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We report JWST Mid-Infrared Instrument (MIRI) Medium Resolution Spectrograph (MRS) observations of the β Pic moving-group member, η Tel A, along with its brown dwarf binary companion, η Tel B. Following point-spread-function subtraction, we recover the spatially resolved flux from the debris disk around η Tel A, along with the position of the companion exterior to the disk. We present a new 5–26 μ m epoch of spectroscopy for the disk, in which we discover a 20 μ m silicate feature, and the first ever 11–21 μ m spectrum of η Tel B, which indicates a bare photosphere. We derive a new epoch of relative astrometry for the companion, extending the baseline of measurements to 25 yr, and find that it is currently located near the apocenter of an eccentric long-period orbit. The companion's orbit is close enough to the disk that it should significantly perturb the planetesimals within it, resulting in a detectable mid-IR pericenter glow and near alignment with the companion. Contrary to expectations, however, we find that the disk appears to be axisymmetric and potentially misaligned with the companion in the MIRI MRS data. We posit that this may be due to the presence of an additional, as-yet-undetected ∼0.7–30 M J planet orbiting interior to the disk, with a semimajor axis of ∼3–19 au. [ABSTRACT FROM AUTHOR]

We discovered 83 asteroids at the Baldone Astrophysical Observatory (MPC code 069) in 2017–2022. We studied one of the dynamically interesting Apollo (Near Earth object) observed at the Baldone Astronomical Observatory, namely 428694 Saule (2008 OS9) and the Centaur-type asteroid 330836 Orius (2009 HW77). We studied the evolution of the asteroid Saule’s rotation period, obliquity, and spin axis together with its non-gravitational parameter da∕dt{\rm{d}}a/{\rm{d}}t connected with the Yarkovsky effect. Additionally, we studied the orbit of the Amor-type asteroid 2017 UW42, which has the significant non-gravitational parameter A2A2.

Let R be a finite commutative ring with unity, and let G = (V , E) be a simple graph. The zero-divisor graph, denoted by Γ (R) is a simple graph with vertex set as R, and two vertices x , y ∈ R are adjacent in Γ (R) if and only if x y = 0 . In [5], the authors have studied the Laplacian eigenvalues of the graph Γ (Z n) and for distinct proper divisors d 1 , d 2 , ⋯ , d k of n, they defined the sets as, A d i = { x ∈ Z n : (x , n) = d i } , where (x, n) denotes the greatest common divisor of x and n. In this paper, we show that the sets A d i , 1 ≤ i ≤ k are actually orbits of the group action: A u t (Γ (R)) × R ⟶ R , where A u t (Γ (R)) denotes the automorphism group of Γ (R) . Our main objective is to determine new classes of threshold graphs, since these graphs play an important role in several applied areas. For a reduced ring R, we prove that Γ (R) is a connected threshold graph if and only if R ≅ F q or R ≅ F 2 × F q . We provide classes of threshold graphs realized by some classes of local rings. Finally, we characterize all finite commutative rings with unity of which zero-divisor graphs are not threshold. [ABSTRACT FROM AUTHOR]

Fractures of the orbit are frequently noted in craniomaxillofacial trauma. The complexity of the anatomy and the proximity to various vital structures often complicates the surgical management of these fractures. The authors have thus attempted to review the literature on anatomy of the bony orbit and its soft tissue envelope in a simplified manner with due emphasis on surgical anatomy and exploration of the orbit with a surgical perspective. The contents of this narrative literature review may be useful for young maxillofacial surgeons and will aid in the process of management of orbital fractures. [ABSTRACT FROM AUTHOR]

