Equatorial Circular Orbits Research Articles

Dynamics of charged and rotating NUT black holes in Rastall gravity

In this work, the Kerr–Newman-NUT black hole solution in Rastall gravity is proposed and it turns out that the horizon is [Formula: see text] dependence. Black hole dynamics such as the event horizons, ergosurface, zero angular momentum observer (ZAMO), thermodynamic properties, and the equatorial circular orbit around the black hole such as static radius limit, null equatorial circular orbit, and innermost stable circular orbit are investigated in this work. How the NUT and Rastall parameter affect the dynamic of the black hole is also shown.

The effect of nonuniformity of the Earth’s magnetic field on dynamics of electrodynamic space tether system

An electrodynamic space tether system in a circular equatorial orbit under conditions of nonuniformity of the Earth’s magnetic field is considered. The dynamic equations of motion are analyzed to search for equilibrium modes of motion. The oblique equilibrium position of the tether in the orbit plane is found. The stability of the found equilibrium is investigated in linear approximation. The results of numerical modeling are presented.

Ionospheric Experiment with a Low Work Function Tether Loop

An entirely passive and free of consumable ionospheric experiment, based on a low work function tether (LWT) loop with a control unit equipped with some basics sensors at its center, is presented. The loop has a torus shape and a hollow cross-section. It is made of an aluminum substrate coated with a low work function material to stimulate electron emission through thermionic and photoelectric effects. The work presents an electrodynamic model for the experiment and studies the current and voltage profiles developed in the anodic and cathodic segments of the LWT due to the motional electric field. Two modes of operation, with and without switches in the loop to interrupt the electric current, are considered. It is shown that the loop is deorbited by the Lorentz force exerted by the ambient magnetic field on the electric current. An analysis of the attitude dynamics in the presence of the gravity gradient and the Lorentz torques reveals that, for a circular equatorial orbit, the position of the loop with its symmetry axis normal to the orbital plane can be spin-stabilized easily. The required instruments and the scientific information that would be provided by the experiment are discussed.

Publisher’s Note: Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole [Phys. Rev. D 93, 044015 (2016)

Publisher’s Note: Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole [Phys. Rev. D 93, 044015 (2016)

Gravitomagnetism and pulsar beam precession near a Kerr black hole

ABSTRACT A rotating black hole causes the spin axis of a nearby pulsar to precess due to geodetic and gravitomagnetic frame-dragging effects. The aim of our theoretical work here is to explore how this spin precession can modify the rate at which pulses are received on Earth. Towards this end, we obtain the complete evolution of the beam vectors of pulsars moving on equatorial circular orbits in the Kerr space–time, relative to asymptotic fixed observers. We proceed to establish that such spin precession effects can significantly modify observed pulse frequencies and, in specific, we find that the observed pulse frequency rises sharply as the orbit shrinks, potentially providing a new way to locate horizons of Kerr black holes, even if observed for a very short time period. We also discuss implications for detections of sub-millisecond pulsars, pulsar nulling, quasi-periodic oscillations, multiply peaked pulsar Fourier profiles, and how Kerr black holes can potentially be distinguished from naked singularities.

Near-resonance tidal evolution of the Earth-Moon system influenced by orbital-scale climate change**A contributed paper of the International Symposium on Lunar and Planetary Science (ISLPS) on 2018 June 12–15 at Macau University of Science and Technology.

We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and Earth’s rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent and an equatorial circular lunar orbit, considering only the 41 kyr periodicity of Earth’s obliquity ε and the M2 tide, simulations are performed near tidal resonance for 106 yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant ε, that with varying ε is slowed down; the Earth-Moon distance oscillates in phase with ε before the resonance maximum but exactly out of phase after that; the displacement of the oscillation is in positive correlation with the difference between oceanic frequency and tidal frequency.

