Transneptunian object 2003 UB 313 as a source of comets

The possibility of interrelation between long-period comets and 2003 UB 313, a recently discovered large Kuiper Belt body, is investigated. For this purpose, 78 objects crossing the plane of motion of this body at distances from 37.8 to 97.6 AU have been selected from 860 long-period comets. The overpopulation of comets with this characteristic is also considered. The plane of motion of 2003 UB 313 is compared with the orbital planes of other objects in number of comet crossings in the specified distance interval or in some parts of it. A statistically significant overpopulation of elliptic and intermediate comets with the corresponding orbital nodes has been established. Recently discovered and absolutely faint comets show the best effect in this sense. The same is also true for comets with osculating eccentricities e < 1. A similar result is also obtained for comets with “original” a ^?1 > 0.010000. It is hypothesized that the 2003 UB 313 family is present among the 78 comets. Four of them have aphelion distances from 37.8 to 97.6 AU. An ellipticity is traceable in the distribution of some of the 78 distant nodes. This may be considered as a further argument for the suggested hypothesis. Generally, the body 2003 UB 313 may be assumed to play a prominent role in injecting observable comets from the transneptunian region     

Planet X and the origins of the shower and steady state flux of short-period comets

In the planet X model periodic comet showers are associated with passages of the planet's perihelion and aphelion points through a primordial disk of comets believed to lie beyond the orbit of Neptune. A strong feature of this model is that the required orbital elements and mass of planet X are consistent with independently predicted values based on the residuals in the motions of Uranus and Neptune. Here we present a more extensive analysis of the model taking into account the fact that only those comets scattered directly into the zones of influence of Saturn and Jupiter can contribute to a shower whose duration is consistent with observation (≲ 15 myr). These requirements impose a minimum planetary inclination of ≈25°, which in turn restricts the semimajor axis to be ≲100 AU. A fraction of the comets scattered directly into the zones of influence of Uranus and Neptune will evolve on time scales of ∼10⁸ years into the steady state flux of short-period comets. We find that the absolute numbers of shower and steady state are comparable and compatible with the known terrestrial cratering rate, assuming the existence of long-lived extinct comet cores. Canonical planet X model parameters, deduced in part from the scattering dynamics analysis, are: semimajor axis ≈80 AU, eccentricity ≈0.3, inclination ≈45°, and mass ≈5m_⊕. An analysis is given which suggests that planet X, in its present orbit, can create the requisite density gradient of comets near perihelion and aphelion during the lifetime of the Solar System. The required inclination of planet X's orbit (≳25°) may explain the failure of previous surveys to discover the planet as its present latitude is not likely to be near the ecliptic. It it exists, the best immediate hope of finding planet X is the ongoing IRAS search in the 100-μm band and the full sky optical survey by Shoemaker and Shoemaker. Independent of the question of periodic comet showers, the existence of planet X and the comet disk can readily explain the origin of the steady state flux of short-period comets over a wide range of parameters.     

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 10⁹ years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 10³ to 5 × 10⁴ AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 10⁵ AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 10⁴ < a < 3 × 10⁴ AU. The orbital planes of the comets with initial $\text{a ≧ 3 × 10}{}^4\text{AU}$ acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 10⁴AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiter's orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 10¹⁰ and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.     

Relationship of comets and planets

We analyze our earlier data on the numerical integration of the equations of motion for 274 short-period comets (with the period P<200 yr) on a time interval of 6000 yr. As many as 54 comets had no close approaches to planets, 13 comets passed through the Saturnian sphere of action, and one comet passed through the Uranian sphere of action. The orbital elements of these 68 comets changed by no more than ±3 percent in a space of 6000 yr. As many as 206 comets passed close to Jupiter. We confirm Everhart’s conclusion that Jupiter can capture long-period comets with q = 4–6 AU and i < 9° into short-period orbits. We show that nearly parabolic comets cross the solar system mainly in the zone of terrestrial planets. No relationship of nearly parabolic comets and terrestrial planets was found for the epoch of the latest apparition of comets. Guliev’s conjecture about two trans-Plutonian planets is based on the illusory excess of cometary nodes at large heliocentric distances. The existence of cometary nodes at the solar system periphery turns out to be a solely geometrical effect.     