In the traditional X-ray pulsar Doppler velocimetry approach, a single pulsar only provides the velocity information of spacecraft in the line-of-sight (LOS) direction of a pulsar. Theoretically, we prove that the spacecraft velocity error in any direction can distort the X-ray pulsar profile in orbit around Jupiter. Moreover, using singular value decomposition (SVD), we find that the observability of velocities in both the maximal and middle singular directions is far better than that of the minimal one. Based on theoretical analysis results, we propose a two-dimensional Doppler velocimetry approach using a single X-ray pulsar to provide more velocity information for spacecraft. Firstly, we use SVD to give two well-observable singular directions for velocity estimation. And then, to eliminate duplicate computations in the accumulative process of X-ray pulsar signals, we build the piecewise complete dictionary of accumulated pulsar profiles, which has no identical accumulated pulsar profile. Finally, using the chi-square value of X-ray pulsar sup-profiles as an evaluation standard, we develop the two-level velocity estimation based on dictionary folding (DF) to measure the two-dimensional Doppler velocity. Experimental results demonstrate that compared with the traditional one-dimensional pulsar velocimetry approach, the two-dimensional Doppler velocimetry approach using a single X-ray pulsar provides more velocity information and is more robust to the initial velocity error. The accuracies of velocities in both two singular directions reach 0.3 m/s. In addition, compared with the traditional epoch folding, the elapsed time of the DF reduce by more than 70% and gets 4 min. • We develop a new idea that provides two-dimensional Doppler velocity for spacecraft. • We prove the propagation property of velocity error in the orbit around a planet. • Two directions for Doppler velocity are calculated by singular value decomposition. • We build the piecewise complete dictionary to remove numerous duplicate computations. • We propose dictionary folding to substitute for epoch folding and improve real-time. [ABSTRACT FROM AUTHOR]

The solar system’s distant reaches exhibit a wealth of anomalous dynamical structure, hinting at the presence of a yet-undetected, massive trans-Neptunian body—Planet Nine (P9). Previous analyses have shown how orbital evolution induced by this object can explain the origins of a broad assortment of exotic orbits, ranging from those characterized by high perihelia to those with extreme inclinations. In this work, we shift the focus toward a more conventional class of TNOs and consider the observed census of long-period, nearly planar, Neptune-crossing objects as a hitherto-unexplored probe of the P9 hypothesis. To this end, we carry out comprehensive N -body simulations that self-consistently model gravitational perturbations from all giant planets, the Galactic tide, as well as passing stars, stemming from initial conditions that account for the primordial giant planet migration and Sun's early evolution within a star cluster. Accounting for observational biases, our results reveal that the orbital architecture of this group of objects aligns closely with the predictions of the P9-inclusive model. In stark contrast, the P9-free scenario is statistically rejected at a ∼5 σ confidence level. Accordingly, this work introduces a new line of evidence supporting the existence of P9 and further delineates a series of observational predictions poised for near-term resolution.

A fundamental question in the study of planetary system demographics is: how common is the solar system architecture? The primary importance of this question lies in the potential of planetary systems to create habitable environments, and dissecting the various components of solar system evolution that contributed to a sustainable temperate surface for Earth. One important factor in that respect is volatile delivery to the inner system and the dependence on giant planets beyond the snow line as scattering agents, particularly as such cold giant planets are relatively rare. Here, we provide an investigation of the eccentricity distribution for giant planet populations both interior and exterior to their system snow lines. We show that the median eccentricity for cold giants is 0.23, compared with a far more circular orbital regime for inner planets. We further present the results of a dynamical simulation that explores the particle scattering potential for a Jupiter analog in comparison with a Jupiter whose eccentricity matches that of the median cold giant eccentricity. These simulations demonstrate that the capacity for such an eccentric cold giant system to scatter volatiles interior to the snow line is significantly increased compared with the Jupiter analog case, resulting in a far greater volume of Earth-crossing volatiles. Thus, many of the known systems with cold giant planets may harbor water worlds interior to the snow line.

We show how to use geometric arguments to prove that the terminal solution to a rough differential equation driven by a geometric rough path can be obtained by driving the same equation by a piecewise linear path. For this purpose, we combine some results of the seminal work of Sussmann on orbits of vector fields [1] with the rough calculus on manifolds developed by Cass, Litterer and Lyons in [2]. [ABSTRACT FROM AUTHOR]

