Close Encounters of the Third Kind, by Dana Polan

Instabilities in planetary systems can result in the ejection of planets from their host system, resulting in free-floating planets (FFPs). If this occurs in a star cluster, the FFP may remain bound to the star cluster for some time and interact with the other cluster members until it is ejected. Here, we use $N$-body simulations to characterise close star-planet and planet-planet encounters and the dynamical fate of the FFP population in star clusters containing $500-2000$ single or binary star members. We find that FFPs ejected from their planetary system at low velocities typically leave the star cluster 40% earlier than their host stars, and experience tens of close ($<1000$ AU) encounters with other stars and planets before they escape. The fraction of FFPs that experiences a close encounter depends on both the stellar density and the initial velocity distribution of the FFPs. Approximately half of the close encounters occur within the first 30 Myr, and only 10% occur after 100 Myr. The periastron velocity distribution for all encounters is well-described by a modified Maxwell-Bolzmann distribution, and the periastron distance distribution is linear over almost the entire range of distances considered, and flattens off for very close encounters due to strong gravitational focusing. Close encounters with FFPs can perturb existing planetary systems and their debris structures, and they can result in re-capture of FFPs. In addition, these FFP populations may be observed in young star clusters in imaging surveys; a comparison between observations and dynamical predictions may provide clues to the early phases of stellar and planetary dynamics in star clusters.

The Centaur population is composed of minor bodies wandering between the giant planets that frequently perform close gravitational encounters with these planets, leading to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence of a well-defined system of rings around a body in such a perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of 100 Myr. We found, on average, that each clone experiences during its lifetime more than 150 close encounters with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters that were able to significantly disrupt or disturb the rings of Chariklo. About 3% of the clones lose their rings and about 4% of the clones have their rings significantly disturbed. Therefore, our results show that in most cases (more than 90%), the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common among these kinds of Centaurs.

During their lifetime, the Near-Earth Asteroids (NEAs) suffer numerous close encounters (CE) with Earth, Mars and Venus. It has been demonstrated that gravitational interactions during close planetary encounters can alter an asteroid’s spin state, and hence, along with collisions, play a role in the rotational evolution of NEAs. The variation of the rotational angular momentum during the encounters can increase or decrease the rotation rate depending on the initial condition. In addition to the rotation rate, close encounters cause variation in the movement of precession and nutation of the asteroid. Using a numerical model that takes into account the spin-orbit coupling of a body with ellipsoidal shape, the subject of this study is to analyze the rotational motion (rotation, precession and nutation) of asteroids during CE with the Earth for different initial conditions. We computed the variation of the obliquity and the variation of spin period after the CE. We found significant change in obliquity and spin period only in cases with strong encounter, that is in cases that the impact parameter of the encounter (1.2 ≤ d ≤ 7 (Earth radii) and the relative velocity (v) are small. Our results also show that the variation of rotational motion due to the close encounter is capable of tumbling the axis of rotation and gravitational rupture may occur in a few cases.

Based on telescopic observations of Jupiter-family comets (JFCs), there is predicted to be a paucity of objects at sub-kilometre sizes. However, several bright fireballs and some meteorites have been tenuously linked to the JFC population, showing metre-scale objects do exist in this region. In 2017, the Desert Fireball Network (DFN) observed a grazing fireball that redirected a meteoroid from an Apollo-type orbit to a JFC-like orbit. Using orbital data collected by the DFN, in this study, we have generated an artificial data set of close terrestrial encounters that come within 1.5 lunar distances (LD) of the Earth in the size-range of 0.01–100 kg. This range of objects is typically too small for telescopic surveys to detect, so using atmospheric impact flux data from fireball observations is currently one of the only ways to characterize these close encounters. Based on this model, we predict that within the considered size-range 2.5 × 108 objects ($0.1{{\ \rm per\ cent}}$ of the total flux) from asteroidal orbits (TJ &amp;gt; 3) are annually sent on to JFC-like orbits (2 &amp;lt; TJ &amp;lt; 3), with a steady-state population of about 8 × 1013 objects. Close encounters with the Earth provide another way to transfer material to the JFC region. Additionally, using our model, we found that approximately 1.96 × 107 objects are sent on to Aten-type orbits and ∼104 objects are ejected from the Solar system annually via a close encounter with the Earth.

