Circular Orbit Research Articles

Фотометрические наблюдения и моделирование формы космического мусора на средневысотных орбитах

The circular medium Earth orbits with a period of about half a day in the inclination range from 50° to 70° are used by various global navigation satellite systems (GNSS), such as GLONASS, GPS, Beidou, Galileo. GNSS operating orbits are one of the important areas in near-Earth space. The information about the space debris (SD) existing in this region and its characteristics is important for risk assessments and mitigation. We report the results of photometrical observations of SD objects in the vicinity of GNSS orbits obtained with the 1.6-meter AZT-33IK telescope of ISTP SB RAS Sayan Solar Observatory in 2018–2023. We show how SD objects existing in this region are distributed relative to GNSS objects. We derive time and phase dependences of the apparent brightness of all measured SD objects. Folded light curves are constructed, rotation periods and their dynamics are determined. The results of modeling the light curve inherent for several SD objects from the GNSS orbital are presented. We suggest a possible space object shape and parameters of proper rotation, which correspond to the observed light curve.

Spacecraft Formation Keeping and Reconfiguration Using Optimal Visual Servoing

This paper proposes a direct visual servoing system for spacecraft guidance in formation flying scenarios. The proposed image-based visual servoing system uses image information for planning and executing formation acquisition, reconfiguration, and maintenance maneuvers. The system assumes that LEDs are located at specific points on the satellites, enabling the visual servoing controller to rely on continuous tracking of these features in the camera’s image plane. Analytical developments demonstrate that the proposed optimal visual control system is stable and optimal, and it acts on both the orbital and attitude dynamics of the spacecraft, considering circular and elliptical reference orbits. The distributed image-based controller defines a cost function that minimizes control efforts, and the paper proses an optimal framework for developing controllers that address the issue. A ROS-based simulation tool was used to test the proposed visual servoing controller in a realistic small-sat formation flying scenario. Results indicate that the proposed distributed control strategy is viable and robust against environmental perturbations and disturbances in sensing and actuation.

Photometrical observations and shape modeling of space debris in medium Earth orbits

The circular medium Earth orbits with a period of about half a day in the inclination range from 50° to 70° are used by various global navigation satellite systems (GNSS), such as GLONASS, GPS, Beidou, Galileo. GNSS operating orbits are one of the important areas in near-Earth space. The information about the space debris (SD) existing in this region and its characteristics is important for risk assessments and mitigation. We report the results of photometrical observations of SD objects in the vicinity of GNSS orbits obtained with the 1.6-meter AZT-33IK telescope of ISTP SB RAS Sayan Solar Observatory in 2018–2023. We show how SD objects existing in this region are distributed relative to GNSS objects. We derive time and phase dependences of the apparent brightness of all measured SD objects. Folded light curves are constructed, rotation periods and their dynamics are determined. The results of modeling the light curve inherent for several SD objects from the GNSS orbital are presented. We suggest a possible space object shape and parameters of proper rotation, which correspond to the observed light curve.

Collisions and dynamics of particles with magnetic dipole moment and electric charge near magnetized rotating Kerr black holes

Analysis of test magnetized and charged particles around black holes immersed in external magnetic fields may help to explain the observed astrophysical phenomena related to black holes, such as the acceleration of particles up to high energies. In this sense, we studied the circular motion of test-charged particles with magnetic dipole orbiting around magnetized rotating Kerr black holes. First, we derive the effective potential for the circular motion of such particles, including interactions between the external magnetic field and the electric charge, and the magnetic interaction between the magnetic dipole. In addition, we analyze the angular momentum and energy of particles corresponding to circular orbits. The effects of magnetic interaction and coupling parameters on the position of innermost stable circular orbits (ISCOs), the energy and angular momentum of the particles at ISCO, and the energy efficiency from the Novikov-Thorne accretion disc have been investigated. We also find cases of degeneracy between magnetic dipole interaction and magnetic coupling parameters, giving the same ISCO radius. Finally, we studied various cases of collisions of neutral, magnetized, and electrically charged particles near rotating Kerr black holes in the presence of external magnetic fields. The critical angular momentum of spinning charged particles is found in which the particles can collide. We also analyze the effects of both magnetic interactions on the center-of-mass energy of the colliding particles.

