Geodetic Precession Research Articles

A search for Planet Nine with small spacecraft: Three-body, post-Newtonian, non-gravitational, planetary and Kuiper Belt effects

A hypothetical gravitating body in the outer Solar System, the so-called Planet Nine, was proposed to explain the unexpected clustering of the Kuiper Belt Objects. As it has not been observed via telescopes, it was conjectured to be a primordial black hole (of the size of a quince) that could be gravitationally detected by laser-launching or solar sailing many small spacecraft. Here, we study various aspects that will affect such a search for Planet Nine. Our basic observable is the angular displacement in the trajectory of a small spacecraft which will be mainly affected by the gravity of Planet Nine, augmented with several other 3-body, non-gravitational, post-Newtonian, planetary and Kuiper Belt effects. First, we calculate the effect of the Sun in the framework of the circular restricted three-body problem of the Sun–Planet Nine-spacecraft for the two particular initial conditions. Then, we study the effects of Kuiper Belt and outer planets, namely Jupiter, Saturn, Uranus, Neptune, as well as non-gravitational perturbations such as magnetic and drag forces exerted by the interstellar medium; and the solar radiation pressure. In addition, we investigate the post-Newtonian general relativistic effects such as the frame-dragging, Schwarzschild effect, and geodetic precession on the spacecraft trajectory. We show that the leading order angular displacement is due to the solar radiation pressure for the lower spacecraft velocities, and the drag force for the higher spacecraft velocities. Among the general relativistic effects, the frame-dragging has the smallest effect; and the Schwarzschild effect due to Sun has the largest effect. However, none of the general relativistic effects produces a meaningful contribution to the detection.

Two Models for the Orbital Modulation of Gamma Rays in Cyg X-3

We model the currently available γ-ray data on Cyg X-3 from the Fermi Large Area Telescope. Thanks to Cyg X-3’s very strong γ-ray activity during 2018–2021, the data quality has significantly improved. We study the strong orbital modulation of the γ-rays observed at high γ-ray fluxes. The modulation, as found earlier, is well modeled by anisotropic Compton scattering of the donor blackbody emission by relativistic electrons in a jet strongly misaligned with respect to the orbital axis. We confirm that this model fits well both the average γ-ray modulation light curve and the spectrum. However, we find that if the jet were aligned with the spin axis of a rotating black hole, it would undergo geodetic precession with a period of ∼50 yr. However, its presence is ruled out by both the γ-ray and radio data. Therefore, we consider an alternative model in which the average jet direction is aligned, but it is bent outside the orbit owing to the thrust of the donor stellar wind, and thus precesses at the orbital period. The γ-ray modulation then appears as a result of the variable Doppler boosting of synchrotron self-Compton jet emission. This model also fits the data well. However, the fitted bending angle is much larger than the theoretical one based on the binary and wind parameters as currently known. Thus, both models disagree with important aspects of our current theoretical understanding of the system. We discuss possible ways to find the correct model.

Motion of massive particles and geodetic precession in the spacetime of a Galilean rotating observer in the Schwarzschild background

Motion of massive particles and geodetic precession in the spacetime of a Galilean rotating observer in the Schwarzschild background

Multipole expansion of the gravitational field in a general class of fourth-order theories of gravity and the application in gyroscopic precession

A viable weak-field and slow-motion approximation method is constructed in F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity, a general class of fourth-order theories of gravity. By applying this method, the metric, presented in the form of the multipole expansion, outside a spatially compact source up to 1/c 3 order is provided, and the closed-form expressions for the source multipole moments are all presented explicitly. The metric consists of the massless tensor part, the massive scalar part, and the massive tensor part, where the former is exactly the metric in General Relativity, and the latter two are the corrections to it. It is shown that the corrections bear the Yukawa-like dependence on the two massive parameters and predict the appearance of six additional sets of source multipole moments, which indicates that up to 1/c 3 order, there exist six degrees of freedom beyond General Relativity within F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity. By means of the metric, for a gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of the Thomas precession, the geodetic precession, and the Lense-Thirring precession are derived, and from them, the corrections to the angular velocities of the three types of precession in General Relativity can be read off. These results indicate that differently from f(R) or f(R,𝒢) gravity, the most salient feature of the general F(R, RμνRμν, Rμν ρσRμν ρσ ) gravity is that it gives the nonvanishing correction to the gyroscopic spin's angular velocity of the Lense-Thirring precession in General Relativity.

