Synodic Period Research Articles

Three-dimensional modelling of Ganymede’s Chapman–Ferraro magnetic field and its role in subsurface ocean induction

In April 2023, the JUpiter ICy moon Explorer (JUICE) began its journey to orbit Jupiter’s largest and only magnetic moon, Ganymede. Part of the mission’s objectives aim to verify existence of the moon’s subsurface ocean and determine its structure through its induced response to external excitation by periodically varying magnetic field. Known contributions to the excitation are those from Jupiter’s dipole (at synodic period) and quadrupole (at half-synodic period) variations, and Ganymede’s inclined eccentric orbit around Jupiter (at orbital period). We propose that Ganymede’s magnetopause, where the Chapman–Ferraro (C-F) magnetic field arises from local currents, also contributes to subsurface ocean induction. This article introduces the first three-dimensional model of the C-F field and its outputs at Ganymede’s subsurface ocean and larger magnetosphere. The field is shown to be non-uniform - strongest near upstream Ganymede’s subflow region and gradually weakening away from it. Magnetopause asymmetry due to the Jovian guide field results in largely synodic variation of the C-F field, with exceptions near Ganymede’s equator and subflow meridian where asymmetry effects are minimal and the variations are half-synodic. The C-F field amplitude is of general order ∼50 nT, which is significant relative to excitation from the Jovian field. Comparisons to Galileo data and magnetohydrodynamic simulation results suggest the model is useful, therefore the magnetopause effects must be considered in future induction modelling of Ganymede’s subsurface ocean ahead of the JUICE mission.

Delivery of DART Impact Ejecta to Mars and Earth: Opportunity for Meteor Observations

NASA’s Double Asteroid Redirection Test (DART) and ESA’s Hera missions offer a unique opportunity to investigate the delivery of impact ejecta to other celestial bodies. We performed ejecta dynamical simulations using 3 million particles categorized into three size populations (10 cm, 0.5 cm, and 30 μm) and constrained by early postimpact LICIACube observations. The main simulation explored ejecta velocities ranging from 1 to 1000 m s−1, while a secondary simulation focused on faster ejecta with velocities from 1 to 2 km s−1. We identified DART ejecta orbits compatible with the delivery of meteor-producing particles to Mars and Earth. Our results indicate the possibility of ejecta reaching the Mars Hill sphere in 13 yr for launch velocities around 450 m s−1, which is within the observed range. Some ejecta particles launched at 770 m s−1 could reach Mars's vicinity in 7 yr. Faster ejecta resulted in a higher flux delivery toward Mars and particles impacting the Earth Hill sphere above 1.5 km s−1. The delivery process is slightly sensitive to the initial observed cone range and driven by synodic periods. The launch locations for material delivery to Mars were predominantly north of the DART impact site, while they displayed a southwestern tendency for the Earth–Moon system. Larger particles exhibit a marginally greater likelihood of reaching Mars, while smaller particles favor delivery to Earth–Moon, although this effect is insignificant. To support observational campaigns for DART-created meteors, we provide comprehensive information on the encounter characteristics (orbital elements and radiants) and quantify the orbital decoherence degree of the released meteoroids.

Монастирі та чернецтво Київської єпархії синодального періоду: регламентація діяльності в системі російського церковного законодавства