Revisiting the gravitomagnetic clock effect

To the first post-Newtonian order, if two test particles revolve in opposite directions about a massive, spinning body along two circular and equatorial orbits with the same radius, they take different times to return to the reference direction relative to which their motion is measured: it is the so-called gravitomagnetic clock effect. The satellite moving in the same sense of the rotation of the primary is slower, and experiences a retardation with respect to the case when the latter does not spin, while the one circling in the opposite sense of the rotation of the source is faster, and its orbital period is shorter than it would be in the static case. The resulting time difference due to the stationary gravitomagnetic field of the central spinning body is proportional to the angular momentum per unit mass of the latter through a numerical factor which so far has been found to be 4π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\pi $$\\end{document}. A numerical integration of the equations of motion of a fictitious test particle moving along a circular path lying in the equatorial plane of a hypothetical rotating object by including the gravitomagnetic acceleration to the first post-Newtonian order shows that, actually, the gravitomagnetic corrections to the orbital periods are larger by a factor of 4 in both the prograde and retrograde cases. Such an outcome, which makes the proportionality coefficient of the gravitomagnetic difference in the orbital periods of the two counter-revolving orbiters equal to 16π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$16\\pi $$\\end{document}, confirms an analytical calculation recently published in the literature by the present author. It is an important result in view of the astrophysical implications of the gravitomagnetic clock effect around Kerr black holes.

Neural Network-Based Formation Flying Using Aerodynamic Forces via Variable Shape Function

Conventional formation flying Earth-orbiting satellites control their orbits to perform their missions using thrusters, but the amount of propellant loaded into a satellite is limited. Therefore, the use of aerodynamic forces for orbit control has been attracting attention, particularly in low Earth orbit. The orbit control can be achieved by appropriately changing the state of satellite, such as attitude and shape, to meet the aerodynamic requirements. In modeling the relationship between satellite state and aerodynamic forces, conventional methods ignore the shielding caused by the nonconvexity of the satellite’s appearance. Ignoring the shielding creates a gap between the modeled and the real aerodynamic forces, resulting in poor control performance. To solve this problem, we propose an aerodynamic force modeling method that incorporates a neural network to estimate the shielding. We train the neural network using data from an aerodynamics simulator. The optimal state that not only generates the required aerodynamic forces but also improves controllability under various mechanical constraints is obtained by solving an optimization problem that incorporates the proposed aerodynamic model. We conduct numerical simulations for establishing and maintaining general circular orbit formations. The results show convergence and continuous stable control of the deputy satellite to the ideal orbit.

Periodicity and lifetime of orbits around elongated asteroids

This paper presents dynamics and control of orbits around an asteroid that is modelled as a uniformly rotating homogeneous rectangular parallelepiped (HRP). Aside from the non-uniform gravitational field of the asteroid, we include the solar radiation pressure (SRP) as a perturbing force. A simple model based on the polyhedral method is employed for calculating the gravity around the HRP. First, circular periodic orbits are identified both in the presence and absence of solar radiation pressure. Then, families of general non-circular periodic orbits in the presence of SRP are determined and subsequently analysed for stability. Next, for a general orbit in the equatorial plane, its stability against a catastrophic impact of an orbiting spacecraft onto the asteroid’s surface is checked in the presence of SRP. Orbits, where the solar radiation pressure is less/more dominant over the central body’s gravity, are identified with the aim of finding the best orbits for parking a spacecraft. Then, for long-period orbits, SRP is averaged and the time averaged evolution of the orbital elements is obtained. For a special set of initial condition, a closed form solution for the evolution of the orbital eccentricity is obtained. Using this solution, a lower limit for the life-time of a spacecraft that is left uncontrolled is derived in a closed form. Finally, active control strategies are developed for orbit-keeping ofspacecraft for any choice of orbital parameters. A linear-quadratic regulator (LQR) is designed to track a given Keplerian orbit with minimum fuel expenditure. Fuel expenditure on various orbits are calculated and compared to determine the orbits of cheapest operation. The work presented is applicable to small body (asteroids and comets) exploration missions which require online cancellation of the perturbing forces with minimal knowledge of the accurate shape, size, and composition of the small body prior to the mission.