Intensity scintillations of radio pulsars are known to originate from interference between waves scattered by the electron density irregularities of interstellar plasma, often leading to parabolic arcs in the two-dimensional power spectrum of the recorded dynamic spectrum. The degree of arc curvature depends on the distance to the scattering plasma and its transverse velocity with respect to the line of sight. We report the observation of annual and orbital variations in the curvature of scintillation arcs over a period of 16 yr for the bright millisecond pulsar, PSR J0437-4715. These variations are the signature of the relative transverse motions of Earth, the pulsar, and the scattering medium, which we model to obtain precise measurements of parameters of the pulsar's binary orbit and the scattering medium itself. We observe two clear scintillation arcs in most of our >5000 observations, and we show that they originate from scattering by thin screens located at distances D 1 = 89.8 ± 0.4 pc and D 2 = 124 ± 3 pc from Earth. The best-fit scattering model we derive for the brightest arc yields the pulsar's orbital inclination angle, i = 137.°1 ± 0.°3, and longitude of ascending node, Ω = 206.°3 ± 0.°4. Using scintillation arcs for precise astrometry and orbital dynamics can be superior to modeling variations in the diffractive scintillation timescale, because the arc curvature is independent of variations in the level of turbulence of interstellar plasma. This technique can be used in combination with pulsar timing to determine the full three-dimensional orbital geometries of binary pulsars and provides parameters essential for testing theories of gravity and constraining neutron star masses.

The spin–orbit misalignment of stellar-mass black hole (sBH) binaries provides important constraints on the formation channels of merging sBHs. Here, we study the role of secular spin–orbit resonance in the evolution of an sBH binary component around a supermassive BH (SMBH) in an AGN disk. We consider the sBH's spin precession due to the J 2 moment introduced by a circum-sBH disk within the warping/breaking radius of the disk. We find that the sBH's spin–orbit misalignment (obliquity) can be excited via spin–orbit resonance between the sBH binary's orbital nodal precession and the sBH spin precession driven by a massive circum-sBH disk. Using an α -disk model with Bondi–Hoyle–Lyttleton accretion, the resonances typically occur for sBH binaries with semimajor axis of 1 au and at a distance of ∼1000 au around a 107 M ⊙ SMBH. The spin–orbit resonances can lead to high sBH obliquities and a broad distribution of sBH binary spin–spin misalignments. However, we note that the Bondi–Hoyle–Lyttleton accretion is much higher than that of Eddington accretion, which typically results in spin precession being too low to trigger spin–orbit resonances. Thus, secular spin–orbit resonances can be quite rare for sBHs in AGN disks. [ABSTRACT FROM AUTHOR]

Gravitational waves, despite predicted within the Theory of General Relativity about a century ago, were observed experimentally only in the last few years, thanks to the recent advances of the LIGO and Virgo detectors. In this work, we introduce a simple theoretical model to study the gravitational irradiation of binary systems and derive the characteristics of the emitted gravitational waves (e.g., in terms of frequency). The simplicity of the model relies first on the consideration of the two-body problem and circular orbits. Second, we follow an energetic approach and make use of only one result of the Theory of General Relativity, to make the procedure clear and suitable for undergraduate education. The numerical solution is finally compared with the experimental data available for a few black hole mergers. Key words: binary systems, gravitational irradiation, gravitational waves, Theory of General Relativity, black hole mergers Les ondes gravitationnelles, bien que predites il y a un siecle dans la Theorie de la Relativite Generale, n'ont ete observees que ces dernieres annees, grace aux avancees recentes des detecteurs LIGO et Virgo. Ici, nous introduisons un modele theorique simple pour etudier la radiation gravitationnelle emise par un systeme binaire et derivons les caracteristiques des ondes gravitationnelles resultantes, par exemple en termes de frequences. La simplicite du modele repose fortement sur la consideration d'un probleme a deux corps en orbites circulaires. Ensuite, nous suivons une approche basee sur l'energie et ne faisons usage que d'un seul resultat de la Theorie de la Relativite Generale, dans le but de rendre la procedure claire et adaptee a l'enseignement au premier cycle. La solution numerique est finalement comparee avec les donnees experimentales pour quelques fusions de trous noirs. [Traduit par la Redaction] Mots-cles : systemes binaires, radiation gravitationnelle, ondes gravitationnelles, Theorie de la Relativite Generale, fusion de trous noirs, 1. Introduction Gravitational waves were first theorised within the frame of Einstein's Theory of General Relativity [1, 2] and they appear following a time variation of the quadrupole moment of [...]

