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David Fabricius, a Reformed pastor in Ostfriesland, was highly regarded by Kepler as an exceptional observer, second only to Tycho Brahe. From 1596 to 1609, Fabricius engaged in extensive correspondence, exchanging numerous letters with Brahe and subsequently with Kepler. These communications also provided values for direct observations on meridian altitudes of planets and stars, as well as elongations between a planet and a star or between two stars. We provide a detailed summary of Fabricius's observations and compare them with the prediction of twenty-first-century models. The analysis indicates that under specific conditions, his observations exhibit sub-arcminute deviations in relation to those calculated from modern theories. Our findings preliminarily indicate that Fabricius' astronomical observational abilities were comparable to, an occasionally superior to, those of Brahe himself. We provide machine-readable tables of his observations. [ABSTRACT FROM AUTHOR]

Vertical gas and dust flows in protoplanetary discs waft material above the mid-plane region in the presence of a protoplanet. This motion may alter the delivery of dust to the planet and its circumplanetary disc, as well as through a planetary-induced gap region and hence the inner disc chemistry. Here, we investigate the impact of a massive embedded planet on this material transport through the gap region. We use 3D global hydrodynamic simulations run using FARGO3D with gas and dust species to investigate the dust filtration and the origin of material that can make it through the gap. We find small dust particles can pass through the gap as expected from results in 2D and that this can be considered in two parts – filtering due to the planetary-induced pressure maximum and filtering due to accretion on to the planet. When gas accretion on to the planet is included, we find that the larger dust grains that cross the gap (i.e. those with |$\mathrm{St} \sim 10^{-4}$|⁠) originate from regions near the mid-plane. We also find that dust and gas that enter the planet-carved gap region pass through the Hill sphere of the planet, where the temperature is likely to be strongly enhanced compared with the mid-plane regions from which this material originated. Considering the application of our simulations to a Jupiter-mass planet at |$\sim 100\ \mathrm{au}$|⁠ , this suggests that CO ice is very likely to desorb from grains in the close proximity of the planet, without requiring any fine-tuning of the planet's location with respect to the CO snowline. [ABSTRACT FROM AUTHOR]

The Graha-lāghava ("Easy [computation] of the planets"; epoch date 1520), is an astronomical handbook, authored by Gaṇeśa Daivajña (b. 1507 CE) of Nandigrāma. This work became one of the most popular astronomical texts of the second millennium in India and gave rise to a new astronomical school of parameters, eponymously known as the "Gaṇeśa-pakṣa." We analyze the first of the 16 chapters that make up this work, which covers planetary mean positions and velocities, providing a translation and technical commentary of the text. In our exposition, we also invoke two substantial commentaries on this work that were composed in the 17th-century by brothers Mallāri and Viśvanātha, which help clarify and contextualize Gaṇeśa's contributions. An Appendix to the online edition of the Journal gives the Sanskrit text of the quoted passages. [ABSTRACT FROM AUTHOR]

The architectural construction process on planets is an architectural issue that develops day by day due to extreme environmental conditions and uncertainties. Architectural design needs structural systems to survive. Structural systems on planets encounter load factors that are different from the load factors on Earth. Choosing the optimum structural system is important for the structures planned to be built on planets to survive under the effects and loads of the environment and to adapt to human physiology. Some of the different types of structural systems used on Earth are featured in the literature for building a structure on planets. An evaluation system has been created to determine the correct system type for the first settlements on planets among the prominent structural system types and to narrow down the selection area of these system features. In line with this evaluation system in this study, a structural system model that stands up to harsh environmental conditions and protects human health is proposed for the first settlements on the planets. It is aimed that the evaluation system will be developed in the light of research emerging from developing technologies and can be used in future studies. [ABSTRACT FROM AUTHOR]

The Nebra Disk is one of the earliest astronomical manifestations of humanity in Central Europe. We interpret the striking sevenfold stellar group shown on the disk as a celestial conjunction of the five naked‐eye visible planets together with Pollux and Castor in the constellation Gemini (happening in 2210BC) and the dominating large, filled circle as a bright supernova, probably corresponding to the remnant 3C58 in Cassiopeia. We believe that a close coincidence of these two extremely rare celestial events, that does never happen more than once in a human lifetime, could have impressed people of that epoch in a way that it was conveyed orally over several generations, until some Bronze Age artist created the Nebra Disk. If this interpretation is correct, it could offer a rather exact dating of a supernova explosion observed about 4200 years ago, more precise than any other dating methods for past supernova events, possibly leading to significant new insights into the underlying physics of supernovae. [ABSTRACT FROM AUTHOR]

We present the validation of two TESS super-Earth candidates transiting the mid-M dwarfs TOI-6002 and TOI-5713 every 10.90 and 10.44 days, respectively. The first star (TOI-6002) is located 32.038 ± 0.019 pc away, with a radius of 0.2409−0.0065+0.0066 R⊙, a mass of 0.2105−0.0048+0.0049 M⊙, and an effective temperature of 3229−57+77 K. The second star (TOI-5713) is located 40.946 ± 0.032 pc away, with a radius of 0.2985−0.0072+0.0073 R⊙, a mass of 0.2653 ± 0.0061 M⊙, and an effective temperature of 3225−40+41 K. We validated the planets using TESS data, ground-based multi-wavelength photometry from many ground-based facilities, as well as high-resolution AO observations from Keck/NIRC2. TOI-6002 b has a radius of 1.65−0.19+0.22 R⊕ and receives 1.77−0.110.16S⊕. TOI-5713 b has a radius of 1.77−0.11+0.13 R⊕ and receives 2.42 ± 0.11S⊕. Both planets are located near the radius valley and near the inner edge of the habitable zone of their host stars, which makes them intriguing targets for future studies to understand the formation and evolution of small planets around M-dwarf stars. [ABSTRACT FROM AUTHOR]

The planetary system K2-24 is composed of two transiting low-density Neptunians locked in an almost perfect 2:1 resonance and showing large transit time variations (TTVs), and it is an excellent laboratory to search for signatures of planetary migration. Previous studies performed with K2, Spitzer, and RV data tentatively claimed a significant non-zero eccentricity for one or both planets, possibly high enough to challenge the scenario of pure disk migration through resonant capture. With 13 new CHEOPS light curves (seven of planet b, six of planet c), we carried out a global photometric and dynamical re-analysis by including all the available literature data as well. We obtained the most accurate set of planetary parameters to date for the K2-24 system, including radii and masses at 1% and 5% precision (now essentially limited by the uncertainty on stellar parameters) and non-zero eccentricities eb = 0.0498−0.0018+0.0011, ec = 0.0282−0.0007+0.0003 detected at very high significance for both planets. Such relatively large values imply the need for an additional physical mechanism of eccentricity excitation during or after the migration stage. Also, while the accuracy of the previous TTV model had drifted by up to 0.5 days at the current time, we constrained the orbital solution firmly enough to predict the forthcoming transits for the next ~15 years, thus enabling efficient follow-up with top-level facilities such as JWST or ESPRESSO. [ABSTRACT FROM AUTHOR]

