Kinds Of Orbits Research Articles

Observational features of reflection asymmetric black holes

The Kerr spacetime is symmetric with respect to a well-defined equatorial plane. When testing the equatorial reflection symmetry of an isolated black hole, one is at the same time testing the Kerr hypothesis in General Relativity. In this work, we investigate the possible observational features when a Keplerian disk is surrounding a rotating black hole without reflection symmetry. When such symmetry is broken, generically, the photon trajectories around the black hole and the Keplerian orbits on the accretion disk are distorted vertically away from the equatorial plane by an amount that depends on their distance to the black hole. In the reflection asymmetric spacetime we are considering, these two kinds of orbits are distorted in opposite directions. Interestingly, while the size and shape of black hole shadows closely resemble those of Kerr black holes, distinct observational characteristics can emerge in the disk image and emission line profiles. When observing the disk edge-on, a pronounced concave shape may appear along its innermost edge on the incoming side. Furthermore, distinctive horn-like features might be observed on the spectral line profile at the blue-shifted side. These special features can serve as compelling indicators of the reflection asymmetry present in rotating black holes.

The dynamics around the collinear points of the elliptic three-body problem: A normal form approach

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating–pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we implement a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions.

The Search for the Origin of the Quantum Conditions under the Paradigm of Absolute Space

This study deals with the physical (not the mathematical) origin of the quantum conditions. The assumption of an absolute space together with the speed of 369.5 km/s of the sun leads to cycloidal or helical orbits of the electron around the proton. This kind of orbits is a previously unnoticed fact and not compatible with the model of a closed circular standing wave. It is the aim of this study to search for alternative models. The Alternating Field model (AFM) assumes the existence of alternating fields for both the proton and the electron. The Higgs-field provides the energy requirements. By Puthoff’s effect, adapted for the electrostatic field, the electron changes its Compton frequency according to its position in the field. The interference of the alternating fields of the proton and the electron causes beats that are integer multiples of the orbital frequencies when the electron moves on Bohr’s orbits. Important results of this study are: The electrostatic Schwarzschild-radius is exactly half the value of the classical electron radius. Bohr’s first three principal quantum numbers, 1, 2, 3, are reproduced as 1.000052, 2.000214, and 3.000685. A two-dimensional simulation shows that the AFM causes orbits with ribbon shape. A formula, using only the orbital frequencies of the two innermost circular orbits, can predict the shortest wavelength of the Lyman series. The AFM is still incomplete. E.g., it does not prevent illegal orbits, but only indicates them. Also, the AFM does not use the magnetic core field of the proton. On the other hand, the model has produced results showing that Newton’s absolute space and the QM are compatible.

Balancing Conditions for the Relativistic Correction Using Lorentz Acceleration

In this work, the average effects of the Lorentz acceleration on the charged spacecraft’s orbit are studied encounter with relativistic correction. The relativistic correction as function of the orbital elements, and may be time, is formulated. Lagrange planetary equations are used to calculate the perturbations due to considered perturbing forces. The needed conditions to neutralize the effects of the relativistic corrections, using Lorentz acceleration, are derived. Numerical examples for different kinds of orbits are applied.

Probing a black-bounce-Reissner–Nordström spacetime with precessing and periodic motion

We investigate the precessing and periodic orbits of a test timelike particle around the black-bounce-Reissner–Nordström spacetime which is characterized by its charge and bounce parameter. Its marginally bound orbit and innermost stable circular orbit are obtained in the exact forms. We pay closely attention to its precessing orbits and find the resulting relativistic periastron advance. We also study its periodic orbits and demonstrate that small variations of the charge and bounce parameter can make the motion jump among the periodic and precessing orbits. In these two kinds of orbits, we find a distinct degeneracy that some specific combinations of the charge and bounce parameters can generate exactly the same orbital motion in the black-bounce-Reissner–Nordström spacetime, which can also mimic those of the Schwarzschild black hole. In order to break such a degeneracy, we make use of the precession of S2 star around Sgr A* detected by GRAVITY together with the shadow diameter of Sgr A* measured by Event Horizon Telescope and find preliminary bounds on the charge and bounce parameter.

