Periodicity of the ejection of superluminal components in 3C345

The search for periodic behavior in Blazars has been an important subject,which is helpful for providing significant clues to the structure and physical processes of their central energy engine. A binary black hole system has recently been suggested for causing precession of relativistic jets and rotation of the ejection position angle of VLBI knots in superluminal sources. It has been suggested that in QSO 3C345, the ejection direction of the superluminal knots rotates due to the precession of the central engine and thus the ejection position angle of the successive knots shows a periodic behavior. Some authors argue for a period of precession being～5.6 yr (Abraham & Caproni), ～8-10 yr (Klare et al.) and～9.5 yr (Lobanov & Roland). Applying the helical model proposed by Qian et al. and selecting appropriate parameters to fit the initial trajectories (within 0.3 mas) of all the components (C4 to C10), we derive the relation between the ejection position angle of the components and their precession phase, and thus find a 6.9-year precession period (4.3 yr in the source frame), which can fit the ejection position angle of all these superluminal knots well. Since the VLBI observations have covered more than two precession periods, confirmation in one or more future periods would be important.In addition, we emphasize that the initial parts of the trajectories of these knots can be fitted by a common helical pattern (channel) through a precessing of its initial phase.This scenario (or helical precessing model) is different from the usual ballistic precessing model in which the individual superluminal knots move along straight-lines after ejection (Tateyama & Kingham).     

Relativistic Celestial Mechanics on the verge of its 100 year anniversary

As we are now approaching 2015, both the General Relativity Theory (GRT) and the relativistic Celestial Mechanics based on it will soon arrive at their 100 year anniversaries. There is no border between Newtonian and relativistic Celestial Mechanics. The five-decade period of intensive development of Celestial Mechanics in the second half of the 20th century left many interesting techniques and problems uncompleted. This lecture reviews some problems of Newtonian and relativistic Celestial Mechanics worthy of further investigation. Concerning Newtonian mechanics, these problems include general solution of the three-body problem by means of the series of polynomials, construction of the short-term and long-term theories of motion using the fast converging elliptic function expansions, and representation of the rotation of the planets in the form compatible with the General Planetary Theory reducing the problem to the combined secular system for translatory motion and rotation. Relativistic problems considered here include the determination of the main relativistic effects in the motion of a satellite, e.g. the Moon, and in the rotation of the primary planet using the Newtonian theories of motion and rotation combined with the relativistic transformation of the reference systems, the use of the linearized weak-field GRT metric as a basis of relativistic Celestial Mechanics in the post-Newtonian approximation, and the motion of the Solar System bodies at the cosmological background in the framework of the basic cosmological models. The exposition of the chosen relativistic problems is preceded by reminding the basic features of relativistic Celestial Mechanics with discussing some present tendencies concerning the Parametrized Post-Newtonian formalism, International Astronomical Union resolutions, and standardization of the GRT routines.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

Nodal and periastron precession of inclined orbits in the field of a rapidly rotating neutron star

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates.     

Relativistic time transfer for a Mars lander: from Areocentric Coordinate Time to Barycentric Coordinate Time

As the second step of relativistic time transfer for a Mars lander,we investigate the transformation between Areocentric Coordinate Time(TCA)and Barycentric Coordinate Time(TCB)in the framework of IAU Resolutions.TCA is a local time scale for Mars,which is analogous to the Geocentric Coordinate Time(TCG)for Earth.This transformation has two parts:contributions associated with gravitational bodies and those depending on the position of the lander.After setting the instability of an onboard clock to 10~(-13)and considering that the uncertainty in time is about 3.2 microseconds after one Earth year,we find that the contributions of the Sun,Mars,Jupiter and Saturn in the leading term associated with these bodies can reach a level exceeding the threshold and must be taken into account.Other terms can be safely ignored in this transformation for a Mars lander.     

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain). This revised version was published online in July 2006 with corrections to the Cover Date.     

tempo2, a new pulsar-timing package – I. An overview

Contemporary pulsar-timing experiments have reached a sensitivity level where systematic errors introduced by existing analysis procedures are limiting the achievable science. We have developed tempo2 , a new pulsar-timing package that contains propagation and other relevant effects implemented at the 1-ns level of precision (a factor of ∼100 more precise than previously obtainable). In contrast with earlier timing packages, tempo2 is compliant with the general relativistic framework of the IAU 1991 and 2000 resolutions and hence uses the International Celestial Reference System, Barycentric Coordinate Time and up-to-date precession, nutation and polar motion models. tempo2 provides a generic and extensible set of tools to aid in the analysis and visualization of pulsar-timing data. We provide an overview of the timing model, its accuracy and differences relative to earlier work. We also present a new scheme for predictive use of the timing model that removes existing processing artefacts by properly modelling the frequency dependence of pulse phase.     