Global N-body simulation of gap edge structures created by perturbations from a small satellite embedded in Saturn’s rings

Small satellites embedded in Saturn’s ring – Daphnis and Pan – open a clear gap. Observations by the Voyager and Cassini spacecrafts have revealed various striking features of the gap structure, such as the density waves, sharp edge, and vertical wall structure. In order to explain these features in a single simulation, we perform a high-resolution (N∼106−107) global full N-body simulation of gap formation by an embedded satellite considering gravitational interactions and inelastic collisions among all ring particles and the satellite, while these features have been mostly investigated separately with different theoretical approaches: the streamline models, 1D diffusion models, and local N-body simulation. As a first attempt of a series of papers, we here focus on the gap formation by separating satellite migration with fixing the satellite orbit in a Keplerian circular orbit. We reveal how the striking gap features – the density waves, sharp edge, and vertical wall structure – are simultaneously formed by an interplay of the satellite-ring and ring particle–particle interactions. In particular, we propose a new mechanism to quantitatively explain the creation of the vertical wall structure at the gap edge. Inelastic collisions between ring particles damp their eccentricity excited by the satellite’s perturbations to enhance the surface density at the gap edge, making its sharp edges more pronounced. We find the eccentricity damping process inevitably raises the vertical wall structures the most effectively in the second epicycle waves. Particle–particle collisions generally convert their lateral epicyclic motion into vertical motion. Because the excited epicyclic motion is the greatest near the ring edge and the epicycle motions are aligned in the first waves, the conversion is the most efficient in the gap edge of the second waves and the wall height is scaled by the satellite Hill radius, which are consistent with the observations.

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.

The dynamics of accretion flows near to the innermost stable circular orbit

ABSTRACT Accretion flows are fundamentally turbulent systems, yet are classically modelled with viscous theories only valid on length scales significantly greater than the typical size of turbulent eddies in the flow. We demonstrate that, while this will be a reasonable bulk description of the flow at large radii, this must break down as the flow approaches absorbing boundaries, such as the innermost stable circular orbit (ISCO) of a black hole disc. This is because in a turbulent flow large velocity fluctuations can carry a fluid element over the ISCO from a finite distance away, from which it will not return, a process without analogy in conventional models. This introduces a non-zero directional bias into the velocity fluctuations in the near-ISCO disc. By studying reduced random walk problems, we derive a number of implications of the presence of an absorbing boundary in an accretion context. In particular, we show that the average velocity with which a typical fluid element crosses the ISCO is much larger than is assumed in traditional theories. This enhanced velocity modifies the thermodynamic properties of black hole accretion flows on both sides of the ISCO. In particular, thermodynamic quantities for larger ISCO stresses no longer display pronounced cusps at the ISCO in this new formalism, a result with relevance for a number of observational probes of the intra-ISCO region. Finally, we demonstrate that these extended models reproduce the trans-ISCO behaviour observed in GRMHD simulations of thin discs.

Comparing Central Force Formulation in Newtonian and Special Theory of Relativity

This research aims to give a comparison between classical mechanics and special relativity in term of formulating central force. We derive the Binet equation in relativistic form and find its solution. Then, we discuss the stability of the orbit and make several plots as well as the comparisons of kinematics variables by taking specific example namely circular orbit. Finally, we investigate the relativistic effect in Rutherford scattering by considering some variables including the closest distance and deflection angle. We believe this paper provides a good example for students about the difference between relativistic and classical central force.

A long-period transiting substellar companion in the super-Jupiters to brown dwarfs mass regime and a prototypical warm-Jupiter detected by TESS

We report on the confirmation and follow-up characterization of two long-period transiting substellar companions on low-eccentricity orbits around TIC 4672985 and TOI-2529, whose transit events were detected by the TESS space mission. Ground-based photometric and spectroscopic follow-up from different facilities, confirmed the substellar nature of TIC 4672985 b, a massive gas giant in the transition between the super-Jupiters and brown dwarfs mass regime. From the joint analysis we derived the following orbital parameters: P = 69.0480−0.0005+0.0004 d, Mp = 12.74−1.01+1.01 Mj, Rp = 1.026−0.067+0.065 Rj and e = 0.018−0.004+0.004. In addition, the RV time series revealed a significant trend at the ~350 m s−1 yr−1 level, which is indicative of the presence of a massive outer companion in the system. TIC 4672985 b is a unique example of a transiting substellar companion with a mass above the deuterium-burning limit, located beyond 0.1 AU and in a nearly circular orbit. These planetary properties are difficult to reproduce from canonical planet formation and evolution models. For TOI-2529 b, we obtained the following orbital parameters: P = 64.5949−0.0003+0.0003 d, Mp = 2.340−0.195+0.197 Mj, Rp = 1.030−0.050+0.050 Rj and e = 0.021−0.015+0.024, making this object a new example of a growing population of transiting warm giant planets.

