at present-asteroid orbits and once-around very-long-period elliptical orbits. Objects in the latter type of orbit are known to exist-the very-long-period comets. A large number of these are on elliptical trajectories with periods of revolution of 5 million years; yet they are known to have made no more than one revolution in an orbit passing close to the Sun. By direct calculation it is possible to predict the distribution of the orbital elements of objects moving on long-period ellipses which might have originated in a breakup event in the asteroid belt 5 million years ago. The comet orbits have the predicted distribution in every case where a measure is possible. Some of the distribution anomalies, such as a bias in the directions of perihelion passage, are statistically strong and would be difficult to explain in any other uncontrived way. In addition, a relative deficiency of orbits with perihelia less than 1 AU indicates that the comets must have had small perihelion distances since their origin, rather than that they have been perturbed into small perihelion orbits from a distant “cloud” of comets by means of stellar encounters. The comet orbital data lead to the conclusion that all comets originated in a breakup event in the asteroid belt (5.5±0.6) × 10⁶ years ago. Asteroid and meteoritic evidence can now be interpreted in a way which not only is supportive but also provides fresh insights into understanding their physical, chemical, and dynamical properties. Particularily noteworthy are the young cosmic-ray exposure ages of meteorites, evidence of a previous high-temperature/pressure environment and of chemical differentiation of the parent body, and compositional similarities among comets, asteroids, and meteorites. Certain “explosion signatures” in asteroid orbital element distributions are likewise indicative. Tektites may also have originated in the same event; but if so, there are important implications regarding the absolute accuracy of certain geological dating methods. Little is known about possible planetary breakup mechanisms of the requisite type, though some speculations are offered. In any case, the asteroid belt is an existing fact; and the arguments presented here that a large planet did disintegrate 5 million years ago must be judged on their merits, even in the absence of a suitable theory of planetary explosions.     

Searches for transplutonian planets using long-period comets

We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.     

On the explosive prevention of collisions of asteroidal and cometary bodies with the earth at their late detection

We consider the questions of an explosive impact on asteroids and comets that approach the Earth in the case of a late forecast of the dangerous situation. Based on models for the destruction of the material of a celestial body in the shock wave produced by a strong self-buried explosion, we estimate the radius of the destroyed region, the ejected mass, and the recoil momentum. We determine the charges needed to completely destroy bodies of various sizes and compositions or to divert bodies from the Earth by the required distance. When comets are dangerous bodies, we compare the efficiencies of the explosive and sublimation methods of changing their orbits. We discuss how to increase the efficiency of the explosive impact on a dangerous body through the use of a high relative velocity of the encounter between this body and a charge-carrying rocket.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

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.     

Vaporization of comet nuclei: Light curves and life times

We have examined the effects of vaporization from the nucleus of a comet and show that a latitude dependence of vaporization can, in some cases, explain asymmetries in cometary light curves. We also find that a non-uniform distribution of solar radiation over a comet can considerably shorten the vaporization lifetime compared to the results normally obtained by assuming that the nuclear surface is isothermal.Independent of any latitude effects, comets with CO₂-dominated nuclei and with perihelion distances less than 0.5 AU have vaporization lifetimes less than or comparable to their dynamical ejection times. This may explain the observed deficit of comets with small perihelion distances. Similarly comets with CO₂-dominated nuclei and perihelia near Jupiter's orbit have vaporization lifetimes that are shorter than the time for capture into short-period orbits. We suggest, therefore, that at least some new comets are composed in large part of CO₂, while only H₂O-dominated comets, with lower vaporization rates, can survive to be captured into short-period orbits.     

Origin of oort cloud comets in the interstellar space

Comets must form a major part of the interstellar medium. The solar system provides a flux of comets into the interstellar space and there is no reason to suspect that many other stars and their surrounding cometary systems would not make a similar contribution. Occasionally interstellar comets must pass through the inner solar system, but Whipple (1975) considers it unlikely that such a comet is among the known cases of apparently hyperbolic comets. Even so the upper limit for the density of unobserved interstellar comets is relatively high.In addition, we must consider the possibility that comets are a genuine component of interstellar medium, and that the Oort Cloud is merely a captured part of it (McCrea, 1975). Here we review various dynamical possibilities of two-way exchange of comet populations between the Solar System and the interstellar medium. We describe ways in which a traditional Oort Cloud (Oort, 1950) could be captured from the interstellar medium. However, we note that the so called Kuiper belt (Kuiper, 1951) of comets cannot arise through this process. Therefore we have to ask how necessary the concept of the yet unobserved Kuiper belt is for the theory of short period comets.There has been considerable debate about the question whether short period comets can be understood as a captured population of the Oort Cloud of comets or whether an additional source has to be postulated. The problem is made difficult by the long integration times of comet orbits through the age of the Solar System. It would be better to have an accurate treatment of comet-planet encounters in a statistical sense, in the form of cross sections, and to carry out Monte Carlo studies. Here we describe the plan of action and initial results of the work to derive cross sections by carrying out large numbers of comet — planet encounters and by deriving approximate analytic expressions for them. Initially comets follow parabolic orbits of arbitrary inclination and perihelion distance; cross sections are derived for obtaining orbits of given energy and inclination after the encounter. The results are used in subsequent work to make evolutionary models of the comet population.     

The capture of comets by Jupiter

The capture of comets with parabolic orbits by Jupiter is investigated. The influence of the gravitational force of the Sun on the cometary orbit during the passage of Jupiter's sphere of influence is taken into account. A comparison of the present results with previous calculations demonstrate the importance of the solar perturbations.It is also shown that captures of comets with parabolic orbits and repeated close passages to Jupiter cannot explain all of the observed cometary orbits found in the family of Jupiter.