Orbit Size Research Articles

Orbital distances and options for small body satellites in Non-Keplerian orbits dominated by solar radiation pressure

We offer a comprehensive description for the dynamics of a spacecraft affected by solar radiation pressure (SRP) orbiting a small body. Constrains are given for regions, in which stable motion is possible. For short and long time scales two different analytical frameworks are summarized and applied. (1) For time scales well below one heliocentric revolution we examine the “static” case, involving SRP fixed in both magnitude and direction. We demonstrate a closed-form solution for quasi terminator orbits using parabolic coordinates. (2) Next, we study the “dynamic” case where the asteroid is in an eccentric orbit about the Sun, involving changing solar aspect angle and distance. To solve this Augmented Hill Three-Body Problem (AH3BP), SRP effects are averaged over the anomaly of the orbiter. From this approximation we derive constrains for Sun-synchronous orbits in size and eccentricity. The findings of the analysis (1) and (2) are then applied to small- and medium-sized spacecraft orbiting specific asteroids, comets, dwarf planets and (for comparison) planets. We consider ranges of orbiter mass and surface area exposed to the Sun, as well as small body parameters, including mass and orbit. We show the resulting constrains on orbit size as well as parameters of Sun-synchronous orbits and frozen orbits in tables. While terminator orbits may only vary in size, quasi terminator orbits can cover wide regions best described in the parabolic coordinates of case (1). This region has four parameters for our orbit options. As alternative application for orbit stability we calculate constraints on orbit and particle sizes for dust particles. Numerical integration is used to validate the resilience of these solutions to further perturbation by third bodies or the small body's non-spherical shape. • We estimated orbital distances for spacecrafts in Sun-synchronous orbits around 9 small bodies. • Orbital shapes deviate greatly from Keplerian conic sections due to solar radiation pressure. • Quasi-terminator orbit dynamics are confined and described by up to four parabolas. • For orbiting dust a frozen state is assumed, limits to orbital sizes are given. • Numeric simulations add perturbing effects and validate predictions about orbit stability.

3D Orbital Architecture of a Dwarf Binary System and Its Planetary Companion

Because of the diversity of stellar masses and orbital sizes of binary systems and the complex interaction between star–star, star–planet, and planet–planet, it has been difficult to fully characterize the planetary systems associated with binary systems. Here, we report high-precision astrometric observations of the low-mass binary system GJ 896AB, revealing the presence of a Jupiter-like planetary companion (GJ 896Ab). The planetary companion is associated to the main star GJ 896A, with an estimated mass of 2.3 Jupiter masses and an orbit period of 284.4 days. A simultaneous analysis of the relative astrometric data obtained in the optical and infrared with several telescopes, and the absolute astrometric data obtained at radio wavelengths with the Very Long Baseline Array (VLBA), reveals, for the first time, the fully characterized three-dimensional (3D) orbital plane orientation of the binary system and the planetary companion. The planetary and binary orbits are found to be in a retrograde configuration and with a large mutual inclination angle (Φ = 148°) between both orbital planes. Characterizing the 3D orbital architecture of binary systems with planets is important in the context of planet formation, as it could reveal whether the systems were formed by disk fragmentation or turbulence fragmentation, as well as the origin of spin–orbit misalignment. Furthermore, as most stars are in binary or multiple systems, our understanding of systems such as this one will help to further understand the phenomenon of planetary formation in general.