WASP-107 b seems to be a poster child of the long-suspected high-eccentricity migration scenario. It is on a 5.7 day, polar orbit. The planet is Jupiter-like in radius but Neptune-like in mass with exceptionally low density. WASP-107 c is on a 1100 day, e = 0.28 orbit with at least Saturn mass. Planet b may still have a residual eccentricity of 0.06 ± 0.04: the ongoing tidal dissipation leads to the observed internally heated atmosphere and hydrodynamic atmospheric erosion. We present a population synthesis study coupling octupole Lidov–Kozai oscillations with various short-range forces, while simultaneously accounting for the radius inflation and tidal disruption of the planet. We find that a high-eccentricity migration scenario can successfully explain nearly all observed system properties. Our simulations further suggest that the initial location of WASP-107 b at the onset of migration is likely within the snowline (<0.5 au). More distant initial orbits usually lead to tidal disruption or orbit crossing. WASP-107 b most likely lost no more than 20% of its mass during the high-eccentricity migration, i.e., it did not form as a Jupiter-mass object. More vigorous tidally induced mass loss leads to disruption of the planet during migration. We predict that the current-day mutual inclination between the planets b and c is substantial: at least 25°–55°, which may be tested with future Gaia astrometric observations. Knowing the current-day mutual inclination may further constrain the initial orbit of planet b. We suggest that the proposed high-eccentricity migration scenario of WASP-107 may be applicable to HAT-P-11, GJ-3470, HAT-P-18, and GJ-436, which have similar orbital architectures. [ABSTRACT FROM AUTHOR]

The Andrade rheological model is often employed to describe the response of solar system or extra‐solar planets to tidal perturbations, especially when their properties are still poorly constrained. While for uniform planets with steady‐state Maxwell rheology the analytical form of the Love numbers was established long ago, for the transient Andrade rheology no closed‐form solutions have been yet determined, and the planetary response is usually studied either semi‐analitically in the frequency domain or numerically in the time domain. Closed‐form expressions are potentially important since they could provide insight into the dependence of Love numbers upon the model parameters and the time‐scales of the isostatic readjustment of the planet. First, we focus on the Andrade rheological law in 1‐D and we obtain a previously unknown explicit form, in the time domain, for the relaxation modulus in terms of the higher Mittag‐Leffler transcendental function Eα,β(z) that generalizes the exponential function. Second, we consider the general response of an incompressible planetary model — often referred to as the "Kelvin sphere" — studying the Laplace domain, the frequency domain and the time domain Love numbers by analytical methods. Through a numerical approach, we assess the effect of compressibility on the Love numbers in the Laplace and frequency domains. Furthermore, exploiting the results obtained in the 1‐D case, we establish closed‐form — although not elementary — expressions of the time domain Love numbers and we discuss the frequency domain response of the Kelvin sphere with Andrade rheology analytically. Plain Language Summary: Rheology studies how materials flow when subject to stress. To constrain the rheology of planets, it is useful to consider their response to tidal forces or surface loads that allow to probe their interiors. The Andrade rheological model—introduced in 1910—has recently gained popularity in planetary studies. In contrast with the traditional Maxwell model, the Andrade rheology manifests "transient" creep, an initial stage of flow characterized by a time varying rate of strain. Up to now, the response of a planet characterized by an Andrade rheology has been studied numerically, since exact expressions for the Love numbers were only known in the frequency domain. For the first time, we show that in the case of an incompressible homogeneous planet, analytical Love numbers can also be found in the time domain. They are expressed in terms of the Mittag‐Leffler function, which generalizes the exponential. Using analytical methods, we study the Love numbers of a planet with Andrade rheology in the Laplace, frequency and time domains, also giving some numerical results. Key Points: The Andrade rheological law is widely employed in planetary studies since it accounts for transient flow in a simple wayWe obtain a first analytical expression of the time domain Love numbers for a homogeneous incompressible sphere with Andrade rheologyThe solutions found provide new insight into the planetary response and its sensitivity upon model parameters [ABSTRACT FROM AUTHOR]

This paper deals with the methods of construction of trigonometrical tables and interpolation techniques used by ancient Indian mathematicians to calculate intermediate functional values by taking different values of Sinus Totus. The primary purpose for the development of these techniques is to know the correct positions of stars, planets, and other celestial bodies. Some instances have been given for interpolating sine, and charts comparing the values obtained through these techniques to contemporary values have been presented. [ABSTRACT FROM AUTHOR]

The sixth century is the peak of the use of astronomical terms in Persian poetry and prose. One of the most prominent and prominent works in the use of terms and information of astronomy in Persian literature is the Maghamat of Qazi Hamiduddin Balkhi (559 AD), which he authored in 551. The purpose of the present research is to investigate the use of astronomy in Hamidi Maghamat in a descriptive-analytical way and to answer the question of how and for what purpose Hamiduddin Balkhi used astronomy and its tools in Maghamat. Therefore, by extracting samples from this tract, the authors have analyzed it in terms of the mentioned topic. The results of the research show that Hamiduddin Balkhi has used the science of astronomy skillfully and with full knowledge. Allocating an Maghame (20th) in Maghamat to astronomy shows the importance of the subject. From the point of view of the authors, the most important reasons for the use of astronomy in the authorities are to show the author's abilities and to express his grace and knowledge in the use of astronomy, the imaginative literary and artistic effects of the tract, to introduce the tract to the audience and also to indicate his religious beliefs, so that in this way, his tract be honored and after him, its immortality will be preserved. [ABSTRACT FROM AUTHOR]

This essay examines the conflation between world and planet in H. G. Wells's turn-of-the-century science fiction. Writing when "world=planet" was not a given, Wells actively participated in the formation of the world-planet vocabulary across a range of genres and throughout the first half of the twentieth century. In particular, I look into the planetary experiments of his early fiction, where the materially limited planet continually thwarts the writer's attempts to equate that planet to the world he wished to develop as the ultimate political unit. Emerging through such attempts is a divergence between world and planet that enables us to think about the individual, the world, and the planet all on a commensurate scale, in a manner that is strikingly—and perhaps also troublingly—similar to what recent environmental discourse asks of us today. [ABSTRACT FROM AUTHOR]