Many shortcomings of chaos-based applications stem from the weak dynamic properties of the chaotic maps they use. To alleviate this problem, inspired by the buffeting effect in aeroelasticity, this article proposes the buffeting chaotification model (BCM). Using the especially designed buffeting and modulo operators, the BCM can generate numerous new chaotic maps with strong dynamic properties from existing one-dimensional chaotic maps. The effectiveness of the BCM is mathematically proven according to the Lyapunov exponent, and further numerical experiments confirm the superiority of the chaotic maps generated by the BCM in terms of the dynamic properties. The field-programmable gate array implementation also shows that the BCM owns simplicity in hardware devices. To investigate the practical application, a scheme for constructing the pseudorandom number generator is designed. Performance analyses indicate that our generators have a strong ability to produce high-quality pseudorandom sequences rapidly. [ABSTRACT FROM AUTHOR]

We report JWST Mid-Infrared Instrument (MIRI) Medium Resolution Spectrograph (MRS) observations of the β Pic moving-group member, η Tel A, along with its brown dwarf binary companion, η Tel B. Following point-spread-function subtraction, we recover the spatially resolved flux from the debris disk around η Tel A, along with the position of the companion exterior to the disk. We present a new 5–26 μ m epoch of spectroscopy for the disk, in which we discover a 20 μ m silicate feature, and the first ever 11–21 μ m spectrum of η Tel B, which indicates a bare photosphere. We derive a new epoch of relative astrometry for the companion, extending the baseline of measurements to 25 yr, and find that it is currently located near the apocenter of an eccentric long-period orbit. The companion’s orbit is close enough to the disk that it should significantly perturb the planetesimals within it, resulting in a detectable mid-IR pericenter glow and near alignment with the companion. Contrary to expectations, however, we find that the disk appears to be axisymmetric and potentially misaligned with the companion in the MIRI MRS data. We posit that this may be due to the presence of an additional, as-yet-undetected ∼0.7–30 M _J planet orbiting interior to the disk, with a semimajor axis of ∼3–19 au.

Barred galaxies exhibit boxy/peanut or X-shapes (BP/X) protruding from their disks in edge-on views. Two types of BP/X morphologies exist depending on whether the X-wings meet at the center (CX) or are off-centered (OX). Orbital studies indicate that various orbital types can generate X-shaped structures. Here we provide a classification approach that identifies the specific orbit families responsible for generating OX- and CX-shaped structures. Applying this approach to three different N -body bar models, we show that both OX and CX structures are associated with the x 1 orbit family, but OX-supporting orbits possess higher angular momentum (closer to x 1 orbits) than orbits in CX structures. Consequently, as the bar slows down, the contribution of higher angular momentum OX-supporting orbits decreases and that of lower angular momentum orbits increases, resulting in an evolution of the morphology from OX to CX. If the bar does not slow down, the shape of the BP/X structure and the fractions of OX/CX-supporting orbits remain substantially unchanged. Bars that do not undergo buckling but that do slow down initially show the OX structure and are dominated by high angular momentum orbits, transitioning to a CX morphology. Bars that buckle exhibit a combination of both OX- and CX-supporting orbits immediately after the buckling but become more CX dominated as their pattern speed decreases. This study demonstrates that the evolution of BP/X morphology and orbit populations strongly depends on the evolution of the bar angular momentum.

Tomographic reconstructions of a 3D fast-ion constants-of-motion phase-space distribution function are computed by inverting synthetic signals based on projected velocities of the fast ions along the diagnostic lines of sight. A spectrum of projected velocities is a key element of the spectrum formation in fast-ion D-alpha spectroscopy, collective Thomson scattering, and gamma-ray and neutron emission spectroscopy, and it can hence serve as a proxy for any of these. The fast-ion distribution functions are parameterised by three constants of motion, the kinetic energy, the magnetic moment and the toroidal canonical angular momentum. The reconstructions are computed using both zeroth-order and first-order Tikhonov regularisation expressed in terms of Bayesian inference to allow uncertainty quantification. In addition to this, a discontinuity appears to be present in the solution across the trapped-passing boundary surface in the three-dimensional phase space due to a singularity in the Jacobian of the transformation from position and velocity space to phase space. A method to allow for this apparent discontinuity while simultaneously penalising large gradients in the solution is demonstrated. Finally, we use our new methods to optimise the diagnostic performance of a set of six fans of sightlines by finding where the detectors contribute most complementary diagnostic information for the future COMPASS-Upgrade tokamak.