Observational tests of asymptotically flat R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} spacetimes

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.

A VLBA-uGMRT search for candidate binary black holes: study of six X-shaped radio galaxies with double-peaked emission lines

ABSTRACT Identifying methods to discover dual active galactic nucleus (AGN) has proven to be challenging. Several indirect tracers have been explored in the literature, including X/S-shaped radio morphologies and double-peaked (DP) emission lines in the optical spectra. However, the detection rates of confirmed dual AGN candidates from the individual methods remain extremely small. We search for binary black holes (BBH) in a sample of six sources that exhibit both X-shaped radio morphology and DP emission lines using the Very Long Baseline Array (VLBA). Three out of the six sources show dual VLBA compact components, making them strong candidates for BBH sources. In addition, we present deep uGMRT images revealing the exquisite details of the X-shaped wings in three sources. We present a detailed precession modeling analysis of these sources. The black hole separations estimated from the simplistic geodetic precession model are incompatible with those estimated from emission line offsets and the VLBA separations. However, precession induced by a non-coplanar secondary black hole is a feasible mechanism for explaining the observed X-shaped radio morphologies and the black hole separations estimated from other methods. The black hole separations estimated from the double-peaked emission lines agree well with the VLBA compact component separations. Future multifrequency VLBA observations will be critical in ruling out or confirming the BBH scenario in the three galaxies with dual component detections.

A MeerKAT view of the double pulsar eclipses

The double pulsar system, PSR J0737−3039A/B, consists of two neutron stars bound together in a highly relativistic orbit that is viewed nearly edge-on from the Earth. This alignment results in brief radio eclipses of the fast-rotating pulsar A when it passes behind the toroidal magnetosphere of the slow-rotating pulsar B. The morphology of these eclipses is strongly dependent on the geometric orientation and rotation phase of pulsar B, and their time evolution can be used to constrain the geodetic precession rate of the pulsar. We demonstrate a Bayesian inference framework for modelling high-sensitivity eclipse light curves obtained with MeerKAT between 2019 and 2023. Using a hierarchical inference approach, we obtained a precession rate of ΩSOB = 5.16°−0.34°+0.32° yr−1 (68% confidence intervals) for pulsar B, consistent with predictions from general relativity to a relative uncertainty of 6.5%. This updated measurement provides a 6.1% test of relativistic spin-orbit coupling in the strong-field regime. We show that a simultaneous fit to all of our observed eclipses can in principle return a ∼1.5% test of spin-orbit coupling. However, systematic effects introduced by the current geometric orientation of pulsar B along with inconsistencies between the observed and predicted eclipse light curves result in difficult to quantify uncertainties when using this approach. Assuming the validity of general relativity, we definitively show that the spin axis of pulsar B is misaligned from the total angular momentum vector by 40.6° ±0.1° and that the orbit of the system is inclined by approximately 90.5° from the direction of our line of sight. Our measured geometry for pulsar B suggests the largely empty emission cone contains an elongated horseshoe-shaped beam centred on the magnetic axis, and that it may not be re-detected as a radio pulsar until early 2035.

Geodetic precession and shadow of quantum extended black holes

We study the circular motion of massive and massless particles in a recently proposed quantum-corrected Schwarzschild black hole in loop quantum gravity. This solution is supposed to introduce small but non-zero quantum corrections in the low curvature limit. In this paper, we confine our attention to the shadow of the black hole and the geodetic precession (GP) of a freely falling gyroscope in a circular orbit. Despite the mathematical complexity of the metric, our results are exact and show that the black hole shadow decreases slightly in this solution while the quantum corrections introduce a non-trivial term in the GP frequency of the gyroscope.