The search for extraterrestrial intelligence is a fascinating and important endeavor, but it raises significant ethical and safety concerns. In the search for extraterrestrial intelligence, scientists use knowledge of physics to identify potential communication methods and signals that may be used by extraterrestrial civilizations. One of the most notable scientists to highlight these concerns was the late physicist Stephen Hawking, who cautioned that actively attempting to communicate with extraterrestrial civilizations could harm humanity. While it is true that we cannot predict the intentions of any potential extraterrestrial civilizations, some scientists argue that the potential advantages of seeking contact outweigh the potential risks. Deciding to initiate contact with extraterrestrial civilizations is a complex issue that requires balancing scientific curiosity with concerns for our own safety. The “Intelligence Trap” is a concept in psychology that suggests that highly intelligent people are more susceptible to cognitive biases and flawed thinking than less intelligent people. It can be argued that Hawking’s warnings may be an example of the so-called intelligence trap, as some evidence from the field of physics suggests. Nonetheless, Hawking emphasized that it is crucial for scientists and policymakers to carefully weigh the potential risks and benefits of such efforts and proceed with caution.

Context. Since 2018, the ESPRESSO spectrograph at the VLT has been hunting for planets in the southern skies via the radial velocity (RV) method. One of its goals is to follow up on candidate planets from transit surveys such as the TESS mission, with a particular focus on small planets for which ESPRESSO's RV precision is vital. Aims. We aim to confirm and characterise, in detail, three super-Earth candidate transiting planets from TESS using precise RVs from ESPRESSO. Methods. We analysed photometry from TESS and ground-based facilities, high-resolution imaging, and RVs from ESPRESSO, HARPS, and HIRES, to confirm and characterise three new planets: TOI-260 b, transiting a late K dwarf, and TOI-286 b and c, orbiting an early K dwarf. We also updated the parameters for the known super-Earth TOI-134 b (L 168-9 b), which is hosted by an M dwarf. Results. TOI-260 b has a 13.475853−0.000011+0.000013 d period, 4.23 ± 1.60 M⊕ mass, and 1.71 ± 0.08 R⊕ radius. For TOI-286 b we find a 4.5117244−0.0000027+0.0000031 d period, 4.53 ± 0.78 M⊕ mass, and 1.42 ± 0.10 R⊕ radius; for TOI-286 c, we find a 39.361826−0.000081+0.000070 d period, 3.72 ± 2.22 M⊕ mass, and 1.88 ± 0.12 R⊕ radius. For TOI-134 b we obtain a 1.40152604−0.00000082+0.00000074 d period, 4.07 ± 0.45 M⊕ mass, and 1.63 ± 0.14 R⊕ radius. Circular models are preferred for all the planets, although for TOI-260 b the eccentricity is not well constrained. We computed bulk densities and placed the planets in the context of composition models. Conclusions. TOI-260 b lies within the radius valley, and is most likely a rocky planet. However, the uncertainty on the eccentricity and thus on the mass renders its composition hard to determine. TOI-286 b and c span the radius valley, with TOI-286 b lying below it and having a likely rocky composition, while TOI-286 c is within the valley, close to the upper border, and probably has a significant water fraction. With our updated parameters for TOI-134 b, we obtain a lower density than previous findings, giving a rocky or Earth-like composition. [ABSTRACT FROM AUTHOR]

We present the characterization of the two transiting planets around HD 152843 (TOI 2319, TIC 349488688) using an intensive campaign of HARPS-N radial velocities, and two sectors of TESS data. These data reveal a unique and fascinating system: HD 152843 b and c have near equal masses of around 9 |$M_{\hbox{$\oplus $}}$| but differing radii of |$3.05 \pm 0.11$| |$R_{\hbox{$\oplus $}}$| and |$5.94 _{ - 0.16 } ^ { + 0.18 }$| |$R_{\hbox{$\oplus $}}$|⁠ , respectively, and orbital periods of |$11.62071 _{ - 0.000106 } ^ { + 9.6e-05 }$| and |$19.502104 _{ - 8.5e-05 } ^ { + 7.4e-05 }$| d. This indicates that HD 152843 c is in the lowest fifth-percentile in density of the known exoplanet population, and has the longest orbital period among these low-density planets. Further, HD 152843 c's radius places it in the 'Saturn valley', the observed lack of planets larger than Neptune, but smaller than Saturn. The orbital periods of these planets indicate they are near a |$5:3$| mean motion resonance, indicating the possibility of transit timing variations, and hints at the possibility of interaction with a third planet at some point in the evolution of this system. Further, the brightness of the host star and the low density of HD 152843 c make it a key target for atmospheric characterization. [ABSTRACT FROM AUTHOR]

The launches of NASA Kepler and Transiting Exoplanet Survey Satellite (TESS) missions have significantly enhanced the interest in the exoplanet field during the last 15 yr, providing a vast amount of public data that are being exploited by the community thanks to the continuous development of new analysis tools. However, using these tools is not straightforward, and users must dive into different codes, input–output formats, and methodologies, hindering an efficient and robust exploration of the available data. We present the sherlock pipeline, an end-to-end public software that allows the users to easily explore observations from space-based missions such as TESS or Kepler to recover known planets and candidates issued by the official pipelines and search for new planetary candidates that remained unnoticed. The pipeline incorporates all the steps to search for transit-like features, vet potential candidates, provide statistical validation, conduct a Bayesian fitting, and compute observational windows from ground-based observatories. Its performance is tested against a catalogue of known and confirmed planets from the TESS mission, trying to recover the official TESS Objects of Interest (TOIs), explore the existence of companions that have been missed, and release them as new planetary candidates. sherlock demonstrated an excellent performance, recovering 98 per cent of the TOIs and confirmed planets in our test sample and finding new candidates. Specifically, we release four new planetary candidates around the systems WASP-16 (with P |$\sim$|  10.46 d and R |$\sim$|  2.20 |$\mathrm{ R}_{\oplus }$|⁠), HAT-P-27 (with P |$\sim$|  1.20 d and R |$\sim$|  4.33 |$\mathrm{ R}_{\oplus }$|⁠), HAT-P-26 (with P |$\sim$|  6.59 d and R |$\sim$|  1.97 |$\mathrm{ R}_{\oplus }$|⁠), and TOI-2411 (with P |$\sim$|  18.75 d and R |$\sim$|  2.88 |$\mathrm{ R}_{\oplus }$|⁠). [ABSTRACT FROM AUTHOR]