Gravitational waves from bodies orbiting the Galactic center black hole and their detectability by LISA

Aims.We present the first fully relativistic study of gravitational radiation from bodies in circular equatorial orbits around the massive black hole at the Galactic center, Sgr A* and we assess the detectability of various kinds of objects by the gravitational wave detector LISA.Methods.Our computations are based on the theory of perturbations of the Kerr spacetime and take into account the Roche limit induced by tidal forces in the Kerr metric. The signal-to-noise ratio in the LISA detector, as well as the time spent in LISA band, are evaluated. We have implemented all the computational tools in an open-source SageMath package, within the Black Hole Perturbation Toolkit framework.Results.We find that white dwarfs, neutrons stars, stellar black holes, primordial black holes of mass larger than 10−4 M⊙, main-sequence stars of mass lower than ∼2.5 M⊙, and brown dwarfs orbiting Sgr A* are all detectable in one year of LISA data with a signal-to-noise ratio above 10 for at least 105years in the slow inspiral towards either the innermost stable circular orbit (compact objects) or the Roche limit (main-sequence stars and brown dwarfs). The longest times in-band, of the order of 106years, are achieved for primordial black holes of mass ∼10−3 M⊙down to 10−5 M⊙, depending on the spin of Sgr A*, as well as for brown dwarfs, just followed by white dwarfs and low mass main-sequence stars. The long time in-band of these objects makes Sgr A* a valuable target for LISA. We also consider bodies on close circular orbits around the massive black hole in the nucleus of the nearby galaxy M 32 and find that, among them, compact objects and brown dwarfs stay for 103–104years in LISA band with a one-year signal-to-noise ratio above ten.

Simulations of imaging the event horizon of Sagittarius A* from space

Context. It has been proposed that Very Long Baseline Interferometry (VLBI) at submillimeter waves will allow us to image the shadow of the black hole in the center of our Milky Way, Sagittarius A* (Sgr A*), and thereby test basic predictions of the theory of general relativity.Aims. This paper presents imaging simulations of a new Space VLBI (SVLBI) mission concept. An initial design study of the concept has been presented in the form of the Event Horizon Imager (EHI). The EHI may be suitable for imaging Sgr A* at high frequencies (up to ∼690 GHz), which has significant advantages over performing ground-based VLBI at 230 GHz. The concept EHI design consists of two or three satellites in polar or equatorial circular medium-Earth orbits (MEOs) with slightly different radii. Due to the relative drift of the satellites along the individual orbits over the course of several weeks, this setup will result in a dense spiral-shapeduv-coverage with long baselines (up to ∼60 Gλ), allowing for extremely high-resolution and high-fidelity imaging of radio sources.Methods. We simulated observations of general relativistic magnetohydrodynamics (GRMHD) models of Sgr A* for the proposed configuration and calculate the expected noise based on preliminary system parameters. On long baselines, where the signal-to-noise ratio may be low, fringes could be detected assuming that the system is sufficiently phase stable and the satellite orbits can be reconstructed with sufficient accuracy. Averaging visibilities accumulated over multiple epochs of observations could then help improving the image quality. With three satellites instead of two, closure phases could be used for imaging.Results. Our simulations show that the EHI could be capable of imaging the black hole shadow of Sgr A* with a resolution of 4μas (about 8% of the shadow diameter) within several months of observing time.Conclusion. Our preliminary study of the EHI concept shows that it is potentially of high scientific value. It could be used to measure black hole shadows much more precisely than with ground-based VLBI, allowing for stronger tests of general relativity and accretion models.

Effect of ionospheric drag on atmospheric density estimation and orbit prediction