Nonlinear photoassociation through exotic orbits.

We investigate the effects of a particular kind of orbits, which we call exotic orbits, on the process of classical molecular photoassociation. As a starting model system, we consider the process described by the Morse potential with a time-dependent perturbation consisting of the interaction of an external laser field with the molecular dipole. When the external perturbation is turned off, the bound molecular states are classically represented by librational motion, whereas the unbound, the collisional states, are represented by unbound motion, and in both cases, the energy is a constant of motion. When the perturbation is turned on, the total energy is no longer a constant of motion and initial conditions in the unbound region can reach the bound region, and vice versa, through chaotic orbits. Alternatively, we have found that the connection between the bound and unbound sectors can be achieved through exotic orbits, which are comprised by librationlike parts, a localized chaotic region, and an unbounded constant-energy part. Thus, if a colliding atomic pair is in an exotic orbit, it penetrates a chaotic region coming from the unbound sector, subsequently performing librationlike motion, during which the molecule with constant bound energy is formed. Afterwards, the molecule returns to the chaotic region and from this region, it can either access a distinct bound energy or dissociate. We call this phenomenon, in which a metastable molecule is formed, intermittent photoassociation. We show that the key for the emergence of exotic orbits is the relatively short range of the dipole as compared to the interacting potential range. In order to further verify our results, we have considered realistic forms for the potentials and dipole functions of several molecules and found the emergence of exotic orbits, and consequently of intermittent photoassociation, for the MgLi and SrLi molecular parameters.

Transfers between NRHOs and DROs in the Earth-Moon system

The stable near rectilinear halo orbits (NRHOs) and distant retrograde orbits (DROs) are both considered as potential parking orbits for cis-lunar stations. Transfer orbits between NRHOs and DROs can promote the exploitation of their distinct advantages and be helpful for possible cooperations between cis-lunar stations in different kinds of orbits. By using the symmetry of the dynamics in the circular restricted three body problem (CR3BP), the transfers between NRHOs and DROs are investigated through the transfers from southern NRHOs to DROs, which are obtained by using a two-step approach, consisting of the search and optimization phases. Four NRHOs and three DROs, including those in previous studies and the 9:2 L2 NRHO considered as the nominal orbit for the Lunar Orbital Platform-Gateway (LOP-G), are considered in this study. Both the interior and exterior transfer orbits are found, and the exterior transfer orbits always have relatively low transfer costs. The transfer orbits with better performances than the best previous results are successfully constructed. In the cases of some transfers, the close lunar flyby has shown great advantages in changing the orbital plane and adjusting the velocity without fuel consumption. The comparison between transfer orbits to different DROs indicates that the dynamical structures have more significant effects on the transfer cost than the Jacobi energy. Then, some representative transfer orbits are refined in the high-fidelity ephemeris model for real mission scenarios. The comparisons between transfer orbits departing at different epochs indicate that the lunar orbit eccentricity has significant effects on the transfer time and cost, and some transfer orbits with specific epochs can have better performances than the nominal ones in the CR3BP. The results are of great significance for constructing connections between cis-lunar space stations, as well as for designing transport systems in the Earth-Moon system.

Dark energy influence on geodesics of RN–dS space-time

The quintessence influence, as one of the most plausible models of dark energy, on geodesics of Reissner–Nordstrom–de Sitter (RN–dS) black hole is studied. All the possible motions of test particles in the gravitational field are investigated by using the effective potential, and we have done a detailed analysis of the geodesic structure of massless particles and study all kinds of orbits corresponding to the energy levels for this black hole in quintessence field.