We study the evolution of eccentricity and inclination of massive planets in low-density cavities of protoplanetary discs using three-dimensional (3D) simulations. When the planet's orbit is aligned with the equatorial plane of the disc, the eccentricity increases to high values of 0.7–0.9 due to the resonant interaction with the inner parts of the disc. For planets on inclined orbits, the eccentricity increases due to the Kozai–Lidov mechanism, where the disc acts as an external massive body, which perturbs the planet's orbit. At small inclination angles, |${\lesssim}30^\circ$|⁠ , the resonant interaction with the inner disc strongly contributes to the eccentricity growth, while at larger angles, eccentricity growth is mainly due to the Kozai–Lidov mechanism. We conclude that planets inside low-density cavities tend to acquire high eccentricity if favourable conditions give sufficient time for growth. The final value of the planet's eccentricity after the disc dispersal depends on the planet's mass and the properties of the cavity and protoplanetary disc. [ABSTRACT FROM AUTHOR]

This article presents an approach to solve the problem of end-to-end optimization of the low-thrust interplanetary trajectory. At first, the problem of optimizing low-thrust interplanetary trajectory, which passes through the collinear libration points near the planets of departure and arrival is considered. The obtained solutions from this problem can be used as an initial guess to solve the end-to-end optimization problem, i.e., to calculate interplanetary low-thrust trajectories that satisfy the necessary optimality conditions at the match points of the heliocentric and planetocentric segments of trajectory. The minimum-fuel problem is considered. An indirect method based on the maximum principle, and the continuation method is applied to optimize interplanetary spacecraft trajectories. Numerical examples of trajectories from the Earth orbit to the orbit around the destination planet (Mars and Jupiter) are given. The possibility of a significant reduction in the required characteristic velocity is shown in comparison with the estimates obtained by using the zero-radius sphere of influence model. • End-to-end optimization, low-thrust, minimum-fuel trajectory, interplanetary transfer. • Using libration points as an initial guess to figure out the optimal match points of trajectory segments. • Analysing optimality conditions at the match points of the trajectory segments. • Comparison with conventional approach using zero-radius sphere of influence model. • End-to-end trajectory optimization significantly reduces characteristic velocity. [ABSTRACT FROM AUTHOR]

All circumbinary planets (CBPs) currently detected are located in almost co-planar configurations with respect to the binary orbit, due to the fact that CBPs with higher misalignment are more difficult to detect. However, observations of polar circumbinary gas and debris discs in recent years and long-term orbital stability of inclined planets indicate that it is possible to form misaligned CBPs around eccentricity binaries (even polar CBPs). In this work, we focus on the dynamical structures of CBPs in a wide range of parameters in order to provide a guidance for the space where the binary can host planets for a long enough time. To this end, the dynamical model is approximated as a hierarchical three-body problem, and the secular approximation is formulated up to the hexadecapolar order in semimajor axis ratio. Dynamical maps show that there are complex structures in the parameter space. A web of secular resonances is produced in the entire parameter space and it can well explain those numerical structures arising in dynamical maps. Based on perturbative treatments, an adiabatic invariant is introduced and thus dynamical structures can be explored by analysing phase portraits. It is found that (a) the quadrupole-order resonance (nodal resonance) is responsible for the distribution of V -shape region, and high-order and secondary resonances dominate those structures inside or outside V -shape region, and (b) the secondary 1:1 resonance is the culprit causing symmetry breaking of dynamical structures inside polar region. [ABSTRACT FROM AUTHOR]

We investigate the planetary migration of low-mass planets (⁠|$M_p\in [1,15]\, \mathrm{ M}_{\oplus }$|⁠ , here |$\mathrm{ M}_{\oplus }$| is the Earth mass) in a gaseous disc containing a previously formed gap. We perform high-resolution 3D simulations with the fargo3d code. To create the gap in the surface density of the disc, we use a radial viscosity profile with a bump, which is maintained during the entire simulation time. We find that when the gap is sufficiently deep, the spiral waves excited by the planet trigger the Rossby wave instability, forming cyclonic (underdense) vortices at the edges of the gap. When the planet approaches the gap, it interacts with the vortices, which produce a complex flow structure around the planet. Remarkably, we find a widening of the horseshoe region of the planet produced by the vortex at the outer edge of the gap, which depending on the mass of the planet differs by at least a factor of two with respect to the standard horseshoe width. This inevitably leads to an increase in the co-rotation torque on the planet and produces an efficient trap to halt its inward migration. In some cases, the planet becomes locked in co-rotation with the outer vortex. Under this scenario, our results could explain why low-mass planets do not fall towards the central star within the lifetime of the protoplanetary disc. Lastly, the development of these vortices produces an asymmetric temporal evolution of the gap, which could explain the structures observed in some protoplanetary discs. [ABSTRACT FROM AUTHOR]

Discovering transiting exoplanets with relatively long orbital periods (>10 d) is crucial to facilitate the study of cool exoplanet atmospheres (T eq < 700 K) and to understand exoplanet formation and inward migration further out than typical transiting exoplanets. In order to discover these longer period transiting exoplanets, long-term photometric, and radial velocity campaigns are required. We report the discovery of TOI-2447 b (=NGTS-29 b), a Saturn-mass transiting exoplanet orbiting a bright (T = 10.0) Solar-type star (Teff = 5730 K). TOI-2447 b was identified as a transiting exoplanet candidate from a single transit event of 1.3 per cent depth and 7.29 h duration in TESS Sector 31 and a prior transit event from 2017 in NGTS data. Four further transit events were observed with NGTS photometry which revealed an orbital period of P = 69.34 d. The transit events establish a radius for TOI-2447 b of |$0.865 \pm 0.010\, \rm R_{\rm J}$|⁠ , while radial velocity measurements give a mass of |$0.386 \pm 0.025\, \rm M_{\rm J}$|⁠. The equilibrium temperature of the planet is 414 K, making it much cooler than the majority of TESS planet discoveries. We also detect a transit signal in NGTS data not caused by TOI-2447 b, along with transit timing variations and evidence for a ∼150 d signal in radial velocity measurements. It is likely that the system hosts additional planets, but further photometry and radial velocity campaigns will be needed to determine their parameters with confidence. TOI-2447 b/NGTS-29 b joins a small but growing population of cool giants that will provide crucial insights into giant planet composition and formation mechanisms. [ABSTRACT FROM AUTHOR]