The article aims to specify the status of Orthodox monasteries and monasticism in the Kyiv eparchy between the 19th and early 20th centuries within the framework of the then-existing Russian church legislation. Research methodology is grounded in the principles of historicism and scientific objectivity, using critical, systematic and comparative analysis of sources. These methods and principles have enabled a comprehensive study of various phenomena in their dynamics and totality, taking into account all conflicting factors. By employing these diverse methods, the study has traced the impact of Russian church legislation on events and processes regulating the activities of monasteries and monasticism in the Kyiv eparchy during the synodal period. Conclusions. The 18th-century reforms in the Russian Empire’s ecclesiastical sphere designated the Holy Governing Synod as the legislative authority over the Orthodox Church, fully subordinating it to the Russian imperial government. During this century, church legislation was established, which, with minor modifications and additions, remained in effect throughout the 19th and early 20th centuries and applied to Ukrainian Orthodox eparchies. The 18th century marked a period of profound and comprehensive transformations in the history of monasteries and monasticism, characterized by strict regulation of monastic life, daily routines and the rights of the inhabitants. The primary feature of church-state relations in the 19th and early 20th centuries was the state’s total control over the Church’s affairs. The Holy Synod controlled matters such as the establishment of new monasteries, granting them status, accepting individuals into monasticism and determining the number of monastics. The monasteries of the Kyiv eparchy during this period were managed by the eparchial bishop and were entitled to elect an abbot, who was then approved by the Holy Synod through its decree. Monasteries, both male and female, were classified into three categories, either communal or non-communal, with a clearly defined monastic staff determined by the Synod.

Resonant chains in triple-planet systems

The mean motion resonance is the most important mechanism that may dominate the dynamics of a planetary system. In a multi-planetary system consisting of $N planets, the planets may form a resonant chain when the ratios of orbital periods of planets can be expressed as the ratios of small integers $T_1: T_2: :T_N=k_1: k_2: k_N$. Due to the high degree of freedom, the motion in such systems could be complex and difficult to depict. In this paper, we investigate the dynamics and possible formation of the resonant chain in a triple-planet system. We defined the appropriate Hamiltonian for a three-planet resonant chain and numerically averaged it over the synodic period. The stable stationary solutions -- apsidal corotational resonances (ACRs) -- of this averaged system, corresponding to the local extrema of the Hamiltonian function, can be searched out numerically. The topology of the Hamiltonian around these ACRs reveals their stabilities. We further constructed the dynamical maps on different representative planes to study the dynamics around the stable ACRs, and we calculated the deviation ($ of the resonant angle in the evolution from the uniformly distributed values, by which we distinguished the behaviour of critical angles. Finally, the formation of the resonant chain via convergent planetary migration was simulated and the stable configurations associated with ACRs were verified. We find that the stable ACR families arising from circular orbits always exist for any resonant chain, and they may extend to a high eccentricity region. Around these ACR solutions, regular motion can be found, typically in two types of resonant configurations. One is characterised by libration of both the two-body resonant angles and the three-body Laplace resonant angle, and the other by libration of only two-body resonant angles. The three-body Laplace resonance does not seem to contribute to the stability of the resonant chain much. The resonant chain can be formed via convergent migration, and the resonant configuration evolves along the ACR families to eccentric orbits once the planets are captured into the chain. Ideally, our methods introduced in this paper can be applied to any resonant chain of any number of planets at any eccentricity.

«Combustion Tables» in Twelfth-Century Latin Europe: A Preliminary Study

The Latin manuscript sources studied in this article jointly document the existence and erstwhile circulation of a highly atypical set of computational tables for planetary longitudes, coupled with extensive tables for ascensions, which served astrologers in Latin Europe as early as the 1130s. An associated text of c.1220 refers to the tables for the five planets as « combustion tables » (tabule combustionis), which reflects the way the tables in question use the time and position of the last conjunction between a planet and the Sun - known in medieval terminology as combustio - as an anchor for calculating the planet’s true ecliptic longitude at a later date within its synodic period. Multiple lines of evidence suggest that the combustion tables as well as the associated solar and ascension tables originally circulated alongside the pseudo-Ptolemaic Iudicia, an astrological work of probable Arabic origin (pre-1138). Overall, the surviving manuscript material raises the possibility that the tables and the Iudicia were at one point a single work that supported astrological computations and judgments at an early stage of their respective development in Latin Europe.