Gravitoelectromagnetic Field Strength Tensor in Flat Spacetime Frame: Dynamics of a Gyroscope in the Earth’s Gravitational Field

In this article, we develop gravitoelectromagnetism (GEM) as a formal relativistic theory of gravitation characterized by a field potential fourvector in a flat (Minkowski) spacetime frame. By reorganizing the Lense-Thirring spacetime metric of linearized general relativity, we have determined the appropriate field potential four-vector and the field strength tensor which generates dynamics in the GEM field. The general covariant equation of motion of the spin four-vector of a gyroscope driven by the GEM field strength tensor provides the expected form of the frame-dragging and geodetic effects after introducing a gyromagnetic ratio η = 4 as an internal dynamical property of the gyroscope.

Зависимость геодезической прецессии от выбора системы координат на примере галилеевых спутников Юпитера

The relativistic effect of geodetic precession in the rotation of Jupiter and its Galilean moons (Io, Europa, Ganymede and Callisto) are investigated. For this purpose, the method developed in (Pashkevich, 2016) was modified, which is applicable for studying any bodies of the Solar System that have long-term ephemeris. As a result of its application, the most significant secular terms of geodetic precession were determined. In this study, the values of the angular velocity vectors of the geodetic rotation of the Galilean satellites of Jupiter relative to the barycenter of the Solar System and relative to the barycenter of the system of Jupiter satellites were calculated. Their differences are shown depending on the choice of coordinate reference system due to the asymmetry of the formula for the angular velocity vector of geodetic rotation for any solar system bodies used for these calculations. The obtained analytical values of the geodetic precession of the rotation parameters of the studied objects can be used for the numerical study of their rotation in the relativistic approximation.

Multiscale constraints on scalar-field couplings to matter: The geodetic and frame-dragging effects

Multiscale constraints on scalar-field couplings to matter: The geodetic and frame-dragging effects

New constraints on the kinematic, relativistic, and evolutionary properties of the PSR J1757−1854 double neutron star system

ABSTRACT PSR J1757−1854 is one of the most relativistic double neutron star binary systems known in our Galaxy, with an orbital period of $P_\text{b}=4.4\, \text{h}$ and an orbital eccentricity of e = 0.61. As such, it has promised to be an outstanding laboratory for conducting tests of relativistic gravity. We present the results of a 6-yr campaign with the 100-m Green Bank and 64-m Parkes radio telescopes, designed to capitalize on this potential. We identify secular changes in the profile morphology and polarization of PSR J1757−1854, confirming the presence of geodetic precession and allowing the constraint of viewing geometry solutions consistent with General Relativity. We also update PSR J1757−1854’s timing, including new constraints of the pulsar’s proper motion, post-Keplerian parameters, and component masses. We conclude that the radiative test of gravity provided by PSR J1757−1854 is fundamentally limited to a precision of 0.3 per cent due to the pulsar’s unknown distance. A search for pulsations from the companion neutron star is also described, with negative results. We provide an updated evaluation of the system’s evolutionary history, finding strong support for a large kick velocity of $w\ge 280\, \rm{km\,s}^{-1}$ following the second progenitor supernova. Finally, we reassess PSR J1757−1854’s potential to provide new relativistic tests of gravity. We conclude that a 3-σ constraint of the change in the projected semimajor axis ($\dot{x}$) associated with Lense–Thirring precession is expected no earlier than 2031. Meanwhile, we anticipate a 3-σ measurement of the relativistic orbital deformation parameter δθ as soon as 2026.

Precession and Lense-Thirring effect of hairy Kerr spacetimes

We investigate the frame-dragging effect of the hairy Kerr spacetimes on the spin of a test gyro and accretion disk. First, we analyze Lense-Thirring (LT) precession frequency, geodetic precession frequency, and the general spin precession frequency of a test gyro attached to a stationary observer in the spacetime. We find that the black hole hair suppresses those precession frequencies in comparison with that which occurs in Kerr spacetime in general relativity. Moreover, using those frequencies as a probe, we differentiate the hairy Kerr black hole (BH) from naked singularity (NS). Specifically, as the observer approaches the central source along any direction, the frequencies grow sharply for the hairy Kerr BH, while for the hairy NS they are finite except at the ring singularity. Then, we investigate the quasiperiodic oscillations (QPOs) phenomena as the accretion disk approaches the hairy Kerr BH or NS. To this end, we analyze the bound circular orbits and their perturbations. We find that as the orbits approach the corresponding innermost stable circular orbit (ISCO), both LT precession frequency and periastron precession frequency behave differently in the hairy Kerr BH and NS. Additionally, the hairy parameters have significant effects on the two frequencies. We expect that our theoretical studies could shed light on astrophysical observations in distinguishing hairy theories from Einstein's gravity, and also in distinguishing BH from NS in spacetime with hair.