Knowledge of the interior density distribution of an asteroid can reveal its composition and constrain its evolutionary history. However, most asteroid observational techniques are not sensitive to interior properties. We investigate the interior constraints accessible through monitoring variations in angular velocity during a close encounter. We derive the equations of motion for a rigid asteroid’s orientation and angular velocity to arbitrary order and use them to generate synthetic angular velocity data for a representative asteroid on a close Earth encounter. We develop a toolkit AIME (Asteroid Interior Mapping from Encounters) which reconstructs asteroid density distribution from these data, and we perform injection-retrieval tests on these synthetic data to assess AIME’s accuracy and precision. We also perform a sensitivity analysis to asteroid parameters (e.g. asteroid shape and orbital elements), observational setup (e.g. measurement precision and cadence), and the mapping models used. We find that high precision in rotational period estimates (≲0.27 s) is necessary for each cadence, and that low perigees (≲ 18 Earth radii) are necessary to resolve large-scale density non-uniformities with uncertainties of $\sim 0.1{{\ \rm per\ cent}}$ of the local density under some models.

In considering the Shakespeare that Anne Bronte knew, three kinds of close textual encounters emerge. First, the Shakespearian text the Bronte family might have read, and the context in which they read it; second, Anne Bronte's actual copy of Shakespeare's plays and how she might have read them; and third the kinds of Shakespeare allusions which are traceable in her two novels, Agnes Grey and The Tenant of Wildfell Hall . These close encounters with a reader and her writing will further our understanding of Shakespeare's importance in relation to Anne Bronte's creativity as well as to her life. Shakespeare's impact on the work of the Bronte sisters is considerable. In Charlotte's novel, Shirley , there is a chapter entitled ' Coriolanus '. Shakespeare is there appropriated as an emotional and political nexus for the relationship between Caroline Helstone and Robert Moore. Shakespeare is appropriated, to a lesser extent, in Jane Eyre and The Professor . In Emily's Wuthering Heights , Shakespeare's influence is much more submerged, just one of the imaginative and influential threads that Emily weaves together. Although it includes the Life of Sir Walter Scott , the Lord Wharton Bible and Milton's Paradise Lost , no edition of Shakespeare is listed in the inventory of 'Books belonging to or inscribed by members of the Bronte family and held in the Bronte Parsonage Museum'. This should not be too surprising. The inventory is small and the most commonly read books tend not to survive. The Brontes' knowledge of Shakespeare can be safely assumed. Lynne Reid Banks imagines the reading environment of the Brontes in her 1986 biographical novel, Dark Quartet: The Story of the Brontes : When he [the Reverend Patrick] saw Branwell in a reverie over some book, written in a more permissive age, Patrick wondered if he was wise in allowing his children access to any volume in his library or that at Ponden Hall, which they frequently visited to borrow books. At first he had felt that they were safe from the grosser allusions in Shakespeare, for instance, by virtue of an inability of their essentially innocent minds to understand. Now he was no longer sure.

Numerical modeling has long suggested that gravitationally bound (or so-called rubble-pile) near-Earth asteroids (NEAs) can be destroyed by tidal forces during close and slow encounters with terrestrial planets. However, tidal disruptions of NEAs have never been directly observed nor have they been directly attributed to any families of NEAs. Here we show population-level evidence for the tidal disruption of NEAs during close encounters with Earth and Venus. Debiased model distributions of NEA orbits and absolute magnitudes based on observations by the Catalina Sky Survey during 2005–2012 underpredict the number of NEAs with perihelion distances coinciding with the semimajor axes of Venus and Earth. A detailed analysis of the orbital distributions of the excess NEAs shows that their characteristics agree with the prediction for tidal disruptions, and they cannot be explained by observational selection effects or orbital dynamics. Accounting for tidal disruptions in evolutionary models of the NEA population partly bridges the gap between the predicted rate of impacts by asteroids with diameters of tens of meters and observed statistics of fireballs in the same size range.