Field amplification effect of resonant magnetic perturbation on ion orbits in tokamak plasma

<sec> The fast ion transport associated with resonant magnetic perturbation (RMP) contains rich physical spanning single particle motion of fast particle and plasmas response physics with RMP and their interaction. Full numerical simulation considering such physical ingredients should be performed in a long run for clarifying the underlying physical features of the fast ion confinement with RMP. Thus, the appropriate application of RMP is not only to avoid the detrimental effects but also to serve as an actuator to exert targeted control over the energetic particle profile. To achieve this goal, a comprehensive knowledge of the effects of RMP including plasma response on fast ions is necessary. </sec> <sec> In this work, the plasma response to RMP in HL-2A device is simulated by the MARS-F code under different parameters including finite resistivity, toroidal rotation frequency and toroidal mode number, and the three-dimensional (3D) magnetic field topology considering RMP is obtained. Then, Boris algorithm is used to track the ion orbit under these 3D fields, and the physical mechanism of ion orbit characteristics changed by the perturbed field is explored in detail. It is found that with the increase of finite resistivity, the average value of perturbed magnetic field decreases, and the orbit radial expansion turns smaller. The variation of toroidal rotation frequency can change the distribution of perturbed magnetic field, resulting in different orbit radial expansions for different kinds of orbits. What is more, if the toroidal mode number increases, the amplitude of perturbed magnetic field after response decreases obviously, thus resulting in little effect on orbit radial expansion. In a word, the plasma responded RMP field enhances the orbit radial expansion, and the maximum orbital radial expansion increases with the augment of average value of perturbed magnetic field on the orbit. Meanwhile, the amplitude of orbit expansion increases significantly when the ions pass through the region where the perturbed magnetic field is strongly amplified. This effect can explain the increase of ion prompt loss and enhancement of plasma radial transport in edge localized mode mitigation experiments by RMP. </sec>

Mathematical Algorithm for Solving Two–Body Problem

Abstract In this paper, computational algorithm with the aid of Mathematica software is specifically designed for the gravitational two–body problem. Mathematical module is established to find the position and velocity vectors. Application of this module for different kind of orbits (elliptic, parabolic and hyperbolic) leads to accurate results, which proved module efficiency and to be skillful. The classical power series method is to be utilized as the methodology.

The geometry of isochrone orbits: from Archimedes’ parabolae to Kepler’s third law

In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and Harmonic potentials are called \it{isochrone}. In this paper, we solve the following general problem: are there any other isochrone potentials, and if so, what kind of orbits do they contain? To answer these questions, we adopt a geometrical point of view initiated by Michel H\'enon in 1959, in order to explore and classify exhaustively the set of isochrone potentials and isochrone orbits. In particular, we provide a geometric generalization of Kepler's third law, and give a similar law for the apsidal angle, for any isochrone orbit. We also relate the set of isochrone orbits to the set of parabolae in the plane under linear transformations, and use this to derive an analytical parameterization of any isochrone orbit. Along the way we compare our results to known ones, pinpoint some interesting details of this mathematical physics problem, and argue that our geometrical methods can be exported to more generic orbits in potential theory.

CultCube: Experiments in autonomous in-orbit cultivation on-board a 12-Units CubeSat platform

The feasibility and design of the CultCube 12U CubeSat hosting a small Environmental Control and Life Support Systems (ECLSS) for the autonomous cultivation of a small plant in orbit is described. The satellite is aimed at running experiments in fruit plants growing for applications in crewed vehicles for long-term missions in space. CultCube is mainly composed of a pressurized vessel, constituting the outer shell of the ECLSS, and by various environmental controls (water, nutrients, air composition and pressure, light, etc.) aimed at maintaining a survivable habitat for the fruit plants to grow. The plant health status and growth performances is monitored using hyperspectral cameras installed within the vessel, able to sense leaves’ chlorophyll content and temperature, and allowing the estimation of plant volume in all its life cycle phases. The paper study case is addressed to the in-orbit experimental cultivation of a dwarf tomato plant (MicroTom), which was modified for enhancing the anti-oxidants production and for growing in stressful environments. While simulated microgravity tests have been passed by the MicroTom plant, the organism behaviour in a real microgravity environment for a full seed-to-seed cycle needs to be tested. The CultCube 12U CubeSat mission presents no particular requirements on the kind of orbit, whereas its minimum significative duration corresponds to one seed-to-seed cycle for the plant, which is 90 days for the paper study case. In the paper, after an introduction on the importance of an autonomous testbed for plant cultivation, in the perspective of the implementation of bioregenerative systems on-board future manned long-term missions, the satellite design and the MicroTom engineered plant for in-orbit growth are described. In addition to the description of the whole set of subsystems, with focus on the payload and its controllers and instrumentation, the system budgets are presented. Finally, the first tests conducted by the authors are briefly reported.