We devise and exploit a data-driven, semi-empirical framework of galaxy formation and evolution, coupling it to recipes for planet formation from stellar and planetary science, to compute the cosmic planet formation rate, and the properties of the planets' preferred host stellar and galactic environments. We also discuss how the rates and formation sites of planets are affected when considering their habitability, and when including possible threatening sources related to star formation and nuclear activity. Overall, we conservatively estimate a cumulative number of some 10 20 Earth-like planets and around 10 18 habitable Earths in our past lightcone. Finally, we find that a few 10 17 are older than our own Earth, an occurrence which places a loose lower limit a few 10 − 18 to the odds for a habitable world to ever host a civilization in the observable Universe. [ABSTRACT FROM AUTHOR]

Low-mass planets migrating inwards in laminar protoplanetary discs (PPDs) experience a dynamical corotation torque (DCT), which is expected to slow down migration to a stall. However, baroclinic effects can reduce or even reverse this effect, leading to rapid inward migration. In the radiatively inefficient inner disc, one such mechanism is the buoyancy response of the disc to an embedded planet. Recent work has suggested that radiative cooling can quench this response, but for parameters that are not necessarily representative of the inner regions of PPDs. We perform global 3D inviscid radiation hydrodynamics simulations of planet–disc interaction to investigate the effect of radiative cooling on the buoyancy-driven torque in a more realistic disc model. We find that the buoyancy response exerts a negative DCT – albeit partially damped due to radiative cooling – resulting in sustained, rapid inward migration. Models that adopt a local cooling prescription significantly overestimate the impact of the buoyancy response, highlighting the importance of a realistic treatment of radiation transport that includes radiative diffusion. Our results suggest that low-mass planets should migrate inwards faster than has been previously expected in radiative discs, with implications for the formation and orbital distribution of super-Earths and sub-Neptunes at intermediate distances from their host stars, unless additional physical processes that can slow down migration are considered. [ABSTRACT FROM AUTHOR]

Over 200 protoplanetary disk systems have been resolved by the Atacama Large Millimeter/submillimeter Array (ALMA), and the vast majority suggest the presence of planets. The dust gaps in transition disks are considered evidence of giant planets sculpting gas and dust under appropriate disk viscosity. However, the unusually high accretion rates in many T Tauri stars hosting transition disks challenge this theory. As the only disk currently observed with high turbulence, the high accretion rate (∼10−8.3 M ⊙ yr−1) observed in DM Tau indicates the presence of strong turbulence within the system. Considering the recent theoretical advancements in magnetized disk winds are challenging the traditional gap-opening theories and viscosity-driven accretion models, our study presents a pioneering simulation incorporating a simplified magnetized disk wind model to explain the observed features in DM Tau. Employing multifluid simulations with an embedded medium mass planet, we successfully replicate the gap formation and asymmetric structures evident in ALMA Band 6 and the recent Karl G. Jansky Very Large Array 7 mm observations. Our results suggest that when magnetized disk wind dominates the accretion mode of the system, it is entirely possible for a planet with a medium mass to exist within the gap inside 20 au of DM Tau. This means that DM Tau may not be as turbulent as imagined. However, viscosity within the disk should also contribute a little turbulence to maintain disk stability. [ABSTRACT FROM AUTHOR]

A systematic, population-level discrepancy exists between the densities of exoplanets whose masses have been measured with transit timing variations (TTVs) versus those measured with radial velocities (RVs). Since the TTV planets are predominantly nearly resonant, it is still unclear whether the discrepancy is attributed to detection biases or to astrophysical differences between the nearly resonant and non resonant planet populations. We defined a controlled, unbiased sample of 36 sub-Neptunes characterised by Kepler, TESS, HARPS, and ESPRESSO. We found that their density depends mostly on the resonant state of the system, with a low probability (of 0.002−0.001+0.010) that the mass of (nearly) resonant planets is drawn from the same underlying population as the bulk of sub-Neptunes. Increasing the sample to 133 sub-Neptunes reveals finer details: the densities of resonant planets are similar and lower than non-resonant planets, and both the mean and spread in density increase for planets that are away from resonance. This trend is also present in RV-characterised planets alone. In addition, TTVs and RVs have consistent density distributions for a given distance to resonance. We also show that systems closer to resonances tend to be more co-planar than their spread-out counterparts. These observational trends are also found in synthetic populations, where planets that survived in their original resonant configuration retain a lower density; whereas less compact systems have undergone post-disc giant collisions that increased the planet's density, while expanding their orbits. Our findings reinforce the claim that resonant systems are archetypes of planetary systems at their birth. [ABSTRACT FROM AUTHOR]

Context. The Kepler high-precision planetary sample has revealed a 'radius valley' separating compact super-Earths from sub-Neptunes with lower densities. Super-Earths are generally assumed to be rocky planets that were probably born in situ, while the composition and formation of sub-Neptunes remains debated. Numerous statistical studies have explored planetary and stellar properties and their correlations to provide observational clues. However, no conclusive result on the origin of the radius valley or the composition of sub-Neptunes has been derived to date. Aims. To provide more constraints, our aim is to investigate the distributions of the orbital spacing of sub-Neptunes and super-Earth planets in Kepler systems and compare their distributions with theoretical predictions of planet pairs of different formation pathways and compositions in synthetic planetary systems. Methods. Based on the Kepler planetary sample, we derived the distributions of period ratios of sub-Neptune and super-Earth planet pairs. Using synthetic planetary systems generated by the Generation III Bern Model, we also obtained theoretical predictions of period ratio distributions of planet pairs of different compositions and origins. Results. We find that Kepler sub-Neptune pairs show a significant preference to be near first-order mean motion resonances by a factor of 1.7−0.3+0.3. This is smaller than the model predictions for 'water-rich' pairs but larger than that of 'water-poor' pairs by confidence levels of ~2σ. Kepler super-Earth pairs show no significant preference for mean motion resonances from a random distribution. The derived normalised fraction of near first-order resonances of actual Kepler super-Earth pairs is consistent with that of synthetic water-poor planet pairs but significantly (≳3σ) smaller than that of synthetic water-rich planet pairs. Conclusions. The orbital migration has been more important for sub-Neptunes than for super-Earths, suggesting a partial ex situ formation of the former and an origin of the radius valley caused in part by distinct formation pathways. However, the model comparisons also show that sub-Neptunes in Kepler multiple systems are not likely (~2σ) to all be water-rich planets born ex situ but a mixture of the two (in situ and ex situ) pathways. Whereas, Kepler super-Earth planets are predominantly composed of water-poor planets that were born inside the ice line, likely through a series of giant impacts without large-scale migration. [ABSTRACT FROM AUTHOR]