Relativistic contributions to the rotation of Mars

Context. The orientation and rotation of Mars can be described by a set of Euler angles (longitude, obliquity, and rotation angles) and estimated from radioscience data (tracking of orbiters and landers), which can then be used to infer the planet's internal properties. The data are analyzed using a modeling expressed within the barycentric celestial reference system (BCRS). This modeling includes several relativistic contributions that need to be properly taken into account to avoid any misinterpretation of the data. Aims. We provide new and more accurate (to the 0.1 mas level) estimations of the relativistic corrections to be included in the BCRS model of the orientation and rotation of Mars. Methods. There are two types of relativistic contributions with regard to Mars's rotation and orientation: (i) those that directly impact the Euler angles and (ii) those resulting from the time transformation between a local Mars reference frame and BCRS. The former contribution essentially corresponds to the geodetic effect, as well as to the smaller Lense-Thirring and Thomas precession effects, and we computed their values assuming that Mars evolves on a Keplerian orbit. As for the latter contribution, we computed the effect of the time transformation and compared the rotation angle corrections obtained, based on the assumption that the planets evolve on Keplerian orbits, with the corrections obtained, based on realistic orbits as described by the ephemerides. Results. The relativistic correction in longitude mainly comes from the geodetic effect and results in a geodetic precession (6.754 mas yr−1) and geodetic annual nutation (0.565 mas amplitude). For the rotation angle, the correction is dominated by the effect of the time transformation. The main annual, semiannual, and terannual terms display amplitudes of 166.954 mas, 7.783 mas, and 0.544 mas, respectively. The amplitude of the annual term differs by about 9 mas from the estimate usually considered by the community. We identified new terms at the Mars-Jupiter and Mars-Saturn synodic periods (0.567 mas and 0.102 mas amplitude) that are relevant considering the current level of uncertainty of the measurements, as well as a contribution to the rotation rate (7.3088 mas day−1). There is no significant correction that applies to the obliquity.

Constraints on ultralight axions, vector gauge bosons, and unparticles from geodetic and frame-dragging measurements

The geodetic and frame-dragging effects are the direct consequences of the spacetime curvature near Earth which can be probed from the Gravity probe B (GP-B) satellite. The satellite result matches quite well with Einstein’s general relativistic result. The gyroscope of the satellite which measures the spacetime curvature near Earth contains lots of electrons and nucleons. Ultralight axions, vector gauge bosons, and unparticles can interact with these electrons and nucleons through different spin-dependent and spin-independent operators and change the drift rate of the gyroscope. Some of these ultralight particles can either behave as a long range force between some dark sector or Earth and the gyroscope or they can behave as a background oscillating dark matter fields or both. These ultralight particles can contribute an additional precession of the gyroscopes, limited to be no larger than the uncertainty in the GP-B measurements. Compared with the experimental results, we obtain bounds on different operator couplings.

Relativistic Effects in the Rotation of Dwarf Planets and Asteroids

Abstract The effect of the geodetic rotation (which includes two relativistic effects: geodetic precession and geodetic nutation) is the most significant relativistic effect in the rotation of the celestial bodies. For the first time in this research, this relativistic effect is determined in the rotation of dwarf planets (Ceres, Pluto, and Charon) and asteroids (Pallas, Vesta, Lutetia, Europa, Ida, Eros, Davida, Gaspra, Steins, and Itokawa) in the Solar System with known values of their rotation parameters. Calculations of the values of their geodetic rotation are made by a method for studying any bodies in the Solar System with a long-term ephemeris. Values of geodetic precession and geodetic nutation for all these celestial bodies were calculated in ecliptic Euler angles relative to their proper coordinate systems and in their rotational elements relative to the fixed equator of the Earth and the vernal equinox (at the epoch J2000.0). The obtained analytical values of the geodetic rotation for the celestial bodies can be used to numerically investigate their rotation in the relativistic approximation, and also used to estimate the influence of relativistic effects on the orbital–rotational dynamics for the bodies of exoplanetary systems.