Fast-ion orbit analysis in Thailand Tokamak-1

Thailand Tokamak-1 (TT-1) will be a small research tokamak being operated by the Thailand Institute of Nuclear Technology (TINT) in Nakhonnayok province, Thailand. The device partly uses the infrastructure of the former HT-6M alongside new hardware. Auxiliary heating sources, such as ion cyclotron range of frequency (ICRH) and/or neutral beam injection (NBI), maybe also included in subsequent operations. This study aims to investigate the characteristics and behavior of fast ions produced by NBI heating in various operation scenarios. This work employs the collisionless Lorentz-orbit (LORBIT) code for simulating the motion of ions in the TT-1. When a hydrogen ion (H+) with an energy of 20 keV travels in the plasma with the plasma current of 100 kA, the toroidal magnetic field of 1.0 T, the average Larmor radius is found to approximately be 0.48 cm for a passing transit particle and 2.17 cm for a trapped particle. The Larmor radius reduces as the plasma current is increased or a stronger magnetic field is used. Furthermore, when the ion has pitch angles in the range of 85∘−100∘, the ion orbit clearly demonstrates a banana shape with a width and height of 7.0 and 18.8 cm, respectively. The size of the banana orbit shows an inverse correlation with the plasma current. In the last part of this work, we investigate the motion of ions that had initial positions along the paths of a co-current and counter-current NBI. It is shown that the number of lost ions can be reduced if the initial radial positions of the ions are in the range of 0.64–0.68 m.

Effects of the noninteger-cycle pulse and the initial phase on the Magnus approximation to study Rydberg atoms in intense laser fields

The Magnus expansion method is popular for the study of Rydberg atoms in intense laser fields. In such studies, the pulse length is usually set as an integer multiple of wavelength, at the same time, the initial phase of the laser pulse is usually set as zero, i.e., without considering the effect of the initial phase in the calculation. However, this will result in some items multiplied by zero. Then, contributions from these items will be lost. Here, we investigated the effects of the noninteger-cycle pulse and initial phase of the laser on the calculated transition probability of Rydberg atoms in intense laser fields. Our calculation results show that these effects are trivial when the nondipole approximation is adopted. In dipole approximation i.e., when the wavelength of the laser field exceeds the characteristic size of atomic or molecular orbitals, these effects are trivial only in the case of a long pulse duration and a large principal quantum number, however for ultrashort laser pulses (pulse duration that lasts less than five light cycles), these effects are evident.

Extended planetary chaotic zones

ABSTRACT We consider the chaotic motion of low-mass bodies in two-body high-order mean-motion resonances with planets in model planetary systems, and analytically estimate the Lyapunov and diffusion time-scales of the motion in multiplets of interacting subresonances corresponding to the mean-motion resonances. We show that the densely distributed (though not overlapping) high-order mean-motion resonances, when certain conditions on the planetary system parameters are satisfied, may produce extended planetary chaotic zones – ‘zones of weak chaotization,’ – much broader than the well-known planetary connected chaotic zone, the Wisdom gap. This extended planetary chaotic zone covers the orbital range between the 2/1 and 1/1 resonances with the planet. On the other hand, the orbital space inner (closer to the host star) with respect to the 2/1 resonance location is essentially long-term stable. This difference arises because the adiabaticity parameter of subresonance multiplets specifically depends on the particle’s orbit size. The revealed effect may control the structure of planetesimal discs in planetary systems: the orbital zone between the 2/1 and 1/1 resonances with a planet should be normally free from low-mass material (only that occasionally captured in the first-order 3/2 or 4/3 resonances may survive); whereas any low-mass population inner to the 2/1 resonance location should be normally long-lived (if not perturbed by secular resonances, which we do not consider in this study).

Further description of the Kerguelen sandpaper skate Bathyraja irrasa (Rajiformes: Arhynchobatidae) based on additional specimens, including egg cases and embryos.

Adult specimens, additional juvenile specimens, egg cases and embryos were used to provide a more detailed anatomical description of the Kerguelen sandpaper skate Bathyraja irrasa, a species of skate endemic to the Kerguelen Plateau and listed as Vulnerable by the IUCN Red List of Threatened Species. The morphological and meristic data reveal a relatively high level of intraspecific variation, mostly related to size. Egg cases are described for the first time and were shown to vary in colour and fouling depending on the length of time spent in the marine environment. Embryos removed from egg cases represent all stages of embryonic development in this species and include the largest embryo recorded for this species, i.e., 230 mm total length (LT ), which increases the range of size at hatching of B. irrasa to 178-230 mm LT . A number of morphometric and meristic characters varied ontogenetically in B. irrasa, in particular relative tail length, number of tail thorns in the median row and the size of orbits. This study highlights the importance of describing intraspecific variation in species and the importance of egg cases to taxonomic and biological research on oviparous species.