Motion and trajectories of photons in a three-dimensional rotating Hořava-AdS black hole

We study the motion of photons in the background of a three-dimensional rotating Ho\v{r}ava AdS black hole that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance on the null geodesics structure, by solving analytically the equations of motion. Mainly we find that, through a fine tuning of the parameters of the theory, new kinds of orbits are allowed, such as unstable circular orbits and trajectories of first kind. Also, we show that an external observer will see that photons arrive at spatial infinity in a finite coordinate time.

A simple method of identifying π orbitals for non-planar systems and a protocol of studying π electronic structure

The characteristic of π electrons has a crucial role in determining various properties of chemical systems, such as reactivity, aromaticity and spectroscopy. There are a large number of methods could be used for investigating π electronic structure, for example, the well-known electron localization function and multicenter bond order. For completely planar systems, the π molecular orbitals can be unambiguously identified and thus studying their π electronic structure is easy. However, for non-planar systems, identification of π orbitals and then analysis of π electrons are often not trivial. In this work, based on localized molecular orbitals (LMOs), we propose a conceptually simple and easy way to automatically identify π orbitals for any kind of systems, which makes subsequent analyses of π electrons straightforward. In addition, we show that the identified π LMOs can also be used to reliably estimate π component of molecular orbitals or other kinds of orbitals. The method proposed in this work has been implemented into our wavefunction analysis code Multiwfn as a key ingredient of standard analysis protocol for π electrons. Application examples given in this article illustrated that this protocol makes analysis of π electronic structure for a wide variety of chemical systems unprecedentedly convenient and reliable.

Transfers from near-rectilinear halo orbits to low-perilune orbits and the Moon’s surface

Near-rectilinear halo orbits (NRHOs) are periodic orbits that belong to the families of halo orbits around the L1/L2 points in a three-body system and have low minimum distances to the smaller primary. NRHOs possess some good dynamical and geometrical properties and are now considered as potential orbits for a near-future crewed deep space station. Recently, intensive investigations have been performed with regard to different aspects of a lunar NRHO mission: Earth-NRHO transfers, station keeping, shadow avoidance, and ground station visibility conditions are deeply studied. At the same time, the important operation of soft lunar landing from the working NRHO is still poorly covered in literature. In this research, we analyze both the direct landing scenario and the option of a transfer from the working NRHO to the intermediate low-perilune orbit (LPO). This kind of orbit can serve as a platform for transport communication between the lunar surface and the working NRHO. Lunar regions attainable after a one-impulse NRHO departure maneuver are identified, and the costs required for the soft landing are analytically estimated based on the classical gravity-turn landing strategy. In the scenario of a two-impulse transfer to the intermediate LPO, a wide range of perilune distances and inclinations is proved to be available. Several resonant NRHOs have been considered as a working orbit: the 4:1 and 9:2 L2 orbits, and the 11:3 L1 orbit. The calculations are performed in a high-fidelity model of motion that includes the JPL's DE430 ephemeris model of the Solar system and solar radiation pressure. The lunar gravitational field is evaluated based on the GRGM1200A spherical harmonic model truncated to degree and order 8.

Motion and collision of particles near DST black holes

We consider the Deser–Sarioglu–Tekin (DST) black hole as a background, and we study the motion of massive particles in the case that we have a collision of two spinning particles in the vicinity of its horizon. New kinds of orbits are allowed for small deviations of General Relativity, but the behavior of the collision is similar to the one observed for General Relativity. Some observables like the bending of light and the perihelion precession are analyzed.