On the Existence of Long-Period Comet Families of the Giant Planets

Astronomy Letters - We analyze the minimum orbital intersection distances (MOIDs) for a sample of long-period comets (1360) and the giant planets of the Solar System. Our calculations have revealed...     

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).     

On the dynamic connection of comets with Uranus

We consider the connection with Uranus for: (1) 945 near-parabolic comets (the period P > 200 years, the perihelion distance q > 0.1 AU), (2) 1277 Kreutz comets (P > 200 years, q < 0.01 AU), and (3) 414 short-period comets (P < 200 years). It turns out that none of near-parabolic comets passed through Uranus’s activity sphere, none of the Kreutz comets approach Uranus closer than 11 AU, and only two short-period comets, C/2006 U7 and C/2006 F2, could have a close approach to Uranus during 5000 years.     

Galactic perturbations on nearly-parabolic cometary orbits

The effect of galactic perturbations on long-period comet orbits is examined via numerical and analytical means. Relations are found between a comet's initial perihelion position and the positions of succeeding perihelia. It was found that the galactic effects were strongest on the comets initially at galactic latitudes close to 40°. In such cases the galactic perturbations caused the orbit to become almost circular before becoming nearly parabolic again. This effect allows comets with semimajor axes of about 25 000 AU to make only a few passages through the inner solar system in a time interval of 10⁹yr. Thus the galactic field is an important factor in the evolution of long-period comet orbits. The observed distribution of perihelia of long-period comets indicates that galactic effects have been active.     

On the hypothesis of the eruption origin of near-parabolic comets

The hypothesis on the genetic connection of near-parabolic comets with Jupiter, Saturn, and the transPlutonian region (5–3000 AU) proposed by E.M. Drobyshevskii is considered. It has been shown that, on average, 5.6 comets per an area of 10⁶ AU² passed through the transPlutonian region during the whole history of observations. Six-hundred nineteen comets crossed the ecliptic at heliocentric distances ranging from 0 to 2 AU. As has been shown, from the total number of 945 near-parabolic comets, eight comets closely approached Jupiter and five closely approached Saturn. The Kreutz comets, 1277 objects, did not approach Jupiter closer than 3 AU. Their minimal distance to Saturn was 5.5 AU. The minimal distance of the Kreutz comets from the edge of the transPlutonian region was 28.8 AU. The analysis led to the conclusion that the concept on the origin of the near-parabolic comets suggested by Drobyshevskii is groundless.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

On the relationship of long-period comets to known and unknown planets

Statistical aspects of the question of the dynamical relationship of long-period comets to giant planets (Saturn, Uranus, Neptune), dwarf planets (Pluto, 2003 EL₆₁, 2003 UB₃₁₃), and five hypothetical planets are investigated. Data for 859 and 888 comets (2005, 2006) with periods P > 200 years are used in the statistics. No comets of the Kreutz, Marsden, Kracht, and Meyer groups are considered. The minimum interorbital distances of comets from the listed planetary bodies are mainly analyzed. Effects testifying to the kinematical relationship of some of the comets to planets have been established by testing the cometary data relative to 67 planes. The distribution of the perihelia of long-period comets is also discussed.     

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.     

Meteor outbursts from long-period comet dust trails

Long-period comets have narrow one-revolution old dust trails that can cause meteor outbursts when encountered by Earth. To facilitate observing campaigns that will characterize and perhaps help find Earth-threatening, long-period comets from their trace of meteoric debris, we use past accounts of outbursts from 14 different showers to calculate the future dust trail positions near Earth’s orbit. We also examine known near-Earth, long-period comets and identify five potential new showers, which can be utilized to learn more about these objects. We demonstrate that it is the one-revolution trail that is responsible for meteor outbursts. A method that calculates in what year these showers are likely to return and at what hour is presented. The calculations improve on earlier approximate methods that used the Sun’s reflex motion to gauge the trail motion relative to Earth’s orbit.     

On the hypothesis of the genetic connection of comets with Pluto and the transneptunian object 2003 UB 313

The hypothesis suggested by Guliev on transneptunian objects as sources of comets is considered. The motion equations for 137 near-parabolic comets over a time interval of 5000 years were numerically integrated. No interaction between 78 comets and the transneptunian object 2003 UB 313 has been revealed: the comets were farther than 3 AU from it. It has been shown that 59 comets—candidates to Pluto’s family-approached Pluto at a distance larger than 0.7 AU. The fulfilled analysis allows us to conclude that Guliev’s hypothesis on transneptunian objects as sources of comets is groundless.     