Coxeter Pop-Tsack Torsing

Given a finite irreducible Coxeter group W with a fixed Coxeter element c, we define the Coxeter pop-tsack torsing operator Pop T :W→W by Pop T (w)=w·π T (w) -1 , where π T (w) is the join in the noncrossing partition lattice NC(w,c) of the set of reflections lying weakly below w in the absolute order. This definition serves as a “Bessis dual” version of the first author’s notion of a Coxeter pop-stack sorting operator, which, in turn, generalizes the pop-stack sorting map on symmetric groups. We show that if W is coincidental or of type D, then the identity element of W is the unique periodic point of Pop T and the maximum size of a forward orbit of Pop T is the Coxeter number h of W. In each of these types, we obtain a natural lift from W to the dual braid monoid of W. We also prove that W is coincidental if and only if it has a unique forward orbit of size h. For arbitrary W, we show that the forward orbit of c -1 under Pop T has size h and is isolated in the sense that none of the non-identity elements of the orbit have preimages lying outside of the orbit.

Abelian quotient of subgroups of solvable linear groups

In this paper, we study the relations of the sizes of abelian quotient of a subgroup of finite linear groups and the largest orbit size of the linear group actions. We study two conjectures raised by Keller and the author. We show that these two conjectures are not true in general, but also prove some special cases under the condition that the group is solvable.

Anatomy of Classical Boron-Boron Bonding: Overlap and sp Dissonance.

Classical bonding is predominantly understood using the insipid spn hybridization for σ-bonds as well as π bonds and their delocalized variants. Because hybridization ignores intricate differences in the energy and size of valence atomic orbitals, its naïve application to classically bonded boron atoms leads to numerous surprises in bond strengths, frontier MOs/bands, and even geometry. Here we show that the sp dissonance caused by size mismatch between the valence s and p orbitals of boron plays a crucial role in its bonding, subtly distinct from that of carbon and silicon. Unlike the heavier p block elements, boron prefers to actively engage its compact 2s orbitals in bonding. This leads to the overreach of p-p σ-type overlap that reduces its magnitude in the entire B─B bonding range. Consequently, the π-type overlap remains substantial, making its electronic structure visibly distinct in saturated and unsaturated regimes. The deltahedral frameworks offer a compromise by breaking this symmetry-enforced dichotomy of classical σ- and π-type bonding and following alternate electron counts that suit the electron deficiency of the boron. The pathological anatomy of classical B─B σ-bonding also explains the origins of puzzling metallic character and disorder in their classical boride networks even with ideal electron count, unlike deltahedral borides. The implications of sp dissonance are illustrated in classical boron networks of various hybridizations, explaining the unusual preference for unique sp3 lattice with strained four-membered rings in CrB4, origins of observed σ holes in MgB2 that lead to its superconducting nature, and the absence of Peierls distortion in LiB.

Reconstruction of orbital wall fractures with superior orbital fissure syndrome using individualized preformed titanium mesh: a pilot study

The aim was to preliminarily evaluate the effect of individualized preformed titanium mesh in the treatment of orbital wall fractures with superior orbital fissure syndrome (SOFS). This study consisted of 10 patients of orbital wall fracture and SOFS who were treated at the Affiliated Stomatology Hospital of Southwest Medical University. On the basis of preoperative computed tomography data, individualized titanium mesh was produced by mirror engineering and rapid prototyping, and it was implanted into defects in the orbital walls to restore the normal anatomy. Early orbital wall reconstruction was performed to improve the SOFS. Postoperatively, the ocular and facial appearance and eye function were evaluated. The orbital structure, volume, and size of the SOF were restored in the 10 patients using the individualized titanium mesh. The symptoms of SOFS completely disappeared in all patients with no severe postoperative complications. Significant recovery of ocular and facial appearance and eye function was reported. This pilot study demonstrated that individualized preformed titanium mesh can accurately restore the orbital walls and the structure and size of the SOF, and it is useful in the treatment of SOFS without intraorbital bone fragment displacement.