Modeling the barotropic tidal dynamics of the Kuril region

A 3D boundary-value problem for computation barotropic tidal dynamics is solved at Kuril region, including southern part of the Okhotsk Sea, the Kuril Straits and its continental slope. The model is realised in statement for the contravariant components of velocity vector of the Programmed Complex “Cardinal”. Modeling the tidal dynamics of the straits of the Kuril Сhain and its continental slope is of particular importance due to the high geostrategic prestige of the region. The exceptional complexity of the relief of the area containing dozens of underwater volcanoes requires solving the problem in a complete non-hydrostatic formulation; this necessitates a multiprocessor implementation of the model with a high grid resolution for model representativity. An efficient methods for tidal dynamic reproduction at the 2D vertical cross-cuts domain is described. A statement of boundary problem at vertical cross-cuts is considered both in non-hydrostatic formulation and hydrostatic approximation. The results of computation contain the field of level tidal currents generated by the dominant wave K1 and summary wave in the synodic period; results of comparison the bottom vertical velocity at submarine mountain and on sharp depth changes in the hydrostatic and non-hydrostatic statements, result related to structure vertical velocity at cross-cut, the frequency spectrum and energy of tidal currents.

Благочинные монастырей в системе церковного управления Российской империи в конце XVIII–начале XX века

The paper deals with the study of the role of deans of monasteries in the system of Church administration and their influence on the activities of Orthodox monastic monasteries in the Russian Empire of the late XVIII – early XX centuries. Based on legislative acts and archival records, the author analyzes the scope of activity of deans in the structure of church authorities of the Synodal period. It is concluded that the deans, in accordance with the instructions, as well as the instructions of the bishop and the consistory, exercised direct control over Orthodox monasteries: the composition of the brethren, economic, financial and charitable activities.

Synodic Period Channel Modeling and Coding Scheme for Deep Space Optical Communications

Synodic Period Channel Modeling and Coding Scheme for Deep Space Optical Communications

Transformation of Russian Apocryphal Literature in the 19th century

The article analyzes Russia apocryphal literature, that interprets the texts of the Old and New Testaments in its own way. This literature, having been published in Orthodox magazines during the Synodal period, in the 19th century, characterizes by the appearance of parables, traditions, and legends based on well-known apocryphal plots in it. The collection “Lilii Polevye” is examined, which includes many pre-revolutionary transcriptions of the apocrypha, which has been reprinted several times in our time.

Exploring the population and social structure of the Kyiv Eparchy through monastery service records from the 19th to early 20th century

The article aims to examine the informative potential and utility of service records from monasteries within the Kyiv Eparchy, spanning the period from the 19th to the early 20th century, in elucidating the status of Orthodox monastic communities and the social composition of their monastic life. The research methodology adheres to principles of objectivity, historicism, systematic analysis and critical evaluation of sources. Utilizing a method of historical reconstruction, this study seeks to construct a comprehensive understanding of the status of monasteries and the social makeup of their monastic communities from disparate historical evidence. A notable scholarly contribution of this study lies in its pioneering effort to investigate, analyze and assess the informational value of service records from monasteries within the Kyiv Eparchy during the specified period. Conclusively, service records, or formulary information, served as a prevalent form of annual reporting within monastic institutions throughout the 19th century. These unpublished documents serve as primary sources for documenting monastic life during the synodal period, playing a pivotal role in the administrative and communal life of monasteries and their inhabitants. Beyond simply detailing the composition of monastery brotherhoods and listing the names of monks and novices, these records contain rich insights into the individual lives of monastics. Examining such sources facilitates the identification of the number of monastics in Kyiv Eparchy monasteries, the motivations driving their monastic commitment, their roles within monastic communities, average demographics, social standing, educational attainment and even personal characteristics and behaviours. By leveraging these archival materials, scholars are afforded the opportunity to analyze the fluctuating demographics and composition of monastic communities within the Kyiv Eparchy throughout the synodal period, thereby enabling prosopographical investigations and contributing to a deeper understanding of Orthodox monasticism in the region.