Particle and field environment of Uranus

In 1985 the spin axis of Uranus points within 10° of the Sun and the planet's position is very near the solar apex direction. A Uranus mission with an encounter near 1985 might expect to measure the unusual particle and field configuration of a “pole-on” magnetosphere and also properties of the interstellar medium. We give here estimates of the particle and field environment of Uranus based on extrapolation of solar wind data from 1 AU and on scaling relations for an Earth-type magnetosphere. Since the magnetic moment of Uranus is unknown, all magnetospheric parameters are derived as a function of the dipole strength. The onset of special magnetospheric properties are identified as the dipole moment increases from small to large values. A fairly complete set of magnetospheric parameters is given for a specific dipole moment to illustrate the case of a large moment.     

Improvement of the position of planet X based on the motion of nearly parabolic comets

Based on the motion of nearly parabolic comets, we have improved the position of planet X in its orbit obtained by Batygin and Brown (2016). By assuming that some of the comets discovered to date could have close encounters with this planet, we have determined the comets with a small minimum orbit intersection distance with the planet. Five comets having hyperbolic orbits before their entry into the inner Solar system have been separated out from the general list. By assuming that at least one of them had a close encounter with the planet, we have determined the planet’s possible position. The planet’s probable ephemeris positions at the present epoch have been obtained by assuming the planet to have prograde and retrograde motions. In the case of a prograde motion, the planet is currently at a distance Δ whose value belongs to the interval Δ ∈ (1110, 1120) AU and has a right ascension α and declination δ within the intervals α ∈ (83?, 90?) and δ ∈ (8?, 10?); the true anomaly υ belongs to the interval υ ∈ (176?, 184?). In the case of a retrograde motion: α ∈ (48?, 58?), δ ∈ (?12?, ?6?), Δ ∈ (790, 910) AU, and υ ∈ (212?, 223?). It should be noted that in the case of a retrograde motion of the planet, its ephemeris position obtained from the motion of comets agrees with the planet’s position obtained byHolman and Payne (2016) from highly accurate Cassini observations and is consistent with the results of Fienga et al. (2016).     

Tidal Breakup of Comets

In the context of the survival of periodic comets of different origins, rotational breakup and tidal disruption could be important, especially of the short period comets injected from the Kuiper belt. This is because long-period comets from the distant Oort cloud tend to be subject to thermal stress and volatile 'explosion' far more severely. A simple calculation using the Öpik method of random planetary close encounters was performed to estimate the probability of tidal disruption of comets and scattered Kuiper belt objects (SKBOs) during their orbital migration. It was found that a large fraction of the short period comets and SKBOs might have been internally fragmented by single or multiple close encounters with the outer planets.     

Where are the Uranus Trojans?

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

Dynamical capture and physical decay of short-period comets

The brightness evolution of short-period comets is discussed in connection with their physical lifetimes. It is shown that changes in the fraction of the free-subliming area of the nuclear surface may be more important than mass decrease in determining brightness variations. The decrease in the activity of short-period comets caused by the buildup of a dust mantle may be interrupted—and partially reversed—by dust blowoffs that leave exposed areas of fresh ices. Short-period comets may thus be subject to random brightness fluctuations that make quite uncertain any derivation of their physical lifetime based on comparisons of their absolute brightness at different apparitions. As an alternate procedure, the numerical integration of the whole sample of short-period comet orbits carried out by A. Carusi, L.Kresák, E. Perozzi and G. B. Valsecchi (1984, Long-Term Evolution of Short-Period Comets. Istituto Astrofisica Spaziale Internal Report 12, Rome) is used to draw conclusions about the transfer rate of their perihelia from Jupiter's region to the region of the terrestrial planets (heliocentric distances<1.5 AU). It is found that about one short-period comet per century reaches the region of the terrestrial planets. From this result and under the assumption of a steady-state comet population, an average lifetime of the order of 6 × 10³ years (～10³ revolutions) is derived for a typical kilometer-sized short-period comet of perihelion distance q ～ 1 AU. Such a rather long comet lifetime, as compared to some previous derivations, is consistent with the survival of some periodic comets on small-q orbits of long dynamical time scales.     

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.