Relativistic Effect of Geodetic Precession in the Rotation of Dwarf Planets and Asteroids of the Solar System

Relativistic Effect of Geodetic Precession in the Rotation of Dwarf Planets and Asteroids of the Solar System

Investigating bounds on the extended uncertainty principle metric through astrophysical tests

In this paper, we consider the gravitational tests for the extended uncertainty principle (EUP) metric, which is a large-scale quantum correction to Schwarzschild metric. We calculate gravitational redshift, geodetic precession, Shapiro time delay, precession of Mercury and S2 star's orbits. Using the results of experiments and observations, we obtain the lower bounds for the EUP fundamental length scale . We obtain the smallest bound for gravitational redshift, and the largest bound for the precession of S2's orbit.

Spin Precession in the Gravity Wave Analogue Black Hole Spacetime

It was predicted that the spin precession frequency of a stationary gyroscope shows various anomalies in the strong gravity regime if its orbit shrinks, and eventually, its precession frequency becomes arbitrarily high very close to the horizon of a rotating black hole. Considering the gravity waves of a flowing fluid with a vortex in a shallow basin, which acts as a rotating analogue black hole, one can observe the predicted strong gravity effect on the spin precession in the laboratory. Attaching a thread with the buoyant particles and anchoring it to the bottom of the fluid container with a short-length miniature chain, one can construct a simple local test gyroscope to measure the spin precession frequency in the vicinity of the gravity wave analogue black hole. The thread acts as the axis of the gyroscope. By regulating the orbital frequency of the test gyroscope, one can also measure the strong gravity Lense–Thirring effect and geodetic/de-Sitter effect with this experimental set-up as the special cases. For example, to measure the Lense–Thirring effect, the length of the miniature chain can be set to zero, so that the gyroscope becomes static. One can also measure the geodetic precession with this system by orbiting the test gyroscope in the so-called Keplerian frequency around the non-rotating analogue black hole that can be constructed by making the rotation of the fluid/vortex negligible compared to its radial velocity.

Geodetic Precession of the Sun, Solar System Planets, and their Satellites

Abstract The effect of the geodetic precession is the most significant relativistic effect in the rotation of celestial bodies. In this article, the new geodetic precession values for the Sun, the Moon, and the Solar System planets have been improved over the previous version by using more accurate rotational element values. For the first time, the relativistic effect of the geodetic precession for some planetary satellites (J1–J4, S1–S6, S8–S18, U1–U15, N1, and N3–N8) with known quantities of the rotational elements was studied in this research. The calculations of the values of this relativistic effect were carried out by the method for studying any bodies of the Solar System with long-time ephemeris. As a result, the values of the geodetic precession were first determined for the Sun, planets in their rotational elements, and for the planetary satellites in the Euler angles relative to their proper coordinate systems and in their rotational elements. In this study, with respect to the previous version, additional and corrected values of the relativistic influence of Martian satellites (M1 and M2) on Mars were calculated. The largest values of the geodetic rotation of bodies in the Solar System were found in Jovian satellite system. Further, in decreasing order, these values were found in the satellite systems of Saturn, Neptune, Uranus, and Mars, for Mercury, for Venus, for the Moon, for the Earth, for Mars, for Jupiter, for Saturn, for Uranus, for Neptune, and for the Sun. First of all, these are the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14) and the satellites of Saturn: Pan (S18), Atlas (S15), Prometheus (S16), Pandora (S17), Epimetheus (S11), Janus (S10), and Mimas (S1), whose values of geodetic precession are comparable to the values of their precession. The obtained numerical values for the geodetic precession for the Sun, all the Solar System planets, and their satellites (E1, M1, M2, J1–J5, J14–J16, S1–S6, S8–S18, U1–U15, N1, and N3–N8) can be used to numerically study their rotation in the relativistic approximation and can also be used to estimate the influence of relativistic effects on the orbital–rotational dynamics of bodies of exoplanetary systems.