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).     

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.     

Origin of short period comets

Reasons for interest in the origin of short-period comets and the difficulties of computing their long-term dynamcal evolution are reviewed. The relative advantages of a source region in an extended inner core of the Oort cloud or a compact comet belt just beyond the planetary system are finely balanced, and it is premature to consider the problem solved. A complication is that some comets belonging to the Jupiter family may be part of a time-dependent system, possibly the remains of a giant comet such as Chiron which could have been part of the system 104 yr ago. The origin of short-period comets plays a pivotal role in many areas of solar system science: planet formation, the source of water (possibly life) on the terrestrial planets, the cratering record on the terrestrial planets and satellites of the outer planets, and the environmental impact posed by massive bodies and their decay products in the Earth's near-space environment.     

The provenance and evolution of comets

The process of comet formation through the hierarchical aggregation of originally submicron-sized interstellar grains to form micron-sized particles and then larger bodies in the protoplanetary disc, culminating in the formation of planetesimals in the disc extending from Jupiter to beyond Neptune, is briefly reviewed. The planetesimal theory for the origin of comets implies the existence of distinct cometary reservoirs, with implications for the immediate provenance of observed comets (both long-period and short-period) and their evolution as a result of planetary perturbations and physical decay, for example splitting and sublimation. The principal mode of cometary decay and collisional interaction with the terrestrial planets is through the formation and evolution of streams of cometary debris and hitherto undiscovered families of cometary asteroids. Recent dynamical results, in particular the sungrazing and sun-colliding end-state for short-period comet and asteroid orbits, are briefly discussed.     

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.     

Collision with meteoroids as one of the possible mechanisms for the splitting of cometary nuclei

Results are presented of a statistical analysis of dynamic parameters for 114 comets with split nuclei. A list of the objects includes actually split comets, fragments of cometary pairs, lost comets with designation D, and comets with large-scale atmospheric features. Some aspects of the hypothesis that splitting is caused by collisions of cometary nuclei with meteoroid swarms are investigated. To verify the hypothesis, an analysis is conducted of the positions of split comets’ orbits relative to 58 meteor streams from Cook’s catalogue. The calculations give the number (N) of orbital nodes of split comets relative to the plane of each swarm within a distance of 0.001, 0.005, 0.01, 0.05, and 0.1 AU from each swarm. A special algorithm is proposed for determining the degree of redundancy of N by finding the expected value and dispersion for the number of the nodes. The comparison of N with the expected value, together with the consideration of the dispersion, reveals a redundancy of N in 29 cases. Therefore, collisions of comets with meteoroid swarms can be considered as one of the possible causes of comet splitting. A similar testing is conducted for the asteroid belt and Kuiper belt as potential sources of a vast number of sporadic meteoroids. Based on the results of the calculations, the former may be considered as the most effective region of splitting of periodic comets.     

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.     

Change in the orbital period of a binary system due to dynamical tides for main-sequence stars

We investigate the change in the orbital period of a binary system due to dynamical tides by taking into account the evolution of a main-sequence star. Three stars with masses of one, one and a half, and two solar masses are considered. A star of one solar mass at lifetimes t = 4.57 × 10⁹ yr closely corresponds to our Sun. We show that a planet of one Jupiter mass revolving around a star of one solar mass will fall onto the star in the main-sequence lifetime of the star due to dynamical tides if the initial orbital period of the planet is less than P _orb ≈ 2.8 days. Planets of one Jupiter mass with an orbital period P _orb ≈ 2 days or shorter will fall onto a star of one and a half and two solar masses in the mainsequence lifetime of the star.     

Dynamics and Origin of Comets: New Problems Appeared after the <Emphasis Type="Italic">Rosetta</Emphasis> Space Mission

The data obtained in the recent Rosetta space mission to comet 67P/Churyumov–Gerasimenko have had a profound impact on the understanding of the nature of comets. In addition to revising the notions on the physical properties and structure of comets, this addresses dynamical aspects of the formation of the observed cometary populations (short- and long-period comets, Centaurs, trans-Neptunian objects, and Oort-cloud objects). In the review, we discuss new problems that have appeared in the theory of dynamical evolution and origin of comets due to the Rosetta mission.     