The characterization of super-Earth- to Neptune-sized exoplanets relies heavily on our understanding of their formation and evolution. In this study, we link a model of planet formation by pebble accretion to the planets' long-term observational properties by calculating the interior evolution, starting from the dissipation of the protoplanetary disk. We investigate the evolution of the interior structure in 5–20 M⊕ planets, accounting for silicate redistribution caused by convective mixing, rainout (condensation and settling), and mass loss. Specifically, we have followed the fate of the hot silicate vapor that remained in the planet's envelope after planet formation as the planet cools. We find that disk dissipation is followed by a rapid contraction of the envelope from the Hill or Bondi radius to about one-tenth of that size within 10 Myr. Subsequent cooling leads to substantial growth of the planetary core through silicate rainout accompanied by inflated radii, in comparison to the standard models of planets that formed with core-envelope structure. We examined the dependence of rainout on the planet's envelope mass, on the distance from its host star, on its silicate mass, and on the atmospheric opacity. We find that the population of planets that formed with polluted envelopes can be roughly divided into three groups based on the mass of their gas envelopes: bare rocky cores that have shed their envelopes, super-Earth planets with a core-envelope structure, and Neptune-like planets with diluted cores that undergo gradual rainout. For polluted planets that formed with envelope masses below 0.4 M⊕, we anticipate that the inflation of the planet's radius caused by rainout will enhance the mass loss by a factor of 2–8 compared to planets with unpolluted envelopes. Our model bridges the gap between the predicted composition gradients in massive planets and the core-envelope structure in smaller planets. [ABSTRACT FROM AUTHOR]

Me 2-1 is a high-excitation planetary nebula whose morphology and physical structure have not yet been investigated. We present narrow-band images in several emission lines, and high- and intermediate-resolution long-slit spectra aimed at investigating its morphology and 3D structure, and its physical parameters and chemical abundances. By applying deconvolution techniques to the images, we identified in Me 2-1: an elliptical ring; two elongated, curved structures (caps) that contain three pairs of bright point-symmetric (PS) knots; a shell interior of the ring; and a faint halo or attached shell. The caps are observed in all images, while the PS knots are only observed in the low-excitation emission line ones. These structures are also identified in the high-resolution long-slit spectra, allowing us to study their morphokinematics. The 3D reconstruction shows that Me 2-1 consists of a ring seen almost pole-on, and a virtually spherical shell, to which the caps and PS knots are attached. Caps and PS knots most probably trace the sites where high-velocity collimated bipolar outflows, ejected along a wobbling axis, collide with the spherical shell, are slowed down, and remain attached to it. Although the main excitation mechanism in Me 2-1 is found to be photoionization, a contribution of shocks in the PS knots is suggested by their emission line ratios. The combination of collimated outflows and a ring with a spherical shell is unusual among planetary nebulae. We speculate that two planets, each with less than one Jupiter mass, could be involved in the formation of Me 2-1 if both enter a common envelope evolution during the asymptotic giant branch phase of the progenitor. One planet is tidally disrupted, forming an accretion disk around the central star, from which collimated bipolar outflows are ejected; the other planet survives, causing wobbling of the accretion disk. The physical parameters and chemical abundances obtained from our intermediate-resolution spectrum are similar to those obtained in previous analyses, with the abundances also pointing to a low-mass progenitor of Me 2-1. [ABSTRACT FROM AUTHOR]

Planets orbiting binary systems are relatively unexplored compared to those around single stars. Detections of circumbinary planets and planetary systems offer a first detailed view into our understanding of circumbinary planet formation and dynamical evolution. The BEBOP (binaries escorted by orbiting planets) radial velocity survey plays a special role in this adventure as it focuses on eclipsing single-lined binaries with an FGK dwarf primary and M dwarf secondary allowing for the highest radial velocity precision using the HARPS and SOPHIE spectrographs. We obtained 4512 high-resolution spectra for the 179 targets in the BEBOP survey which we used to derive the stellar atmospheric parameters using both equivalent widths and spectral synthesis. We furthermore derive stellar masses, radii, and ages for all targets. With this work, we present the first homogeneous catalogue of precise stellar parameters for these eclipsing single-lined binaries. [ABSTRACT FROM AUTHOR]

According to the strange quark matter hypothesis, strange planets may exist, which are planetary mass objects composed of almost equal numbers of up, down, and strange quarks. A strange planet can revolve around its host strange star in a very close-in orbit. When it finally merges with the host, strong gravitational wave emissions will be generated. Here, the gravitational waveforms are derived for the merging process, taking into account the effects of the strange star's magnetic field on the dynamics. Effects of the inclination angle are also considered. Templates of the gravitational waveforms are derived. It is found that the magnetic interactions significantly speed up the merging process. Coalescence events of such strange planetary systems occurring in our Galaxy as well as in local galaxies can be effectively detected by current and future gravitational experiments, which may hopefully provide a new method to test the strange quark matter hypothesis and probe the magnetic field of compact stars. [ABSTRACT FROM AUTHOR]

Radial drift of solid particles in the protoplanetary disk is often invoked as a threat to planet formation, as it removes solid material from the disk before it can be assembled into planets. However, it may also concentrate solids at particular locations in the disk, thus accelerating the coagulation process. Planetesimals are thought to drift much faster in an eccentric disk, due to their higher velocities with respect to the gas, but their drift rate has only been calculated using approximate means. In this work, we show that in some cases previous estimates of the drift rate, based on a modification of the results for an axisymmetric disk, are highly inaccurate. In particular, we find that under some easily realized circumstances, planetesimals may drift outwards, rather than inwards. This results in the existence of radii in the disk that act as stable attractors of planetesimals. We show that this can lead to a local enhancement of more than an order of magnitude in the surface density of planetesimals, even when a wide dispersion of planetesimal size is considered. [ABSTRACT FROM AUTHOR]

311P/PANSTARRS is an active asteroid with characteristics of both asteroids and comets, and it is one of the targets of China's Tianwen-2 mission. Because of its small size of about 400 m, the Yarkovsky effect may have a significant influence on its long-term dynamics. This paper discussed the changes in the long-term motion of 311P/PANSTARRS caused by the Yarkovsky effect. By assuming different surface compositions, this simulation introduced the semi-major axis drift by propagating orbits of orbital clones. It also discusses non-gravitational effects such as close encounters, non-destructive impacts, and the YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect. The study calculates the probabilities of close encounters and impacts with major planets and estimates the timescale for 311P/PANSTARRS to reach its rotational period splitting limit. The results of the simulations show that the Yarkovsky effect may cause 311P/PANSTARRS to exit from the resonance region faster when compared to a purely gravitational model. 311P/PANSTARRS will leave the current resonance region after roughly 10 Myr, and have a chance to become a Mars-crossing asteroid through ν 6 secular resonance due to the diurnal Yarkovsky effect if its surface is covered by a regolith layer. It is concluded that 311P/PANSTARRS is stable at least 10 Myr time scale even if taking the Yarkovsky effect and the YORP effect into account. Furthermore, the YORP effect may not significantly affect the semi-major axis drift of 311P/PANSTARRS. [ABSTRACT FROM AUTHOR]