Using the equations of motion from Hill’s problem, with added accelerations for different forms of dynamical friction, we provide the (to-date) broadest scale-free study of friction-driven binary formation in gaseous disks and stellar clusters. We focus mainly on binary formation between stellar-mass black holes in active galactic nuclei (AGNs), considering both gas dynamical friction (GDF) from AGN disks and stellar dynamical friction (SDF) from the nuclear star cluster. We first find simple, dimensionless friction coefficients that approximate the effects of standard models for GDF and SDF. We perform extensive simulations of Hill’s problem under such friction, and we present a picture of binary formation through encounters between single stars on nearby orbits, as a function of friction parameter, eccentricity, and inclination. Notably, we find that the local binary formation rate is a linear function of the friction coefficient so long as the friction is weak. Due to the dimensionless nature of our model problem, our findings are generalizable to binary formation at all scales (e.g., intermediate-mass black holes in a star cluster, planetesimals in a gaseous disk).

The current International Astronomical Union (IAU) definition of “planet” is problematic because it is vague and excludes exoplanets. Here, we describe aspects of quantitative planetary taxonomy and examine the results of unsupervised clustering of solar system bodies to guide the development of possible classification frameworks. Two unsurprising conclusions emerged from the clustering analysis: (1) satellites are distinct from planets and (2) dynamical dominance is a natural organizing principle for planetary taxonomy. To generalize an existing dynamical dominance criterion, we adopt a universal clearing timescale applicable to all central bodies (brown dwarfs, stars, and stellar remnants). Then, we propose two quantitative, unified frameworks to define both planets and exoplanets. The first framework is aligned with both the IAU definition of planet in the solar system and the IAU working definition of an exoplanet. The second framework is a simpler mass-based framework that avoids some of the difficulties ingrained in current IAU recommendations.

The discovery of planetary systems beyond the solar system has revealed a diversity of architectures, most of which differ significantly from our system. The initial detection of an exoplanet is often followed by subsequent discoveries within the same system as observations continue, measurement precision is improved, or additional techniques are employed. The HD 104067 system is known to consist of a bright K-dwarf host star and a giant planet in a ∼55 days period eccentric orbit. Here we report the discovery of an additional planet within the HD 104067 system, detected through the combined analysis of radial velocity (RV) data from the High Resolution Echelle Spectrometer and High Accuracy Radial velocity Planet Searcher instruments. The new planet has a mass similar to Uranus and is in an eccentric ∼14 days orbit. Our injection-recovery analysis of the RV data exclude Saturn-mass and Jupiter-mass planets out to 3 au and 8 au, respectively. We further present Transiting Exoplanet Survey Satellite observations that reveal a terrestrial planet candidate ( R _p = 1.30 ± 0.12 R _⊕ ) in a ∼2.2 days period orbit. Our dynamical analysis of the three planet model shows that the two outer planets produce significant eccentricity excitation of the inner planet, resulting in tidally induced surface temperatures as high as ∼2600 K for an emissivity of unity. The terrestrial planet candidate may therefore be caught in a tidal storm, potentially resulting in its surface radiating at optical wavelengths.