Scheduling Solution for Space Debris Observations

The scheduling model of orbital debris can be considered as composed by a set of optical ground station which move with the surface of the Earth, a set of space situation awareness centre which can be assumed connected to ground station, and orbital debris travelling through different kind of orbit generating visibility windows when the line of sight (LOS) to ground station exists. To solve this, scheduling problem can be considered as the allocation of observing time of the telescope to collect measurements of the debris (i.e., to improve orbit or attitude determination, spin rate evolution, etc.). The increasing number of space debris to be observed with optical ground station has caused the combinatorial explosion in the number of intervals to be scheduled. Therefore, new scheduling approach to provide a solution to the new requests is needed. In the framework of the Agreement between Italian Space Agency (ASI) and National Institute of Astrophysics (INAF) “Supporto alle attivita IADC e validazione pre-operativa per SST” (N.2015-028-R.0), S5Lab research group has developed a network of observatory fully dedicated for space debris observations. Moreover, a scheduler called NICO (Networked Instrument Coordinator for debris Observations) has been developed specifically designed for the harmonization of individual user requests by considering meteorological and astronomical constraints. This paper outlines the advantages of the developed custom solution based on modular architecture. NICO’s architecture is based on a multilayer system: the front end is designed to allow external registered users to specify their observing requests and to assign specific scientific priority; the back-end is changed for the business logic by determining the visibility windows for each request and to solve the conflict. The implemented conflict solver solution is based on genetic algorithms. This paper outlines the results of the application of NICO scheduler to the 2018-IADC (Inter-Agency Space Debris Coordination Committee) international optical observing campaigns.

Structure of geodesics in the regular Hayward black hole space-time

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when $\ell$, a convenient encoding of the central energy density $3/8\pi\ell^{2}$, is $0.6M$, and $b$ is $3.9512M$ as a specific value of angular momentum, escape orbits exist only under $b>3.9512M$. The precession direction is also associated with values of $b$. With $b=3.70M$ the bound orbits shift clockwise but counter-clockwise with $b=5.00M$ in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).

Earth-Mars cyclers for a sustainable human exploration of Mars

Since the early history of Space Exploration, Mars conquest has been the most important target. After Apollo mission's Moon landing, several concepts and projects, concerning a mission on the Red Planet, were developed. One of the most important contributes was given by Buzz Aldrin, who theorized the use of particular kind of orbits, called cycler orbits, as baseline for an enduring Mars colonization.A cycler orbit is a kind of orbit which repeats every integer multiple of synodic period and which encounters two bodies with a precise schedule. In the case, the bodies considered are Earth and Mars. It is possible to inject a space station in the cycler orbit which allows a continuous transfer of a crew from Low Earth Orbit to Mars Low Orbit and vice-versa. Small taxi vehicles are used to rendezvous the cycler station from the two bodies, significantly reducing the amount of propellant.In this paper a mission architecture based on this new concept was analysed, in order to develop an alternative mission profile compared to the actual architectures proposed for human missions. The work starts with an analysis of several classes of cycler. Through a trade-off analysis an unique class of cycler was identified as baseline for a further mission analysis. The mission analysis consists of an evaluation of orbital perturbation, the computation of ΔV required for injection and rendezvous manoeuvres and an identification of close approach windows of the cycler with the two planets, allowing an evaluation of mission duration.Eventually, the presented mission concept was compared with more classical concepts, focusing on a key figure to enable Mars colonization, sustainability.Finally the proposed architecture should be seen as a preliminary assessment of an alternative solution to the currently proposed enabling architectures for the Martian exploration.

Particular type of a gap in the spectrum of multiband superconductors

We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic orbitals of different symmetries. This gap has composite superconducting-hybridization origin, because it exists only if both the superconductivity and the hybridization between different kinds of orbitals are present. So for many classes of superconductors with multiorbital structure such spectrum changes should take place. These particular changes in the spectrum at some distance from the Fermi level result in slow convergence of the spectral weight of the optical conductivity even in quite conventional superconductors with isotropic s-wave pairing mechanism.