Parish Chronicle as a Source for Local History and Regional Church History of the Synodal Period (on the example of the chronicle of the fortress church of the apostles Peter and Paul in Petropavlovsk)

Parish Chronicle as a Source for Local History and Regional Church History of the Synodal Period (on the example of the chronicle of the fortress church of the apostles Peter and Paul in Petropavlovsk)

Revealing Coupled Periodicities in Sunspot Time Series Using Bispectrum—An Inverse Problem

Sunspot daily time series have been available for almost two centuries providing vast and complicated information about the behavior of our star and especially the interaction of the motion of the planets and other possible interstellar phenomena and their effects on the surface of the Sun. The main result obtained from the sunspot time series analysis is the imprint of various periodicities, such as the planets’ orbital periods and the planetary synodic periods on the sunspots signature. A detailed spectrum representation is achieved by means of a periodogram and a virtual extension of the time length segments with zeroed samples for longer representations. Furthermore, the dependence or coupling of these periodicities is explored by means of a bispectrum. We establish the exact interdependencies of the periodic phenomena on the sunspot time series. Specific couplings are explored that are proved to be the key issues for the coupled periodicities on the sunspot time series. In this work, contrary to what has been presented in the literature, all periodic phenomena are limited within the time period of an 11-year cycle as well as the periodicities of the orbits of the planets. The main findings are the observed strong coupling of the Mercury, Venus, and Mars periodicities, as well as synodic periodicities with all other periodicities that appear on the sunspot series. Simultaneously, the rotation of the Sun around itself (25.6 to 33.5 days) provides an extensive coupling of all recorded periodicities. Finally, there is strong evidence of the existence of a quadratic mechanism, which couples all the recorded periodicities, but in such a way that only frequency pairs that sum up to specific periods are coupled. The justification for this kind of coupling is left open to the scientific community.

Dynamical instability in multi-orbiter systems with gas friction

ABSTRACT Closely packed multiplanet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A similar situation applies to stellar-mass black holes embedded in active galactic nuclei discs around supermassive black holes. We use N-body integrations to evaluate how the frictional damping of orbital eccentricity affects the growth of dynamical instability for a wide range of K (the difference in the planetary semimajor axes in units of the mutual Hill radius) and (unequal) planet masses. We find that, in general, the stable region (large K) and unstable region (small K) are separated by a “grey zone”, where the (in)stability is not guaranteed. We report the numerical values of the critical spacing for stability Kcrit and the “grey zone” range in different systems, and provide fitting formulae for arbitrary frictional forcing strength. We show that the stability of a system depends on the damping time-scale τ relative to the zero-friction instability growth time-scale tinst: two-planet systems are stable if tinst ≳ τ; three-planet systems require tinst ≳ 10τ−100τ. When K is sufficiently small, tinst can be less than the synodic period between the planets, which makes frictional stabilization unlikely to occur. As K increases, tinst tends to grow exponentially, but can also fluctuate by a few orders of magnitude. We also devise a linear map to analyse the dynamical instability of the “planet + test mass” system, and find qualitative agreement with N-body simulations.

Приходской клир как объект ложного доносительства со стороны прихожан. Зарисовка на тему повседневности Казанской епархии второй половины XIX в.

The article attempts to highlight such a little-studied, but important and interesting phenomenon of the daily parish life of the late synodal period as the discrediting of the clergy by parishioners. The relations between pastors and the flock in the designated period went far beyond the limits of liturgical practice and had their own specific psychological, cultural, social and economic refraction. It would not be an exaggeration to say that the clergy were an integral, but not always an organic part of the socio-cultural space of the parish, occupying a separate position in it due to a special legal and spiritual status. Meanwhile, the integration that took place had visible side effects, predetermining the rigid and multifaceted dependence of the clergy on the flock. Their relationship was in a permanent search for a balance between different centers of power, needs and interests. This often resulted in a sharp dissonance, which turned into slanders, false denunciations of priests, deacons and acolytes, prompting the diocesan authorities to initiate inquiries and investigations. The very fact of the presence of such a phenomenon in parish life not only speaks about the specifics of the ethical background of rural society, but also the extremely vulnerable position of the clergy. Archival files deposited in the fund of the Kazan Spiritual Consistory and stored in the State Archive of the Republic of Tatarstan reveal a tragic picture of cases of confrontation between clergy and flock, indicating the dominance of illegal approaches of peasants in resolving conflicts that have arisen. For the completeness of its reflection, the article uses the method of a rich description, and attention is purposefully paid to the smallest details of each of the cases involved. The sources involved in the publication are being introduced into scientific circulation for the first time.