The planets’ gravitational interaction causes rhythmic changes in Earth’s orbital parameters (also called Milanković cycles), which have powerful applications in geology and astrochronology. For instance, the primary astronomical eccentricity cycle due to the secular frequency term ( g _2 − g _5 ) (∼405 kyr in the recent past) utilized in deep-time analyses is dominated by the orbits of Venus and Jupiter, i.e., long eccentricity cycle. The widely accepted and long-held view is that ( g _2 − g _5 ) was practically stable in the past and may hence be used as a “metronome” to reconstruct accurate geologic ages and chronologies. However, using state-of-the-art integrations of the solar system, we show here that ( g _2 − g _5 ) can become unstable over long timescales, without major changes in, or destabilization of, planetary orbits. The ( g _2 − g _5 ) disruption is due to the secular resonance σ _12 = ( g _1 − g _2 ) + ( s _1 − s _2 ), a major contributor to solar system chaos. We demonstrate that entering/exiting the σ _12 resonance is a common phenomenon on long timescales, occurring in ∼40% of our solutions. During σ _12 -resonance episodes, ( g _2 − g _5 ) is very weak or absent and Earth’s orbital eccentricity and climate-forcing spectrum are unrecognizable compared to the recent past. Our results have fundamental implications for geology and astrochronology, as well as climate forcing, because the paradigm that the long eccentricity cycle is stable, dominates Earth's orbital eccentricity spectrum, and has a period of ∼405 kyr requires revision.

We conducted a photometric and kinematic analysis of the young open cluster NGC 2345 using CCD UBV data from 2 m Himalayan Chandra Telescope, Gaia Data Release 3, Two Micron All-Sky Survey, and the Photometric All-Sky Survey data sets. We found 1732 most probable cluster members with membership probability higher than 70%. The fundamental and structural parameters of the cluster are determined based on the cluster members. The mean proper motion of the cluster is estimated to be ${\mu }_{\alpha }\cos \delta $ = −1.34 ± 0.20 and μ _δ = 1.35 ± 0.21 mas yr ^−1 . Based on the radial density profile, the estimated radius is ∼12.′8 (10.37 pc). Using color–color and color–magnitude diagrams, we estimate the reddening, age, and distance to be 0.63 ± 0.04 mag, 63 ± 8 Myr, and 2.78 ± 0.78 kpc, respectively. The mass function slope for main-sequence stars is determined as 1.2 ± 0.1. The mass function slope in the core, halo, and overall region indicates a possible hint of mass segregation. The cluster’s dynamical relaxation time is 177.6 Myr, meaning ongoing mass segregation, with complete equilibrium expected in 100–110 Myr. Apex coordinates are determined as −40.°89 ± 0.12, − 44.°99 ± 0.15. The cluster’s orbit in the Galaxy suggests early dissociation into field stars due to its close proximity to the Galactic disk.

Many studies have recently documented the orbital response of eccentric binaries accreting from thin circumbinary disks, characterizing the change in the binary semimajor axis and eccentricity. We extend these calculations to include the precession of the binary’s longitude of periapse induced by the circumbinary disk, and we characterize this precession continuously with binary eccentricity e _b for equal mass components. This disk-induced apsidal precession is prograde with a weak dependence on the binary eccentricity when e _b ≲ 0.4 and decreases approximately linearly for e _b ≳ 0.4; yet at all e _b binary precession is faster than the rates of change to the semimajor axis and eccentricity by an order of magnitude. We estimate that such precession effects are likely most important for subparsec separated binaries with masses ≲10 ^7 M _⊙ , like LISA precursors. We find that accreting, equal-mass LISA binaries with M < 10 ^6 M _⊙ (and the most massive M ∼ 10 ^7 M _⊙ binaries out to z ∼ 3) may acquire a detectable phase offset due to the disk-induced precession. Moreover, disk-induced precession can compete with general relativistic precession in a vacuum, making it important for observer-dependent electromagnetic searches for accreting massive binaries—like Doppler boost and binary self-lensing models—after potentially only a few orbital periods.