The range of validity of the two-body approximation in models of terrestrial planet accumulation: I. Gravitational perturbations

The dynamical evolution of simulated meteoroid stream of the Quadrantids ejected from the parent body of the asteroid (196256) 2003 EH1 expects possible scenario for resonant motion. We found a peculiar behavior for this stream. Here, we show that the orbits of some ejected particles are strongly affected by the Lidov&amp;#8211;Kozai mechanism that protects them from close encounters with Jupiter. Lack of close encounters with Jupiter leads to a rather smooth growth in the parameter MEGNO (Mean Exponential Growth factor of Nearby Orbits) and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream. A rather smooth path with nearly constant semi-major axis is obtained due to lack of close encounters with Jupiter. The coupled oscillation of the three orbital parameters, e, i, and &amp;#969;, for stable ejected particles is observed.However, close encounters with Jupiter are not treated by the Kozai formalism and can transfer particles away from the Kozai trajectories for unstable ejected particles over time. Other ejected particles have chaotic motion from simulations of the orbit of meteoroids are not affected by the Lidov &amp;#8211; Kozai mechanism. We suppose that the reasons are the frequent close approaches of the ejected particles with Jupiter and they located near mean motion resonance 2:1J with Jupiter. The motion of these objects has considered to be chaotic in a long-time scale, and the close encounters with Jupiter are supposed to be the cause of the faster chaos. Another reason is that a non-resonant state near the mean motion resonance 2:1J has a strong influence on the motion of the Quadrantid meteor stream. This &amp;#8220;weak chaos&amp;#8221; is largely confined to the true anomaly. Consequently, the shape of the orbit can be computed reliably over much longer time scales than can the body&amp;#8217;s position within the orbit. High value of the parameter MEGNO are due to frequent changes in semimajor axis induced by multiple close encounters with Jupiter near Hill sphere. We finally note that the chaotic behavior of the simulation particles of meteor stream may be caused not only by close encounter with planets but also by unstable mean motion or secular resonances.We conjecture that the reasons of chaos are the overlap of stable secular resonances and unstable mean motions resonances and close and/or multiple close encounters with the major planets. The orbits of some ejected particles are strongly affected by the Lidov&amp;#8211;Kozai mechanism that protects them from close encounters with Jupiter that leads to a rather smooth growth in the parameter MEGNO and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream.The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme No. 0721-2020-0049)&amp;#160;ReferencesAbedin, A., Spurn&amp;#253;, P., Wiegert, P., Pokorn&amp;#253;, P., Borovi cka, J., Brown, P., 2015. On the age and formation mechanism of the core of the Quadrantid meteoroid stream. Icarus 261, 100&amp;#8211;117.Cincotta, P.M., Girdano, C.M., Simo, C., 2003. Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits. Phys. Nonlinear Phenom. 182 (3&amp;#8211;4), 151&amp;#8211;178.Chirikov, B.V., 1979. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52 (5), 263&amp;#8211;379.Galushina, T.Yu, Sambarov, G.E., 2017. The dynamical evolution and the force model for asteroid (196256) 2003 EH1. Planet. Space Sci. 142, 38.Galushina, T.Yu, Sambarov, G.E., 2019. Dynamics of asteroid 3200 Phaethon under overlap of different resonances. Sol. Syst. Res. 53 (3), 215&amp;#8211;223.Gonczi, R., Rickman, H., Froeschle, C., 1992. The connection between Comet P/Machholz and the Quadrantid meteor. Mon. Not. Roy. Astron. Soc. 254, 627.Hughes, D.W., Taylor, I.W., 1977. Observations of overdense Quadrantid radio meteors and the variation of the position of stream maxima with meteor magnitude. Mon. Not. Roy. Astron. Soc. 181, 517.Kozai, Y., 1962. Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591&amp;#8211;598.Lidov, M.L., 1962. The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719.Williams, I.P., Ryabova, G.O., Baturin, A.P., Chernitsov, A.M., 2004a. The parent of the Quadrantid meteoroid stream and asteroid 2003 EH1. Mon. Not. Roy. Astron. Soc. 355 (4), 1171&amp;#8211;1181.