A.N. Muravyov, the Younger Brother of M.N. Muravyov-Vilensky, as Phenomenon of Russian Religious Life

The article is devoted to the study of life and work of Andrey Muravyov (1806–1874) who was one of the signifi cant spiritual Orthodox writers, church historians, pilgrims and poets. He was Honorary Member of the Imperial Academy of Sciences since 1963 and contributed substantially to Kiev historical center preservation. He can be considered a unique phenomenon of theological thought of the Synodal period.

Vyatka Church Seals of Synodal Period: an Attempt at Classification (Collection of Sphragistics at P.V. Alabin Kirov Regional Local Lore Museum)

This article proposes a classification of Vyatka church seals from the 18th to the early 20th century based on materials from the collection of sphragistics at the P. V. Alabin Kirov Regional Local Lore Museum. The criteria for classification include the affiliation of the seals with specific individuals and institutions, as well as the specific images depicted on the seals. The article identifies four groups of seals: seals of church administration, seals of spiritual educational institutions, seals of churches, and personal seals of clergy. The study reveals that state symbols, such as the doubleheaded eagle, were typically depicted on seals of church administration and spiritual educational institutions. Seals of parish churches depicted real church buildings or saints until the first third of the 19th century when they were replaced by a standardized image of a three-domed church. Seals belonging to Vyatka bishops were typically twosided with images of a blessing hand and the Holy Trinity. From the mid-19th century, they were replaced by one-sided seals with images of two blessing hands. All personal seals of bishops have circular legends with their names. Seals belonging to other clergy members contain information about the owner’s name, initials, surname, and sometimes their rank. The most popular symbol for all groups of seals was the All-Seeing Eye, symbolizing God’s omniscience.

Spacecraft Floating Potential Measurements for the Wind Spacecraft

Analysis of 8,804,545 electron velocity distribution functions, observed by the Wind spacecraft near 1 au between 2005 January 1 and 2022 January 1, was performed to determine the spacecraft floating potential, ϕ sc. Wind was designed to be electrostatically clean, which helps keep the magnitude of ϕ sc small (i.e., ∼5–9 eV for nearly all intervals) and the potential distribution more uniform. We observed spectral enhancements of ϕ sc at frequencies corresponding to the inverse synodic Carrington rotation period with at least three harmonics. The two-dimensional histogram of ϕ sc versus time also shows at least two strong peaks, with a potential third, much weaker peak. These peaks vary in time, with the intensity correlated with solar maximum. Thus, the spectral peaks and histogram peaks are likely due to macroscopic phenomena like coronal mass ejections (solar cycle dependence) and stream interaction regions (Carrington rotation dependence). The values of ϕ sc are summarized herein and the resulting data set is discussed.

Documents of monasteries of the Kyiv Metropolis synodal period in Ukrainian archives

The investigation of this topic is relevant as the documents of the monasteries of the Kyiv Metropolis Synodal period contain important evidence of religious life, social customs, and economic relations in the historical context of Ukraine, which allows for a better understanding of the dynamics of the development of church institutions and their influence on society. The purpose of the study was to analyse the documentary base of the monasteries of the Kyiv Metropolis Synodal period in Ukrainian archives, its scope, and main content. The methodological basis of the research was the principles of logic and objectivity, as well as methods of classification, generalisation, structural and functional analysis, statistical and historical-comparative methods. The archival funds of Ukraine were examined for the presence of documents from the monasteries of the Kyiv Metropolis Synodal period. It was established that the documents of the monasteries of the Kyiv Metropolis during the Synod period constitute an important archival fund in Ukraine, containing valuable information about the activities of church institutions, as well as about the economic, social, cultural, and political aspects of that time. The main places of their preservation were identified – in the Central State Historical Archives of Ukraine in Kyiv, the State Archives of Cherkasy Region, and the Manuscript Institute of the Vernadsky National Library of Ukraine. It was determined that the peculiarity of monastery funds should be considered in accordance with the peculiarities of the existence of the monasteries themselves within the Kyiv Metropolis, which is due to the heterogeneity of the historical process of the formation of monasteries, as a result of which two groups can be distinguished within the metropolis – Kyivan and southern groups. The available archival collections were analysed, and it was found that the largest complex of archival documents that has survived belongs to the Kyiv-Pechersk Lavra; at the same time, it was noted that archival documents in Ukrainian institutions are unevenly distributed. The practical value of the work lies in the possibility of further in-depth study of issues related to the study of archival funds of Ukraine, as well as in improving their organisation