Accurate prediction of aerodynamic forces in Low Earth Orbit (LEO) remains a key challenge for space situational awareness (SSA) and space traffic management (STM) activities. A neglected aspect of the LEO aerodynamics problem is the force resulting from the charged aerodynamic interaction of LEO objects with the ionosphere, i.e. ionospheric aerodynamics. This work studies the effect accounting for ionospheric drag may have on the motion of LEO objects. This work aims to assess the influence of ionospheric aerodynamics on atmospheric density estimation and orbit prediction capabilities essential to SSA and STM services. The approach taken in this work was to apply Particle-in-Cell (PIC) simulations to develop a surrogate model that describes the variation of a charged drag coefficient (CD,C) as a function of plasma scaling parameters. This surrogate model was then incorporated into an orbit propagator, and the influence of ionospheric drag on body motion is studied for a range of conditions. Results indicate that, when inferring atmospheric neutral density from orbit data, neglecting the contribution of ions without accounting for electrodynamic phenomena, may cause an over-prediction of neutral density ranging between 1% and 45% for the space weather condition considered (F10.7=150,ap=5). Including electrodynamic phenomena was seen to increase this over-prediction for all cases. Objects with thick plasma sheaths were shown to be particularly sensitive to ionospheric drag forces; thick plasma sheaths caused by either a reduction in object scale (rB) or increase in surface potential (ϕ). This result has important implications for modelling space debris populations as thick plasma sheaths may arise at natural floating potentials (-0.75V) when debris fragmentation occurs. For example, accounting ionospheric drag on a spherical debris object with a radius of 0.005 m, area-to-mass ratio of 0.0157 m2/kg and floating potential of -0.75 V in a circular equatorial orbit at 350 km altitude was predicted to cause a change in along-track position of 299 m (and a reduction in semi-major axis of 4 m) over a 24-h period. Results also have important implications for modern satellites, where the trend is toward nano/micro-satellite platforms (e.g. CubeSats) with high-voltage powers systems that may inadvertently cause large artificial surface potentials and therefore enhanced ionospheric aerodynamic forces.

System Design for the Event Horizon Imaging Experiment Using the PECMEO Concept

The concept for space interferometry from Polar or Equatorial Circular Medium Earth Orbits (the PECMEO concept) is a promising way to acquire the image of the “shadow” of the event horizon of Sagittarius A^* with an angular resolution of circa 5 microarcseconds. The concept is intended to decrease the size of the main reflector of the instrument to about 3 m using a precise orbit reconstruction based on Global Navigation Satellite System (GNSS) navigation, inter-satellite range and range-rate measurements, and data from the Attitude and Orbit Determination System (AODS). The paper provides the current progress on the definition of the subsystems required for the concept on the basis of simulations, radio regulations, and available technology. The paper proposes the requirement for the localization of the phase centre of the main reflector. The paper provides information about the visibility of GNSS satellites and the needed accuracies of the AODS. The paper proposes the frequency plan for the instrument and its Inter-Satellite Links (ISLs). The concepts for measurement of range and range rate using ISLs (as well as for the data exchange at these ISLs) are presented. The block diagram of the interferometer is described and its sensitivity is estimated. The link budget for both ISLs is given as well as their critical components. The calculated measurement quality factors are given. The paper shows the expected performance of the sub-systems of the interferometer. The requirements for the localization of the main reflectors and the information about the availability of the GNSS satellites are based on the simulations results. The frequency plan is obtained according to the PECMEO concept and taking into account the radio regulations. The existing technology defines the accuracies of the AODS as well as the link budgets and the measurement accuracies for both ISLs and the sensitivity of the instrument. The paper provides input information for the development of the orbit reconstruction filter and the whole PECMEO system.

Space-to-space Radio Interferometry System from Medium Earth Orbits

This paper presents a new concept to perform space-to-space Very Long Baseline Interferometry which enables the imaging of cosmic sources at high-resolution and high-sensitivity with small antennas. Several individual apertures are embarked on separate identical satellites staggered in height into Polar or Equatorial Circular Medium Earth Orbits (PECMEO orbits). These orbits are stable and allow GNSS-based on-the-fly centimeter-level relative positioning. Coherent operation is possible by exchanging local oscillator components and measured signals through Inter-Satellite Links (ISL). On-board cross correlation is performed at each satellite over a delay window compatible with the accuracy of the on-the-fly relative positioning and the result sent to the ground. Image reconstruction is completed on the ground thanks to sub-millimeter baseline retrieval from accurate GNSS orbits, ISL ranging and spacecraft attitude information. The application of this concept to image the Super Massive Black Hole Sgr A^* is hinted.