Relativistic time transfer for a Mars lander:from proper time to Areocentric Coordinate Time

As the first step in relativistic time transfer for a Mars lander from its proper time to the time scale at the ground station,we investigate the transformation between proper time and Areocentric Coordinate Time(TCA)in the framework of IAU Resolutions.TCA is a local time scale for Mars,which is analogous to the Geocentric Coordinate Time(TCG)for Earth.This transformation contains two contributions:internal and external.The internal contribution comes from the gravitational potential and the rotation of Mars.The external contribution is due to the gravitational fields of other bodies(except Mars) in the Solar System.When the(in)stability of an onboard clock is assumed to be at the level of 10~(-13),we find that the internal contribution is dominated by the gravitational potential of spherical Mars with necessary corrections associated with the height of the lander on the areoid,the dynamic form factor of Mars,the flattening of the areoid and the spin rate of Mars.For the external contribution,we find the gravitational effects from other bodies in the Solar System can be safely neglected in this case after calculating their maximum values.     

A phenomenological model for the precession of planets and bending of light

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.     

Spectrophotometric variability of the magnetic CP star 56 Arietis in spectral region from 1950 to 3200 Å

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.     

Consideration of Relativistic Effects in the Rotation of Mars and its Satellites

Solar System Research - This study is dedicated to the consideration of the relativistic effects (geodetic precession and nutation that make up the geodetic rotation) in the rotation of Mars and...     

Addressing some critical aspects of the BepiColombo MORE relativity experiment

The Mercury Orbiter Radio science Experiment (MORE) is one of the experiments on-board the ESA/JAXA BepiColombo mission to Mercury, to be launched in October 2018. Thanks to full on-board and on-ground instrumentation performing very precise tracking from the Earth, MORE will have the chance to determine with very high accuracy the Mercury-centric orbit of the spacecraft and the heliocentric orbit of Mercury. This will allow to undertake an accurate test of relativistic theories of gravitation (relativity experiment), which consists in improving the knowledge of some post-Newtonian and related parameters, whose value is predicted by General Relativity. This paper focuses on two critical aspects of the BepiColombo relativity experiment. First of all, we address the delicate issue of determining the orbits of Mercury and the Earth–Moon barycenter at the level of accuracy required by the purposes of the experiment and we discuss a strategy to cure the rank deficiencies that appear in the problem. Secondly, we introduce and discuss the role of the Solar Lense–Thirring effect in the Mercury orbit determination problem and in the relativistic parameters estimation.     

Stellar orbits in elliptical galaxies with relativistically active nuclei

In a model galaxy composed of a relativistically active nucleus, a main body, and a halo, all three components considered as homogeneous prolate ellipsoids, we explore the probable association of the internal characteristics of the nucleus and the observed orbits of the stars near the surface of the main body. Using the authors’ theoretical framework of post-Newtonian general relativistic galactic dynamics, proposed earlier, we prove that a fast-rotating and possibly expanding or contracting nucleus affects the distribution of the box-type orbits near the surface of the main body resulting in a flattening of the main body. The nuclear rotation always results in a flattening, and the contraction contributes less to the flattening than the expansion. However, the contributions of a rotating and changing nucleus are not additive. The study of the post-Newtonian effects in the nucleus on the stellar orbits in the main body, and the consequent modifications of the corresponding non-relativistic results, could in principle provide useful information concerning the kinematical and dynamical characteristics of the nuclei of the elliptical galaxies. The explanation (of at least the post-Newtonian part) of the flattening of elliptical galaxies attempted here seems to be the first theoretical one proposed in the literature.     

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

Solar System Research - Geodetic precession is the most significant relativistic effect in the rotation of celestial bodies. In this work, for the first time, this relativistic effect is determined...     

Differential Rotation Driven by Precession

The tidal force in the Earth–Moon system exerted on the Earth's equatorial bulge results in the Earth's precession. It was proposed a long time ago that the strong shear flow driven by the precession of the Earth may power the Earth's dynamo in its liquid core. We present a nonlinear analytical study investigating how the Poincaré force in a rotating, precessing spherical system drives a large-amplitude differential rotation which plays a major role in the modern theory of the geodynamo. The analysis is based on a perturbation approach in terms of the small Poincaré force parameter. It is found that the amplitude of the precession-driven differential rotation is consistent with that estimated from the geomagnetic secular variation.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.     

Post-Newtonian satellite orbits

The first post-Newtonian approximation of general relativity is used to account for the motion of solar system bodies and near-Earth objects which are slow moving and produce weak gravitational fields. The \(n\)-body relativistic equations of motion are given by the Einstein-Infeld-Hoffmann equations. For \(n=2\), we investigate the associated dynamics of two-body systems in the first post-Newtonian approximation. By direct integration of the associated planar equations of motion, we deduce a new expression that characterises the orbit of test particles in the first post-Newtonian regime generalising the well-known Binet equation for Newtonian mechanics. The expression so obtained does not appear to have been given in the literature and is consistent with classical orbiting theory in the Newtonian limit. Further, the accuracy of the post-Newtonian Binet equation is numerically verified by comparing secular variations of known expression with the full general relativistic orbit equation.     

Precession of the lunar core

Goldreich (Goldreich, P. [1967]. J. Geophys. Res. 72, 3135) showed that a lunar core of low viscosity would not precess with the mantle. We show that this is also the case for much of lunar history. But when the Moon was close to the Earth, the Moon’s core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (Dwyer, C.A., Stevenson, D.J. [2005]. An Early Nutation-Driven Lunar Dynamo. AGU Fall Meeting Abstracts GP42A-06) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core. So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0-29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.