TOI-1416: A system with a super-Earth planet with a 1.07 d period

TOI-1416 (BD+42 2504, HIP 70705) is a V =10 late G- or early K-type dwarf star. TESS detected transits in its Sectors 16, 23, and 50 with a depth of about 455 ppm and a period of 1.07 days. Radial velocities (RVs) confirm the presence of the transiting planet TOI-1416 b, which has a mass of 3.48 ± 0.47 M⊕ and a radius of 1.62 ± 0.08 R⊕, implying a slightly sub-Earth density of 4.50−0.83+0.99 g cm−3. The RV data also further indicate a tentative planet, c, with a period of 27.4 or 29.5 days, whose nature cannot be verified due to strong suspicions of contamination by a signal related to the Moon’s synodic period of 29.53 days. The nearly ultra-short-period planet TOI-1416 b is a typical representative of a short-period and hot (Teq ≈ 1570 K) super-Earth-like planet. A planet model of an interior of molten magma containing a significant fraction of dissolved water provides a plausible explanation for its composition, and its atmosphere could be suitable for transmission spectroscopy with JWST. The position of TOI-1416 b within the radius-period distribution corroborates the idea that planets with periods of less than one day do not form any special group. It instead implies that ultra-short-period planets belong to a continuous distribution of super-Earth-like planets with periods ranging from the shortest known ones up to ≈30 days; their period-radius distribution is delimited against larger radii by the Neptune Desert and by the period-radius valley that separates super-Earths from sub-Neptune planets. In the abundance of small, short-periodic planets, a notable plateau has emerged between periods of 0.6–1.4 days, which is compatible with the low-eccentricity formation channel. For the Neptune Desert, its lower limits required a revision due to the increasing population of short-period planets; for periods shorter then 2 days, we establish a radius of 1.6 R⊕ and a mass of 0.028 Mjup (corresponding to 8.9 M⊕) as the desert’s lower limits. We also provide corresponding limits to the Neptune Desert against the planets’ insolation and effective temperatures.

Physical properties of the slow-rotating near-Earth asteroid (2059) Baboquivari from one apparition

In this study, we carried out photometric, spectroscopic, and for the first time, polarimetric observations of the Amor-type near-Earth asteroid (2059) Baboquivari. Our findings represent the first reliable determination of Baboquivari's physical properties. We used data from a 1m-class telescope (T100) along with ALCDEF data for photometric analyses and a 1.5-m-class telescope (RTT150) for polarimetric, spectroscopic, and additional photometric observations. We obtained the synodic rotation period of Baboquivari as 129.93 ​± ​2.31 ​h and the standard phase function parameters H and G as 16.05 ​± ​0.05, 0.22 ​± ​0.02, respectively. Our colour index (V-R) measurement of 0.45 ​± ​0.02 is consistent with spectroscopic observations, indicating an S (or sub-S) spectral type. Using the polarimetric and spectroscopic data, we found that the geometric albedo is 0.15 ​± ​0.03, and the spectral type is Sq. Based on the estimated albedo and absolute magnitude, Baboquivari has an effective diameter of 2.12 ​± ​0.21 ​km. Due to the scattered data in the light curve, its slow rotation and location among the NEAs suggest that Baboquivari may be a non-principal axis (NPA) rotator.