To date, rings are found around a Centaur (10199) Chariklo, trans-neptunian objects (TNOs) (136108) Haumea, and (50000) Quaoar. These discoveries suggest that asteroidal ring systems may be common, particularly in the outer solar system. Since collisions are a ubiquitous and fundamental evolutionary process throughout the solar system, we conjecture that asteroidal ring systems must have experienced close encounters with small objects as part of their evolutionary process. Here, we investigate the response of ring systems when they experience gravitational disturbance by a close encounter with another small object, by calculating the change in eccentricity and the fraction of lost ring particles. We find that a perturber needs to be as massive as or more massive than the ringed object, and needs to pass in the immediate vicinity of the ring in order to cause significant disruption. The change in eccentricity expected for Chariklo's inner ring and Quaoar's outer ring agrees with the analytical expression derived from the impulse approximation, while that for Haumea's ring agrees with the analytical expression called “exponential regime”. If we define a lifetime of a ring as the mean time to experience disruptive close encounters that can raise the eccentricity of ring particles >0.1, the lifetime for ring systems around Chariklo, Haumea, and Quaoar are >104 Gyr. We conclude that ring systems around Chariklo, Haumea, and Quaoar are highly unlikely to suffer from close encounters with another small object even if those systems are as old as 4 Gyr. Close encounter with a small object may not be responsible for the finite eccentricity observed for Chariklo's ring system, although eccentricity of ring particles could be increased to ∼10−4 in 4 Gyr. We also find that the lifetime is shorter for smaller ringed objects, and it still exceeds 4 Gyr for km-sized ringed objects in the outer solar system. Therefore, regardless of the size of ringed objects, asteroidal ring systems in the outer solar system are unlikely to suffer severe damage by close encounter with a small object. On the other hand, the lifetime is estimated to be on the order of 100 Myr for km-sized asteroids and 10 Myr for 100 m-sized asteroids in the near-Earth region and the main belt. This finding offers a dynamical explanation why ring systems have not been found in the inner solar system.

The orbital evolution of comet P/Lexell has been characterized by a sequence of three close planetary encounters within 12 years; the first of these encounters was with Jupiter, 1767, and lead to a reduction of the perihelion distance from 2.9 AU to 0.67 AU. Then the comet encountered the Earth at a distance of 0.015 AU, in 1770, and was discovered. The final, very close encounter with Jupiter, in 1779, removed the comet from observability, sending it into an orbit of perihelion distance in excess of 5 AU (Kazimirchak-Polonskaya, 1967).

Spectroscopic and photometric observations of the star Parenago 1540 (V = 11.3), located 10 arcmin west of the Trapezium in Orion, have shown the star to be a pre-main-sequence double-lined spectroscopic binary. Thirty-seven radial-velocity measurements were obtained from which the orbital elements of the binary were determined, in particular an orbital period P = 33.73 + 0.03 days and an eccentricity of e = 0.12 + 0.01. High-dispersion spectra reveal strong Li 6707 A absorption lines in each of the components of P1540. A spectrum at lower dispersion also shows strong Ca II H and K emission lines, not resolved into individual components. P1540 also has an x-ray emission of 4 x 10(30) ergs s(-1). UBVRI photometry, combined with relative luminosities at V determined from spectra, have been used to determine the locus of each component in the theoretical H-R diagram. Assuming membership in the Orion star-forming region, both stars lie substantially above the ZAMS in the pre-main-sequence domain of the diagram. All of these data support the conclusion that both components of P1540 are pre-main-sequence stars. The masses of the individual components, determined from theoretical evolutionary tracks and the regiment of satisfying the dynamical mass ratio, are approximately 2.25 M and 1.7 M. Interestingly, no pair of stars satisfying both the dynamical and photometric constraints is compatible with coeval formation of the stars. If coeval formation is demanded, then the pre-main-sequence evolutionary tracks of the components of P1540 are not consistent with theoretical single-star evolutionary tracks presented by Cohen and Kuhi. Alternatively, the noncoevality of the components of P1540 might be attributed to an exchange occurring during a close stellar encounter. The space velocity of P1540 indicated that the binary is escaping from the Orion Nebula region, perhaps as the result of such a close encounter in the Trapezium cluster.

The singing and related vocalizing of great crested flycatchers, Myiarchus crinitus (Aves, Tyrannidae), included at least 12 different vocalizations. Each vocalization correlated with (and thus made information available about) a distinctive range of behaviour, from unassertive to more actively responsive, provocative or even confrontational. Four were used by individuals primarily when alone and not initiating close social encounters. The eight other vocalizations were uttered primarily in close encounters: one in preliminaries to such events, two predominantly in encounters with opponents, another in close associating of mates, two in duetting, and two infrequently, mostly in confrontations. The division of the repertoire into sets of vocalizations providing information about either low or elevated probabilities that a signaller will undertake the behavioural initiatives that precede, shape or sustain social interactions parallels a division found in other recently studied passerines. Such information is pertinent to individuals' decisions to forego or start close interactions with, for instance, competitors or mates. The information should be useful to a great many species, not just birds, but also mammals and various other animals — species in which individuals keep each other informed by singing when they are apart.