The radius valley, i.e. a dearth of planets with radii between 1.5 and 2 Earth radii, provides insights into planetary formation and evolution. Using homogenously revised planetary parameters from Kepler 1-min short cadence light curves, we remodel transits of 72 small planets mostly orbiting low-mass stars, improving the precision and accuracy of planet parameters. By combining this sample with a similar sample of planets around higher mass stars, we determine the depth of the radius valley as a function of stellar mass. We find that the radius valley is shallower for low-mass stars compared to their higher mass counterparts. Upon comparison, we find that theoretical models of photoevaporation underpredict the number of planets observed inside the radius valley for low-mass stars: with decreasing stellar mass, the predicted fraction of planets inside the valley remains approximately constant whereas the observed fraction increases. We argue that this provides evidence for the presence of icy planets around low-mass stars. Alternatively, planets orbiting low-mass stars undergo more frequent collisions and scatter in the stars' high-energy output may also cause planets to fill the valley. We predict that more precise mass measurements for planets orbiting low-mass stars would be able to distinguish between these scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we report near-infrared observations of the classical T Tauri star TW Hya with the SPIRou high-resolution spectropolarimeter and velocimeter at the 3.6-m Canada–France–Hawaii Telescope in 2019, 2020, 2021, and 2022. By applying Least-Squares Deconvolution (LSD) to our circularly polarized spectra, we derived longitudinal fields that vary from year to year from –200 to +100 G, and exhibit low-level modulation on the 3.6 d rotation period of TW Hya, despite the star being viewed almost pole-on. We then used Zeeman–Doppler Imaging to invert our sets of unpolarized and circularly polarized LSD profiles into brightness and magnetic maps of TW Hya in all four seasons, and obtain that the large-scale field of this T Tauri star mainly consists of a 1.0–1.2 kG dipole tilted at about 20° to the rotation axis, whereas the small-scale field reaches strengths of up to 3–4 kG. We find that the large-scale field is strong enough to allow TW Hya to accrete material from the disc on the polar regions at the stellar surface in a more or less geometrically stable accretion pattern, but not to succeed in spinning down the star. We also report the discovery of a radial velocity signal of semi-amplitude |$11.1^{+3.3}_{-2.6}$| m s−1 (detected at 4.3σ) at a period of 8.3 d in the spectrum of TW Hya, whose origin may be attributed to either a non-axisymmetric density structure in the inner accretion disc, or to a |$0.55^{+0.17}_{-0.13}$| MꝜ candidate close-in planet (if orbiting in the disc plane), at an orbital distance of 0.075 ± 0.001 au. [ABSTRACT FROM AUTHOR]

This article examines the transformation of the "heart of the world" concept and its influence on the understanding of what causes planetary motion. It begins with Aristotle's conception of the sphere of the fixed stars and that of commentators such as Simplicius, Averroes, and Aquinas. The focus then shifts to the notion of a mobile Sun positioned between the upper and lower planets in the geocentric tradition of Macrobius, medieval, and Renaissance thinkers. We then examine the transition to the Copernican Sun, which is both stationary in terms of its central geometric position but also perceived as the "natural" or vital center of the universe. These ideas are then traced from Copernicus and Rheticus to Kepler and Galileo. We will conclude with some considerations concerning Giordano Bruno and William Harvey, and the intriguing connection between the circulation of the blood and the Sun's role as the heart of the world. [ABSTRACT FROM AUTHOR]

There is a growing consensus that Venus is seismically active, although its level of seismicity could be very different from that of Earth due to the lack of plate tectonics. Here, we estimate upper and lower bounds on the expected annual seismicity of Venus by scaling the seismicity of the Earth. We consider different scaling factors for different tectonic settings and account for the lower seismogenic thickness of Venus. We find that 95–296 venusquakes equal to or bigger than moment magnitude (Mw) 4 per year are expected for an inactive Venus, where the global seismicity rate is assumed to be similar to that of continental intraplate seismicity on Earth. For the active Venus scenarios, we assume that the coronae, fold belts, and rifts of Venus are currently seismically active. This results in 1,161–3,609 venusquakes ≥Mw4 annually as a realistic lower bound and 5,715–17,773 venusquakes ≥Mw4 per year as a maximum upper bound for an active Venus. Plain Language Summary: Venus could be seismically active at the moment, but it is uncertain how many earthquakes (or to use the proper term: venusquakes) there could be in a year. Here, we calculate the minimum and maximum number of venusquakes we could expect in a given year on Venus based on different assumptions. If we assume there is not much seismic activity on Venus (comparable to the interior of tectonic plates on Earth), we find that we could expect about a few hundred venusquakes per year with a magnitude bigger than or equal to 4. For an estimate of the maximum amount of venusquakes, we assume that Venus has regions with more seismic activity: the so‐called coronae, fold belts, and rifts. Depending on our assumptions, we then find that more than 17,000 venusquakes with a magnitude bigger than or equal to 4 could occur in a year. Key Points: An inactive Venus with global background seismicity like Earth's continental intraplate seismicity has a few hundred quakes ≥Mw4 per yearA lower bound on an active Venus where fold belts, coronae, and rifts are seismically active predicts a few thousand quakes ≥Mw4 annuallyThe upper bound for an active Venus results in thousands (∼5,000–18,000) venusquakes ≥Mw4 per year [ABSTRACT FROM AUTHOR]

Phased photometric variation provides a method for discovering potential non-transiting exoplanets in high-precision time-series photometry. Applying a Lomb–Scargle algorithm, we search for phased photometric variation in a selection of 140 000 bright dwarf stars with full-frame image light curves from the Southern ecliptic hemisphere of the Transiting Exoplanet Survey Satellite (TESS) mission. We fit the phased photometric variation signal for these candidates using a three-component model comprised of atmospheric reflection/emission, tidal ellipsoidal distortion, and Doppler beaming contributions. We find 27 candidate signals that can be attributed to short-period, massive planets. Our candidates have periods ranging from 0.74 to 1.98 d, and photometric variations with amplitudes ranging from 94 to 528 ppm. The host stars are all bright (9 < T < 11) F- and G-type dwarf stars. We estimate the radial velocity semi-amplitudes to be in excess of 60 m s−1 for each candidate, easily within reach of current high-precision spectrographs. If confirmed, these candidates would be the first non-transiting exoplanets discovered with TESS. [ABSTRACT FROM AUTHOR]