Newton vs Coulomb in AdS/CFT and the weak gravity conjecture

We study (near-)circular orbits of charged particles in the background of charged black holes in asymptotically anti–de Sitter (AdS) spacetimes of arbitrary dimensionality. We calculate the energy and angular momentum of such particles in a large-radius limit. This allows us to compute the anomalous dimension of the dual charged double-twist operators in a large-spin expansion, making a prediction for the bootstrap analysis at large charge and spin. We relate our result to the weak gravity conjecture (WGC) for AdS black holes of all sizes. We also discuss the relation of WGC with the existence of the innermost stable circular orbit (ISCO) in any dimension. Published by the American Physical Society 2024

Circular orbits and collisions of particles with magnetic dipole moment near magnetized Kerr black holes in modified gravity

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

Particle Dynamics and Matter Accretion onto Non‐linear Charged AdS Black Holes in Massive Gravity

AbstractThis article investigates the dynamics of charged particles and accretion process around nonlinear charged AdS black holes (BHs). the impact of key factors such as angular momentum, specific energy, and magnetic field on the behavior of particles are focused. Firstly, the concept of the effective potential is examined, which provides insights into the forces acting on particles and the escape velocity they must overcome. The innermost stable circular orbit (ISCO) is also discussed, which is the closest distance a particle can orbit a BH without being pulled in and explore the conditions for particle escape. Next, the energy efficiency and epicyclic frequency of test particles are studied, which measure the amount of energy particle loses due to friction and the frequency of its oscillations, respectively. The accretion processes is analyzed by examining the radial velocity, energy density, and accretion mass of matter falling into the BH. Using the equation of state, how different types of fluid, such as stiff, dust, quintessence and phantom‐like dark energy fluid, affect the accretion process near a BH is investigated. Throughout this study, the parameter plays a key role in shaping the dynamics of particles and accretion systems is found. This parameter is a measure of the strength of the nonlinear electrodynamics field, and it can have a significant impact on the radius of the ISCO, the energy efficiency of accretion, and other properties. These findings provide new insights into the physics of particle dynamics around nonlinear charged AdS BHs. They could have implications for understanding the behavior of matter in extreme gravitational environments, such as those found near the center of galaxies.

Orbital evolution of eccentric perturbers under dynamical friction: crossing the sound barrier

ABSTRACT In a gaseous medium, dynamical friction (DF) reaches a maximum when the orbital speed of a (point-like) perturber moving on a circular orbit is close to the sound speed. Therefore, in a quasi-steady state, eccentric orbits of perturbers approaching the sound barrier (from below) should rapidly circularize as they experience the strongest drag at pericentre passage. To investigate this effect, we extend the solution for circular DF in a uniform gaseous medium to eccentric Keplerian orbits. We derive an approximation to the steady-state DF force, which is valid for eccentricities as high as e = 0.9 in a limited range of Mach number around the transition to supersonic regime. We validate our analytical result with 3D simulations of the gas density response. Although gaseous DF generally dissipates orbital energy, we find that it can be directed along the motion of the perturber near pericentre passage when the eccentricity is e ≳ 0.9. We apply our results to compute the long-time evolution of the orbital parameters. Most trajectories tend to circularize as the perturber moves into the supersonic regime. However, orbits with eccentricities e ≳ 0.8 below the sound barrier experience a slight increase in eccentricity as they loose orbital energy. Possible extensions to our analytical approach are also discussed.

Renormalizing Love: tidal effects at the third post-Newtonian order

We present the conservative effective two-body Hamiltonian at the third order in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical tidal-interactions. Our derivation of the effective two-body Lagrangian is based on the diagrammatic effective field theory approach and it involves Feynman integrals up to three loops, which are evaluated within the dimensional regularization scheme. The elimination of the divergent terms occurring in the effective Lagrangian requires the addition of counterterms to ensure finite observables, thereby introducing a renormalization group flow to the post-adiabatic Love number. As a limiting case of the renormalized dynamical effective Hamiltonian, we also derive the effective Hamiltonian for adiabatic tides, and, in this regime, calculate the binding energy for a circular orbit, and the scattering angle in a hyperbolic scattering.