The provenance and evolution of comets

The process of comet formation through the hierarchical aggregation of originally submicron-sized interstellar grains to form micron-sized particles and then larger bodies in the protoplanetary disc, culminating in the formation of planetesimals in the disc extending from Jupiter to beyond Neptune, is briefly reviewed. The ‘planetesimal’ theory for the origin of comets implies the existence of distinct cometary reservoirs, with implications for the immediate provenance of observed comets (both long-period and short-period) and their evolution as a result of planetary perturbations and physical decay, for example splitting and sublimation. The principal mode of cometary decay and collisional interaction with the terrestrial planets is through the formation and evolution of streams of cometary debris and hitherto undiscovered ‘families’ of cometary asteroids. Recent dynamical results, in particular the sungrazing and sun-colliding end-state for short-period comet and asteroid orbits, are briefly discussed.     

Comparison of some characteristics of comets 1P/Halley and 67P/Churyumov–Gerasimenko from the <Emphasis Type="Italic">Vega</Emphasis> and <Emphasis Type="Italic">Rosetta</Emphasis> mission data

On March 6 and 9, 1986, for the first time in the history of science, the Russian spacecraft Vega-1 and -2 approached the nucleus of comet 1P/Halley and flew by at a small distance. A while later, on March 14, 1986, the Giotto spacecraft (European Space Agency (ESA)) followed them. Together with the Japanese spacecraft Suisei (Japan Aerospace Exploration Agency (JAXA)), they obtained spaceborne investigations of cometary nuclei. Direct studies of cometary bodies that bear traces of the Solar System formation were continued in the next missions to comets. Starting from 2014 and up to 2016 September, the Rosetta spacecraft (ESA), being in a low orbit around the nucleus of comet 67P/Churyumov–Gerasimenko, has performed extremely sophisticated investigations of this comet. Here, we compare some results of these missions. The paper is based on the reports presented at the memorial conference dedicated to the 30th anniversary of the Vega mission, which took place at the Space Research Institute of the Russian Academy of Sciences in March, 2016, and does not pretend to comprehensively cover the problems of cometary physics.     

Comets and the formation of planets

A morphological study of the physical and dynamical processes of planet formation is presented, with emphasis on the intermediary role of comet nuclei. Although guided by a particular model of the evolution of the pre-planetary solar nebula, implying the freezing-out of hydrogen in the region of the giant planets, the derivations and conclusions are of wider import, applicable to other cosmogonic models as well as to certain phases of star formation. The items evaluated physically, dynamically, or statistically comprise: (1) the total number mass of comets in Oort's cloud; (2) a re-evaluation of the diameters and masses of cometary nuclei; (3) the processes of nucleation from gravitational and Boltzmann instabilities of gaseous media to agglomerations of particulate matter as conditioned by inbuilt angular momentum; (4) the statistical-dynamical conditions and time scales of orbital interaction of comets with the planets and the consequences of disintegration.A consistent model proposes the formation of comets and planets in pre-planetary rings of the residual solar nebula, with subsequent ejection, chiefly by Jupiter, of the comets to Oort's sphere. Screening by absorbing matter is not only probable, but necessary to protect the comets from dis-integration during the process of ejection.Paper dedicated to Prof. H. C. Urey on the occasion of his 80th birthday on 29 April, 1973.This work has been currently supported by grants from the National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland.     

On the origin of comets

The paper presents a brief history of cometary cosmogony. It discusses critically the eruptive hypothesis, the hypothesis on the relict origin of comets, and the hypothesis on a genetic connection between comets and trans-Plutonian planets. Laplace’s theoretical prediction as to the capture of long-period comets by Jupiter into short-period orbits is confirmed. We conclude that the interstellar hypothesis promising is for the provenance of comets.     

Spectral studies of comets in the ultraviolet range and prospects of the WSO-UV project in these studies

Many problems of determining the chemical composition of comets and studying the physical processes in cometary nuclei can only be solved by using observational data in the UV range of the electromagnetic spectrum (115–300 nm). Cometary observations have a number of features in comparison with such studies of other astronomical objects. The World Space Observatory — Ultraviolet mission, planned for launch in 2021, will overcome most of the challenges in these studies and will be able to become an essential tool of cometary UV research in the following decade.     

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).     