Completely New Gravitational Physics: The Ingenious Outside-Inside Centrifuge Mechanism of Gravity Clarified

The present work implements the idea that gravity is not a fundamental force and that the observed gravitational dynamics is the result of inertial motions within a Keplerian velocity field of the Higgs Quantum Space (HQS), giving mass and ruling the inertial motions of matter-energy. The Higgs theory introduces profound changes in the current view about the nature of empty space. It introduces the idea that a real quantum fluid medium, filling up the whole of space, gives mass to the elementary particles by the Higgs mechanism, an effect analogous to the Meissner effect, giving mass to the photons within superconductors. This HQS necessarily governs the inertial motion of matter-energy and is the locally ultimate reference for rest and for motions. The HQS materializes the local Lorentz frames (LFs), turning them into local proper LFs, intrinsically stationary with respect to the local moving HQS. This HQS also necessarily is responsible for the gravitational dynamics; because it is mass that creates the gravitational fields. The observed absence of the gravitational slowing of the GPS clocks by the solar field and the absence of light anisotropy with respect to the moving earth are both obvious signatures of the true physical mechanism of gravity. These observations demonstrate that the HQS is circulating round the sun and round earth according to Keplerian velocity fields (GM/r)1/2, closely consistent respectively with the planetary motions and the orbital motion of the Moon. In this Keplerian velocity field the planets are closely stationary with respect to the local HQS and carried by the moving HQS round the sun without the need of a central force field. The Keplerian velocity field of the HQS is the only possible imaginable mechanism able to give rise to the ingenious outside-inside centrifuge mechanism of gravity that creates a central field of centrifugal forces toward the gravitational center on all matter bodies not moving strictly along direct circular equatorial orbits. The Keplerian velocity field of the HQS is shown to appropriately create all the observed effects of the gravitational fields on matter, on light and on clocks.

Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are repeated for static observers in the naked singularity background, and strong enhancement of the Lense-Thirring precession frequency compared to the black hole case is established. Then, we study the nature of tidal forces in the rotating naked singularity background, in Fermi normal coordinates. Here, physical quantities characterizing tidal disruptions of celestial objects in equatorial circular orbits are computed numerically. Our results here indicate that there might be significant deviations from corresponding Kerr black hole calculations, up to the level of approximation that we consider.

On the prospects of imaging Sagittarius A* from space

AbstractVery Long Baseline Interferometry (VLBI) at sub-millimeter waves has the potential to image the shadow of the black hole in the Galactic Center, Sagittarius A* (Sgr A*), and thereby test basic predictions of the theory of general relativity. We investigate the imaging prospects of a new Space VLBI mission concept. The setup consists of two satellites in polar or equatorial circular Medium-Earth Orbits with slightly different radii, resulting in a dense spiral-shaped uv-coverage with long baselines, allowing for extremely high-resolution and high-fidelity imaging of radio sources. We simulate observations of a general relativistic magnetohydrodynamics model of Sgr A* for this configuration with noise calculated from model system parameters. After gridding the uv-plane and averaging visibilities accumulated over multiple months of integration, images of Sgr A* with a resolution of up to 4 μ as could be reconstructed, allowing for stronger tests of general relativity and accretion models than with ground-based VLBI.

Accretion disks around black holes in scalar-tensor-vector gravity

Scalar-tensor-vector gravity (STVG) is an alternative theory of gravitation that has successfully explained the rotation curves of nearby galaxies, the dynamics of galactic clusters, and cosmological data without dark matter, but has hardly been tested in the strong gravity regime. In this work, we aim at building radiative models of thin accretion disks for both Schwarzschild and Kerr black holes in STVG theory. In particular, we study stable circular equatorial orbits around stellar and supermassive black holes in Schwarzschild and Kerr STVG spacetimes. We also calculate the temperature and luminosity distributions of accretion disks around these objects. We find that accretion disks in STVG around stellar and supermassive black holes are colder and less luminous than in GR. The spectral energy distributions obtained do not contradict current astronomical observations.

Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with non-zero angular velocity $\Omega$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are finite and regular for NS everywhere except at the singularity itself. Therefore a genuine detection of the event horizon becomes possible in this case. We also show that for a near-extremal NS ($1<a_* < 1.1$), characteristic features appear in the radial profiles of the precession frequency, using which we can further distinguish a near-extremal NS from a BH, or even from NS with larger angular momentum. We then investigate the Lense-Thirring (LT) precession or nodal plane precession frequency of the accretion disk around a BH and NS to show that clear distinctions exist for these configurations in terms of radial variation features. The LT precession in equatorial circular orbits increases with approach to a BH, whereas for NS it increases, attains a peak and then decreases. Interestingly, for $a_*=1.089$, it decreases until it vanishes at a certain radius, and acquires negative values for $a_* > 1.089$ for a certain range of $r$. For $1<a_*<1.089$, a peak appears, but the LT frequency remains positive definite. There are important differences in accretion disk LT frequencies for BH and NS and since LT frequencies are intimately related to observed QPOs, these features might allow us to determine whether a given rotating compact astrophysical object is BH or NS.

Secular evolution of the orbits of hypothetical satellites of Uranus

The problem of the secular perturbations of the orbit of a test satellite with a negligible mass caused by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun is considered. In contrast to the previous studies of this problem, an analytical expression for the full averaged perturbing function has been derived for an arbitrary orbital inclination of the test satellite. A numerical method has been used to solve the evolution system at arbitrary values of the constant parameters and initial elements. The behavior of some set of orbits in the region of an approximately equal influence of the perturbing factors under consideration has been studied for the satellite system of Uranus on time scales of the order of tens of thousands of years. The key role of the Lidov–Kozai effect for a qualitative explanation of the absence of small bodies in nearly circular equatorial orbits with semimajor axes exceeding ~1.8 million km has been revealed.

Designing nonuniform satellite systems for continuous global coverage using equatorial and polar circular orbits

We present a method for designing nonuniform satellite systems for continuous global coverage using a combination of equatorial and near-polar satellite segments in circular orbits. Equations are derived to determine the basic design parameters of the satellite system itself and the conditions of its closure at the joint of near-polar and equatorial segments. We analyze specific features of near-polar and equatorial satellite systems and their advantages and disadvantages compared with existing classes of near-polar phased and kinematically correct satellite systems. We estimate the minimum required number of spacecrafts in satellite systems for a given fold of coverage and present calculated dependences for classes of near-polar phased and equatorial satellite systems with different types of closure. For the class of kinematically correct satellite systems, we analyze the characteristics of systems with a minimum spacecraft flight height and reveal that the number of satellites in the orbital plane depends on the flight height for different folds of coverage. We bring examples of the best near-polar equatorial satellite systems of global coverage for different folds and a class of satellite systems with a fixed number of spacecrafts and orbital planes in them.

Test particles in a magnetized conformastatic spacetime

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function, which generates a singularity-free and asymptotically flat spacetime that describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles and the corresponding explicit value in the case of a punctual magnetic mass. We show that the analytical expressions obtained from our analysis are sufficient for being confronted with observations in order to establish whether such objects can exist in nature.

Symmetric oscillations of charged gyrostat in weakly elliptical orbit with small inclination

This paper deals with a gyrostat satellite in a weakly elliptical near-Earth orbit with small inclination. The gyrostat is supplied with flywheel and possesses electrostatic charge and intrinsic magnetic moment. The gyrostat attitude motion under the action of Lorentz, magnetic and gravity-gradient torques is studied. It is shown that the system of differential equations for attitude motion of gyrostat with triaxial ellipsoid of inertia is reversible with two fixed sets. In the case of a spherical ellipsoid of inertia, the third fixed set occurs. It is revealed that two of these three sets correspond to the respective sets of the generating problem, that is, in the case of a circular equatorial orbit. It is made clear what the families of symmetric oscillations of the generating problem bifurcate and give rise to isolated oscillations. Thus, all periodic oscillations are found for gyrostat with equal moments of inertia on weakly elliptic orbit with small inclination.