Performance analysis of discrete-time GeoX/G/1 retrial queue with various vacation policies and impatient customers

This paper studies the behavior of a batch arrival single server retrial queueing model under three different vacation policies. Three types of vacation policies, single vacation, multiple vacations, and atmost J-vacations with impatient customers in general retrial times are considered. The probability generating function and marginal generating function of orbit size are obtained in a steady state. The stability condition for each vacation model is derived. Performance measures such as mean orbit size, mean system size, mean waiting time of a customer, and the probabilities of the server being in different states have also been determined. Based on performance characteristics, a comparative analysis is performed among the three vacations. Numerical illustrations are displayed to establish the consistency of the theory developed.

Minimal orbit sizes in nilpotent group actions

Let [Formula: see text] be a finite nilpotent group. We prove the following results. (1) If [Formula: see text] is of class 2 and acts faithfully and irreducibly on an elementary abelian group [Formula: see text], then all nontrivial orbits of [Formula: see text] on [Formula: see text] have sizes larger than [Formula: see text]. (2) If [Formula: see text] is cyclic, then every subgroup of [Formula: see text] intersecting trivially with the center of [Formula: see text] has order less than [Formula: see text]. We also show that a result like (2) cannot be obtained when the hypothesis that [Formula: see text] is cyclic is replaced by the hypothesis that the center of [Formula: see text] is cyclic.

Correction of Post-Traumatic Enophthalmos by Orbital Floor Reconstruction with Titanium Mesh

Aim: To see the efficacy of titanium mesh in orbital floor reconstruction to correct the post-traumatic enophthalmos in orbito-zygomatic complex fractures. Methods: This retrospective study was carried out in the department of Oral and Maxillofacial Surgery, University College of Medicine & Dentistry, University of Lahore, Pakistan from January 2017 to January 2020. All patients who had enophthalmos after orbito-zygomatic fractures and were treated for orbital floor reconstruction with titanium mesh were included in the study. Computer tomography (CT scan) was done to diagnose and measure the orbital floor defect. Pre-operative and post-operative hertalex ophthalmometry was done to measure and compare the enophthalmos. Results: Among the 30 patients, 23 were male and 7 were female. The mean age of the patients was 30±5.80 years. Fourteen patients had right and 16 patients had left side orbitozygomatic complex fracture. The mean orbital floor defect size was 1.72±0.78 cm preoperatively measured by CT scan. There was a correction of enophthalmos in 23 patients out of 30(76.66%). Conclusion: Titanium mesh is a commonly used and easily available material for the correction of orbital floor defects. It is efficacious in terms of the correction of post-traumatic enophthalmos resulting from orbito-zygomatic complex fracture. Keywords: Enophthalmos, titanium mesh, orbitozygomatic fractures

Curved accretion disks around rotating black holes without reflection symmetry

Rotating black holes without equatorial reflection symmetry can naturally arise in effective low-energy theories of fundamental quantum gravity, in particular, when parity-violating interactions are introduced. Adopting a theory-agnostic approach and considering a recently proposed Kerr-like black hole model, we investigate the structure and properties of accretion disk around a rotating black hole without reflection symmetry. In the absence of reflection symmetry, the accretion disk is in general a curved surface in shape, rather than a flat disk lying on the equatorial plane. Furthermore, the parameter epsilon that controls the reflection asymmetry would shrink the size of the prograde innermost stable circular orbits, and enhance the efficiency of the black hole in converting rest-mass energy to radiation during accretion. The retrograde innermost stable circular orbits are stretched but the effects are substantially suppressed. In addition, we find that spin measurements based on the gravitational redshift observations of the disk, assuming a Kerr geometry, may overestimate the true spin values if the central object is actually a Kerr-like black hole with conspicuous equatorial reflection asymmetry. The qualitative results that the accretion disk becomes curved and the prograde innermost stable circular orbits are shrunk turn out to be generic in our model when the reflection asymmetry is small.