Crater detection can provide valuable information for humans to explore the topography and understand the history of extraterrestrial planets. Due to the significantly varying scenario distributions, existing detection models trained on known labelled crater datasets are hardly effective when applied to new unlabelled planets. To address this issue, we propose a two-stage adaptive network (TAN) for semi-supervised cross-domain crater detection. Our network is built on the YOLOv5 detector, where a series of strategies are employed to enhance its cross-domain generalisation ability. In the first stage, we propose an attention-based scale-adaptive fusion (ASAF) strategy to handle objects with significant scale variances. Furthermore, we propose a smoothing hard example mining (SHEM) loss function to address the issue of overfitting on hard examples. In the second stage, we propose a sort-based pseudo-labelling fine-tuning (SPF) strategy for semi-supervised learning to mitigate the distributional differences between source and target domains. For both stages, we employ weak or strong image augmentation to suit different cross-domain tasks. Experimental results on benchmark datasets demonstrate that the proposed network can enhance domain adaptation ability for crater detection under varying scenario distributions. [ABSTRACT FROM AUTHOR]

We present new 'almost' time-reversible integrators for solution of planetary systems consisting of 'planets' and a dominant mass ('star'). The algorithms can be considered adaptive generalizations of the Wisdom–Holman method, in which all pairs of planets can be assigned time-steps. These time-steps, along with the global time-step, can be adapted time-reversibly, often at no appreciable additional compute cost, without sacrificing any of the long-term error benefits of the Wisdom–Holman method. The method can also be considered a simpler and more flexible version of the symba symplectic code. We perform tests on several challenging problems with close encounters and find the reversible algorithms are up to 2.6 times faster than a code based on symba. The codes presented here are available on Github. We also find adapting a global time-step reversibly and discretely must be done in block-synchronized manner or similar. [ABSTRACT FROM AUTHOR]

Atacama Large Millimetre/submillimetre Array (ALMA) observations of the thermal emission from protoplanetary disc dust have revealed a wealth of substructures that could evidence embedded planets, but planet-driven spirals, one of the more compelling lines of evidence, remain relatively rare. Existing works have focused on detecting these spirals using methods that operate in image space. Here, we explore the planet detection capabilities of fitting planet-driven spirals to disc observations directly in visibility space. We test our method on synthetic ALMA observations of planet-containing model discs for a range of disc/observational parameters, finding it significantly outperforms image residuals in identifying spirals in these observations and is able to identify spirals in regions of the parameter space in which no gaps are detected. These tests suggest that a visibility-space fitting approach warrants further investigation and may be able to find planet-driven spirals in observations that have not yet been found with existing approaches. We also test our method on six discs in the Taurus molecular cloud observed with ALMA at 1.33 mm, but find no evidence for planet-driven spirals. We find that the minimum planet masses necessary to drive detectable spirals range from ≈0.03 to |$0.5 \, M_{\text{Jup}}$| over orbital radii of 10–100 au, with planet masses below these thresholds potentially hiding in such disc observations. Conversely, we suggest that planets ≳0.5–1  M Jup can likely be ruled out over orbital radii of ≈20– |$60 \, \text{au}$| on the grounds that we would have detected them if they were present. [ABSTRACT FROM AUTHOR]

Several stars show deep transits consistent with discs of roughly |$1\mathrm{\, R}_\odot$| seen at moderate inclinations, likely surrounding planets on eccentric orbits. We show that this configuration arises naturally as a result of planet–planet scattering when the planets possess satellite systems. Planet–planet scattering explains the orbital eccentricities of the discs' host bodies, while the close encounters during scattering lead to the exchange of satellites between planets and/or their destabilization. This leads to collisions between satellites and their tidal disruption close to the planet. Both of these events lead to large quantities of debris being produced, which in time will settle into a disc such as those observed. The mass of debris required is comparable to a Ceres-sized satellite. Through N -body simulations of planets with clones of the Galilean satellite system undergoing scattering, we show that 90 per cent of planets undergoing scattering will possess debris from satellite destruction. Extrapolating to smaller numbers of satellites suggests that tens of per cent of such planets should still possess circumplanetary debris discs. The debris trails arising from these events are often tilted at tens of degrees to the planetary orbit, consistent with the inclinations of the observed discs. Disruption of satellite systems during scattering thus simultaneously explains the existence of debris, the tilt of the discs, and the eccentricity of the planets they orbit. [ABSTRACT FROM AUTHOR]

Equations of motion are derived for (visco)elastic, self-gravitating and variably rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net translational and rotational motion as far as possible. This separation is achieved by introducing degrees of freedom that represent the body's rigid motions; it is made precise by imposing constraints that are physically motivated and that should be practically useful. In essence, a Tisserand frame is introduced exactly into the equations of solid mechanics. The necessary concepts are first introduced in the context of a solid body, motivated by symmetries and conservation laws, and the corresponding equations of motion are derived. Next, it is shown how those ideas and equations of motion can readily be extended to describe a layered fluid–solid body. A possibly new conservation law concerning inviscid fluids is then stated. The equilibria and linearization of the fluid–solid equations of motion are discussed thereafter, along with new equations for use within normal-mode coupling calculations and other Galerkin methods. Finally, the extension of these ideas to the description of multiple, interacting fluid–solid planets is qualitatively discussed. [ABSTRACT FROM AUTHOR]

We measure the dependence of planet frequency on host star mass, M L, and distance from the Galactic center, R L, using a sample of planets discovered by gravitational microlensing. We compare the two-dimensional distribution of the lens-source proper motion, μ rel, and the Einstein radius crossing time, t E, measured for 22 planetary events from Suzuki et al. with the distribution expected from Galactic model. Assuming that the planet-hosting probability of a star is proportional to M L m R L r , we calculate the likelihood distribution of (m, r). We estimate that r = 0.10 − 0.37 + 0.51 and m = 0.50 − 0.70 + 0.90 under the assumption that the planet-hosting probability is independent of the mass ratio. We also divide the planet sample into subsamples based on their mass ratio, q, and estimate that m = − 0.08 − 0.65 + 0.95 for q < 10−3 and 1.25 − 1.14 + 1.07 for q > 10−3. Although uncertainties are still large, this result implies a possibility that, in orbits beyond the snowline, massive planets are more likely to exist around more massive stars whereas low-mass planets exist regardless of their host star mass. [ABSTRACT FROM AUTHOR]