Predictions on the core mass of Jupiter and of giant planets in general

More than 80 giant planets are known by mass and radius. Their interior structure in terms of core mass, number of layers, and composition however is still poorly known. An overview is presented about the core mass M _core and envelope mass of metals M _Z in Jupiter as predicted by various equations of state. It is argued that the uncertainty about the true H/He EOS in a pressure regime where the gravitational moments J ₂ and J ₄ are most sensitive, i.e. between 0.5 and 4 Mbar, is in part responsible for the broad range \(M_{\mathit{core}}=0{-}18\:M_{\oplus }\), \(M_{Z}=0{-}38\:M_{\oplus }\), and \(M_{\mathit{core}}+M_{Z}=14{-}38\:M_{\oplus }\) currently offered for Jupiter. We then compare the Jupiter models obtained when we only match J ₂ with the range of solutions for the exoplanet \(\mathrm{GJ}\:436\mathrm{b}\), when we match an assumed tidal Love number k ₂ value.     

Seasonal changes on Jupiter: 1. Factor of activity of the hemispheres

To identify temporal variations of the characteristics of Jupiter’s cloud layer, we take into account the geometric modulation caused by the rotation of the planet and planetary orbital motion. Inclination of the rotation axis to the orbital plane of Jupiter is 3.13°, and the angle between the magnetic axis and the rotation axis is β ≈ 10°. Therefore, over a Jovian year, the jovicentric magnetic declination of the Earth φ _m varies from–13.13° to +13.13°, and the subsolar point on Jupiter’s magnetosphere is shifted by 26.26° per orbital period. In this connection, variations of the Earth’s jovimagnetic latitude on Jupiter will have a prevailing influence in the solar-driven changes of reflective properties of the cloud cover and overcloud haze on Jupiter. Because of the orbit eccentricity (e = 0.048450), the northern hemisphere receives 21% greater solar energy inflow to the atmosphere, because Jupiter is at perihelion near the time of the summer solstice. The results of our studies have shown that the brightness ratio A _j of northern to southern tropical and temperate regions is an evident factor of photometric activity of Jupiter’s atmospheric processes. The analysis of observational data for the period from 1962 to 2015 reveals the existence of cyclic variations of the activity factor A _j of the planetary hemispheres with a period of 11.86 years, which allows us to talk about the seasonal rearrangement of Jupiter’s atmosphere.     

Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

Search for extrasolar planets by polarimetry

Optical polarimetry is suggested as a new method for detecting “hot Jupiter” planets around stars. The polarimetric search method has been tested experimentally; for this purpose, the necessary astronomical observations and their processing have been performed. The results obtained allow us to assert with caution that the suggested method yields positive results and can be of use both in searching for exoplanets and in refining their masses. According to our results, a tangential transit of the planet 51 Peg b may be observed. The angle between the orbital plane of 51 Peg b and the observer’s direction must then be small, sin i ≈ 1, and the mass of 51 Peg b must be close to 0.46 M _J (Jupiter mass).     

On the MOND external field effect in the solar system

In the framework of the MOdified Newtonian Dynamics (MOND), the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field E of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle: it is the so-called External Field Effect (EFE). In the case of the solar system, E would be A _cen≈10^?10 m?s^?2 because of its motion through the Milky Way: it is orders of magnitude smaller than the main Newtonian monopole terms for the planets. We address here the following questions in a purely phenomenological manner: are the Sun’s planets affected by an EFE as large as 10^?10 m?s^?2? Can it be assumed that its effect is negligible for them because of its relatively small size? Does E induce vanishing net orbital effects because of its constancy over typical solar system’s planetary orbital periods? It turns out that a constant and uniform acceleration, treated perturbatively, does induce non-vanishing long-period orbital effects on the longitude of the pericenter ? of a test particle. In the case of the inner planets of the solar system and with E≈10^?10 m?s^?2, they are 4–6 orders of magnitude larger than the present-day upper bounds on the non-standard perihelion precessions \(\Delta\dot{\varpi}\) recently obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System Barycentric frame. The upper limits on the components of E are E _x ≤1×10^?15 m?s^?2, E _y ≤2×10^?16 m?s^?2, E _z ≤3×10^?14 m?s^?2. This result is in agreement with the violation of the Strong Equivalence Principle by MOND. Our analysis also holds for any other exotic modification of the current laws of gravity yielding a constant and uniform extra-acceleration. If and when other corrections \(\Delta\dot{\varpi}\) to the usual perihelion precessions will be independently estimated with different ephemerides it will be possible to repeat such a test.