Search of arrivals of an m/g/1 retrial queueing system with delayed repair and optional re-service using modified bernoulli vacation

Single server queueing system in retrial is investigated, as well as optional re-service,customer search and delayed repair. Furthermore, the server is permitted to take a vacation under Modified Bernoulli vacation. In this model, some of the customer’s seek voluntary reservice for the identical service taken, dissatisfied with the first attempt without entering the retrial group (probability r1) or leaving the service area (probability 1 – r1). The failing server's repair begins after an arbitrary length of time termed delay time has passed. The supplementary variable technique is used to calculate orbit size, server status, and performance metrics. We explore several special situations of our suggested model and compare the results to previous research.

Hurwitz Orbits of Equal Size

We provide a variety of cases in which two factorizations have Hurwitz orbits of the same size. We begin with prototypical results about factorizations of length two, and show that cycling elements or flipping and inverting elements in any factorization preserves Hurwitz orbit size. We prove that "double reverse" factorizations in groups with special presentations have Hurwitz orbits of equal size, and end with applications to complex reflection groups.

Quasiperiodic oscillations, quasinormal modes and shadows of Bardeen–Kiselev Black Holes

In this article, we study the particle dynamics around a static and spherically symmetric Bardeen-Kiselev black hole (BK BH) which is a solution of the Einstein-non-linear Maxwell field equations along with a quintessential field. We discuss its essential geometrical properties such as scalar invariants and size of innermost stable circular orbits. Dynamics of test particles around the BH is also studied. Moreover, we also computed the fundamental frequencies of a test particle orbiting the BH in a slightly perturbed orbit. Further, the degeneracy relations between the spin of rotating Kerr BH and magnetic charge of the BK BH at the values of the quintessential parameter $\omega_q=-1/3$ and in terms of the same values of innermost stable circular orbits (ISCOs) radius, energy efficiency, twin-peaks quasiperiodic oscillations (QPOs) frequencies and impact parameter for photon are also discussed in detail. Finally, we have investigated the relationship between the shadow radius and the real part of the quasinormal mode (QNM) frequency.

Crystal pop-stack sorting and type [formula omitted] crystal lattices

Given a complex simple Lie algebra g and a dominant weight λ, let Bλ be the crystal poset associated to the irreducible representation of g with highest weight λ. In the first part of the article, we introduce the crystal pop-stack sorting operatorPop◊:Bλ→Bλ, a noninvertible operator whose definition extends that of the pop-stack sorting map and the recently-introduced Coxeter pop-stack sorting operators. Every forward orbit of Pop◊ contains the minimal element of Bλ, which is fixed by Pop◊. We prove that the maximum size of a forward orbit of Pop◊ is the Coxeter number of the Weyl group of g. In the second part of the article, we characterize exactly when a type A crystal is a lattice.

Orbit sizes and the central product group of order 16

Orbit sizes and the central product group of order 16

Analysis of a retrial queueing system with priority service and modified multiple vacations

This paper studies an M/G/1 retrial queueing system with modified multiple vacations, in which a new external arrival may expel the customer being served out of the system and directly starts to be served or join the retrial orbit. Once the server finds the orbit is empty at the end of a service, it will immediately take a random length vacation. If the orbit is still empty when a vacation is finished, the server takes another same vacation. This pattern continues until the orbit is not empty when a vacation is completed or the server has already taken M vacations. By constructing an embedded Markov chain, we provide the sufficient and necessary condition of system stability. The distributions of the orbit size and the system size in steady-state are derived through the supplementary variable method. Then, some system performance measures and the Laplace-Stieltjes transform of sojourn time distribution are obtained. Besides, we perform the cost analysis of the system. Finally, several numerical illustrations are given to investigate the effects of system parameters on the essential system characteristics.