The orbital evolution of comet P/Lexell has been characterized by a sequence of three close planetary encounters within 12 years; the first of these encounters was with Jupiter, 1767, and lead to a reduction of the perihelion distance from 2.9 AU to 0.67 AU. Then the comet encountered the Earth at a distance of 0.015 AU, in 1770, and was discovered. The final, very close encounter with Jupiter, in 1779, removed the comet from observability, sending it into an orbit of perihelion distance in excess of 5 AU (Kazimirchak-Polonskaya, 1967).

I consider the Prograde Gravitational Capture Model (PGCM) to be a default model in that it need not be accepted until all other candidate models are tested and retired. The Giant Impact Model (GIM) was also presented as a default model because the proposers thought that fission, co-formation, and capture models could be retired from consideration. But the GIM does not relate very well to the facts to be explained by a successful model and I think that this model should soon be retired. The PGCM is not just another capture model, it is a complex model in both geological timing and in Solar System space. The model I am presenting attempts to explain several problems that were associated with earlier versions of capture such as (1) Where did the body of the Moon come from?; (2) What is the energy sink for capture?; and (3) How does the capture model relate to the rock and mineral records of Earth and Moon? Furthermore, my version of the capture model relates to Harold Urey’s speculation that the Moon may be a “Rosetta Stone” for interpretation of the history of the Solar System. This capture model was developed over a period of five decades. The initial idea that the Moon has left an imprint on the geological record of Earth was gained from Preston Cloud’s summary articles on the Primitive Earth in the 1968–1972 era. After studying lunar photographs and lunar globes I noticed an obvious surface pattern: i.e., many of the “circular” maria were located very near to a great-circle on the lunar globe. I interpreted this pattern to be compatible with partial tidal disruption of the Moon during a close, but non-collisional, encounter with Earth. A set of numerical simulations (in 1972) of particles lifted from the lunar surface during a close gravitational encounter illustrated under what conditions this could happen. An outstanding question from the simulations was whether this close encounter was simply a non-capture (fly-by) encounter or was it a close encounter associated with a capture sequence of events? By 1977 I had worked out a tentative time-scale for a capture sequence of events that related to the rock records of Earth and Moon. I tentatively set the capture event at 3.95 Ga. But my colleagues and I could not demonstrate that capture is physically possible. We did know that the energy for capture could be stored by tidal deformation processes in the body of the Moon but we could not justify a low Q value of 1, 2, or 3 for the lunar body until 1986. At that time Ross and Schubert (UCLA) published a set of calculations in the Proceedings Volume for the 16th Lunar and Planetary Science Conference justifying a very low Q value for a lunar-like body. Then in 1987 we had our first numerical simulations of capture. At this point we knew that capture of a lunar mass body could be accomplished from a heliocentric orbit that is very similar to that of the Earth’s orbit (within 3% eccentricity). The question now was: “Where did the body of the Moon come from?” After another 10-year waiting period an answer came through in the form of a short article in the journal NATURE on the origin of Vulcanoid planetoids. Devolatilized bodies like Luna and sibling planetoids could form in the zone between Mercury and the Sun as Al Cameron presaged in two articles in 1972 (before he embarked on the GIM excursion). If Luna formed as a Vulcanoid planetoid then it could be transferred to Earth orbit for capture if enough “Lunas” (candidate planetoids) were formed in the source region. My guess is that we need to start with 6 to 8 lunar-like bodies for one to survive the hazardous trip to Earth orbit. The final problem to be worked on was the relation to the rock record of Earth. John Valley (Univ. of Wisconsin) published his ideas on the Cool Early Earth in the journal GEOLOGY in 2002. In my view there could be a Cool Early Earth before the capture episode and that Cool Early Earth era would have an abrupt end at the time of Lunar Capture at 3.95 Ga. The older lunar mare basalts and breccias yielded dates of crystallization at about that time and the oldest and strongest remanent magnetic signature in lunar basalts is of that some general age. So, for me, the concept of a COOL EARLY EARTH was a good one and the story of a PROGRADE GRAVITATIONAL CAPTURE EPISODE was taking shape after a period of several decades. I also see now why no one had been able to piece this together at an earlier time. I still consider it to be a DEFAULT MODEL!