Extreme mass-ratio inspiral as a probe of extra dimensions: The case of spinning massive object

Extreme mass-ratio inspiral (EMRI), as one of most important and promising gravitational wave (GW) sources, which is the ideal tool to test fundamental theories and nature of massive black hole (MBH). In this paper, we consider the EMRI system consisting of a rotating barneworld MBH with tidal charge Q and a stellar-mass compact object (CO), where a non-spinning CO inspirals on the equatorial and circular orbits around the MBH. Under the adiabatic approximate condition, we show the evolution of circular orbital radius by computing the EMRI fluxes and orbital phase modified by tidal charge. We find that the positive and negative values of tidal charges have the difference influences on the EMRI orbital dynamics. In particular, the inspiral motion of CO in the rotating barneworld MBH with a negative tidal charge would be end more earlier than the positive tidal charge case. Accordingly, the EMRI waveforms from the positive tidal charge cases can put more rigorous constraint results comparing with the negative tidal charge cases. Finally, we analyze the phase differences of two EMRI waveforms from Kerr BH and rotating braneworld BH with tidal charge by computing dephasing and mismatch. Our results indicate that LISA can distinguish the EMRI waveforms from rotating braneworld BH with the negative tidal charge as small as Qmin∼−10−6 under the suitable scenarios, which can sever as the unique discriminator of detecting the physics of extra dimensions.

Investigating the hard state of MAXI J1820 + 070: a comprehensive Bayesian approach to black hole spin and accretion properties

ABSTRACT We analyse the X-ray spectrum of the black hole (BH) X-ray binary MAXI J1820 + 070 using observations from XMM-Newton and NuSTAR during ‘hard’ states of its 2018–2019 outburst. We take a fully Bayesian approach, and this is one of the first papers to present a fully Bayesian workflow for the analysis of an X-ray binary X-ray spectrum. This allows us to leverage the relatively well-understood distance and binary system properties (like inclination and BH mass), as well as information from the XMM-Newton RGS data to assess the foreground X-ray absorption. We employ a spectral model for a ‘vanilla’ disc-corona system: the disc is flat and in the plane perpendicular to the axis of the jet and the BH spin, the disc extends inwards to the innermost stable circular orbit around the BH, and the (non-thermal) hard X-ray photons are up-scattered soft X-ray photons originating from the disc thermal emission. Together, these provide tight constraints on the spectral model and, in combination with the strong prior information about the system, mean we can then constrain other parameters that are poorly understood such as the disc colour correction factor. By marginalizing over all the parameters, we calculate a posterior density for the BH spin parameter, a. Our modelling suggests a preference for low or negative spin values, although this could plausibly be reproduced by higher spins and a modest degree of disc truncation. This approach demonstrates the efficacy and some of the complexities of Bayesian methods for X-ray spectral analysis.

Origin of Phobos and Deimos Awaiting Direct Exploration

Two major hypotheses have been proposed for the origin of the Martian moons Phobos and Deimos: the in situ formation theory, supported by the fact that they have circular orbits nearly parallel to the Martian equator, and the asteroid capture theory, supported by the similarity of their reflectance spectra to those of carbonaceous asteroids. Regarding the in situ formation theory, recent theoretical studies have focused on the huge impact scenario, which proposes that debris ejected into orbits during the formation of a giant impact basin on Mars accumulated to form the Martian moons. On the other hand, gas drag from a Martian gas envelope composed of gravitationally attracted solar nebula gas has been proposed as a mechanism for trapping the approaching asteroidal objects in areocentric orbits. In particular, an object entering a temporarily captured orbit in the Martian gravitational sphere would easily evolve into a fully captured moon with a near-equatorial orbit under realistic gas densities. The upcoming Phobos sample return mission is expected to elucidate the origin of both moons, with implications for material transport in the early Solar System and the early evolution of Mars. ▪The origin of Mars' small moons, Phobos and Deimos, has long been an open question.▪The leading hypotheses are asteroid capture, inferred from their appearance like primitive asteroids, and giant impact, implied by the regularity of their orbits.▪The origin of Phobos will be precisely determined by a sample return mission to be conducted in the late 2020s to early 2030s.▪Determining the origin of the Martian moons will provide clues to clarifying how the parent planet Mars formed and came to have a habitable surface environment.