Recent observational surveys of the outer solar system provide evidence that Neptune's distant n :1 mean motion resonances may harbor relatively large reservoirs of trans-Neptunian objects (TNOs). In particular, the discovery of two securely classified 9:1 resonators, 2015 KE _172 and 2007 TC _434 , by the Outer Solar System Origins Survey is consistent with a population of order 10 ^4 such objects in the 9:1 resonance with absolute magnitude H _r < 8.66. This work investigates whether the long-term stability of such populations in Neptune’s n :1 resonances can be used to constrain the existence of distant 5–10 M _⊕ planets orbiting at hundreds of au. The existence of such a planet has been proposed to explain a reported clustering in the orbits of highly eccentric “extreme” trans-Neptunian objects (or eTNOs), although this hypothesis remains controversial. We engage in a focused computational case study of the 9:1 resonance, generating synthetic populations and integrating them for 1 Gyr in the presence of 81 different test planets with various masses, perihelion distances, eccentricities, and inclinations. While none of the tested planets are incompatible with the existence of 9:1 resonators, our integrations shed light on the character of the interaction between such planets and nearby n :1 resonances, and we use this knowledge to construct a simple heuristic method for determining whether or not a given planet could destabilize a given resonant population. We apply this method to the currently estimated properties of Planet 9, and find that a large primordial population in the 15:1 resonance (or beyond), if discovered in the future, could potentially constrain the existence of this planet.

About a dozen exoplanetary systems have been discovered with three or more planets participating in a sequence of mean-motion resonances. The unique and complex architectures of these so-called “resonant chains” motivate efforts to characterize their planets holistically. In this work, we perform a comprehensive exploration of the spin-axis dynamics of planets in resonant chains. Planetary spin states are closely linked with atmospheric dynamics and habitability and are thus especially relevant to resonant chains like TRAPPIST-1, which hosts several temperate planets. Considering a set of observed resonant chains, we calculate the equilibrium states of the planetary axial tilts (“obliquities”). We show that high-obliquity states exist for ∼60% of planets in our sample, and many of these states can be stable in the presence of tidal dissipation. Using case studies of two observed systems (Kepler-223 and TOI-1136), we demonstrate how these high-obliquity states could have been attained during the initial epoch of disk-driven orbital migration that established the resonant orbital architectures. We show that the TRAPPIST-1 planets most likely have zero obliquities, with the possible exception of planet d. Overall, our results highlight that both the orbital and spin states of resonant chains are valuable relics of the early stages of planet formation and evolution.

Young, low-mass brown dwarfs orbiting early-type stars, with low mass ratios ( q ≲ 0.01), appear to be intrinsically rare and present a formation dilemma: could a handful of these objects be the highest-mass outcomes of “planetary” formation channels (bottom up within a protoplanetary disk), or are they more representative of the lowest-mass “failed binaries” (formed via disk fragmentation or core fragmentation)? Additionally, their orbits can yield model-independent dynamical masses, and when paired with wide wavelength coverage and accurate system age estimates, can constrain evolutionary models in a regime where the models have a wide dispersion depending on the initial conditions. We present new interferometric observations of the 16 Myr substellar companion HD 136164 Ab (HIP 75056 Ab) made with the Very Large Telescope Interferometer (VLTI)/GRAVITY and an updated orbit fit including proper motion measurements from the Hipparcos–Gaia Catalog of Accelerations. We estimate a dynamical mass of 35 ± 10 M _J ( q ∼ 0.02), making HD 136164 Ab the youngest substellar companion with a dynamical mass estimate. The new mass and newly constrained orbital eccentricity ( e = 0.44 ± 0.03) and separation (22.5 ± 1 au) could indicate that the companion formed via the low-mass tail of the initial mass function. Our atmospheric fit to a SPHINX M-dwarf model grid suggests a subsolar C/O ratio of 0.45 and 3 × solar metallicity, which could indicate formation in a circumstellar disk via disk fragmentation. Either way, the revised mass estimate likely excludes bottom-up formation via core accretion in a circumstellar disk. HD 136164 Ab joins a select group of young substellar objects with dynamical mass estimates; epoch astrometry from future Gaia data releases will constrain the dynamical mass of this crucial object further.

This article is devoted to the discovery of comets at the Vilnius Observatory together with the orbital analysis of dynamically interesting comets, namely 322P. We studied the orbital evolution of comet 322P with and without non-gravitational effects. It turned out that many of the comet’s orbital clones go into and out of retrograde orbits, sometimes repeatedly. The reason for such dramatic changes in the inclination of the orbit is the origin of comet 322P close to mean motion resonance 3:1 with Jupiter, ejecting them from there and, consequently, bringing the clones closer to the terrestrial group of planets. In this way, the clones of comet 322P enter retrograde orbits and reside there several ky to several My.