New concept for testing General Relativity: the Laser Astrometric Test Of Relativity (LATOR) mission

This paper discusses a Fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, ∝ G². The Laser Astrometric Test Of Relativity (LATOR) mission uses laser interferometry between two micro‐spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long‐baseline (100 m) multi‐channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangle's three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy. LATOR will not only improve the value of the parameterized post‐Newtonian (PPN) γ to unprecedented levels of accuracy of 1 part in 10⁸, it will also reach ability to measure effects of the next post‐Newtonian order (c⁻⁴) of light deflection resulting from gravity's intrinsic non‐linearity. The solar quadrupole moment parameter, J₂, will be measured with high precision, as well as a variety of other relativistic effects including Lense‐Thirring precession. LATOR will lead to very robust advances in the tests of Fundamental physics: this mission could discover a violation or extension of general relativity, or reveal the presence of an additional long range interaction in the physical law. There are no analogs to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advancing fundamental physics with the Laser Astrometric Test of Relativity

The Laser Astrometric Test of Relativity (LATOR) is an experiment designed to test the metric nature of gravitation—a fundamental postulate of the Einstein’s general theory of relativity. The key element of LATOR is a geometric redundancy provided by the long-baseline optical interferometry and interplanetary laser ranging. By using a combination of independent time-series of gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on interplanetary scales (to a precision respectively better than 0.1 picoradians and 1 cm), LATOR will significantly improve our knowledge of relativistic gravity and cosmology. The primary mission objective is i) to measure the key post-Newtonian Eddington parameter γ with accuracy of a part in 10⁹. $\frac{1}{2}(1-\gamma)$ is a direct measure for presence of a new interaction in gravitational theory, and, in its search, LATOR goes a factor 30,000 beyond the present best result, Cassini’s 2003 test. Other mission objectives include: ii) first measurement of gravity’s non-linear effects on light to ～0.01% accuracy; including both the traditional Eddington β parameter and also the spatial metric’s 2nd order potential contribution (never measured before); iii) direct measurement of the solar quadrupole moment J ₂ (currently unavailable) to accuracy of a part in 200 of its expected size of ??10^???7; iv) direct measurement of the “frame-dragging” effect on light due to the Sun’s rotational gravitomagnetic field, to 0.1% accuracy. LATOR’s primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today’s solar system. We discuss the science objectives of the mission, its technology, mission and optical designs, as well as expected performance of this experiment. LATOR will lead to very robust advances in the tests of fundamental physics: this mission could discover a violation or extension of general relativity and/or reveal the presence of an additional long range interaction in the physical law. There are no analogs to LATOR; it is unique and is a natural culmination of solar system gravity experiments.     

Forthcoming close angular approaches of planets to radio sources and possibilities to use them as GR tests

During close angular approaches of solar system planets to astrometric radio sources, the apparent positions of these sources shift due to relativistic effects and, thus, these events may be used for testing the theory of general relativity; this fact was successfully demonstrated in the experiments on the measurements of radio source position shifts during the approaches of Jupiter carried out in 1988 and 2002. An analysis, performed within the frames of the present work, showed that when a source is observed near a planet’s disk edge, i.e., practically in the case of occultation, the current experimental accuracy makes it possible to measure the relativistic effects for all planets. However, radio occultations are fairly rare events. At the same time, only Jupiter and Saturn provide noticeable relativistic effects approaching the radio sources at angular distances of about a few planet radii. Our analysis resulted in the creation of a catalog of forthcoming occultations and approaches of planets to astrometric radio sources for the time period of 2008–2050, which can be used for planning experiments on testing gravity theories and other purposes. For all events included in the catalog, the main relativistic effects are calculated both for ground-based and space (Earth-Moon) interferometer baselines.     

Microarcsecond astrometry using the SKA

The sensitivity and versatility of SKA will provide microarcsec astrometric precision and high quality milliarcsec-resolution images by simultaneously detecting calibrator sources near the target source. To reach these goals, we suggest that the long-baseline component of SKA contains at least 25% of the total collecting area in a region between 1000 and 5000 km from the core SKA. We also suggest a minimum of 60 elements in the long-baseline component of SKA to provide the necessary (u–v) coverage. For simultaneous all-sky observations, which provide absolute astrometric and geodetic parameters, we suggest using 10 independent subarrays each composed of at least six long-baseline elements correlated with the core SKA. We discuss many anticipated SKA long-baseline astrometric experiments: determination of distance, proper motion and orbital motion of thousands of stellar objects; planetary motion detections; mass determination of degenerate stars using their kinetics; calibration of the universal distance scale from 10 to 10⁷ pc; the core and inner-jet interactions of AGN. With an increase by a factor of 10 in absolute astrometric accuracy using simultaneous all sky observations, the fundamental quasar reference frame can be defined to <10 μas and tied to the solar-system dynamic frame to this accuracy. Parameters associated with the earth rotation and orientation, nutation, and geophysical parameters, can be accurately monitored. Tests of fundamental physics include: solar and Jovian deflection experiments, the sky frame accuracy needed to interpret the gravity wave/pulsar-timing experiment, accurate monitoring of spacecraft orbits that impact solar system dynamics.     

Some Aspects of Relativistic Astrometry from Within the Solar System

In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1 µarcsecond optical observations made by an astrometric satellite orbiting around the Sun. The basic assumption of our model is that the Solar System is the only source of gravity, hence we show how we modeled the satellite observations in a many-body perturbative approach limiting ourselves to the order of accuracy of (v/c)². The microarcsecond observing scenario outlined is that for the GAIA astrometric mission.     

Gravity Anomaly During the Mohe Total Solar Eclipse and New Constraint on Gravitational Shielding Parameter

By using a high-precision LaCoste-Romberg gravimeter, continuous and precise measurements were carried out during the March 9, 1997 total solar eclipse in Mohe region in Northeast China. The gravity variations were digitally recorded during the total solar eclipse so as to investigate the possible anomaly of the Sun and the Moon's gravitational fields on the Earth. After the careful processing and analysis of the observed data, no significant anomaly during the very solar eclipse was found. However, there are two ‘gravity anomaly valleys’ with near symmetrical decrease of about 6 ∼ 7 μg at the first contact and the last contact. This is the anomaly phenomenon observed and reported for the first time in the literature. This paper is intended to explain the observed anomaly by conducting the tilt experiment due to the thermal stress and temperature change in the solar eclipse. A new constraint limit on gravitational shielding is thus obtained. Some analysis and discussions are presented although further studies and research are highly needed. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Estimates of dynamic parameters and boundaries of habitable zones of selected stars of the Pulkovo program

A list of selected binary stars is presented that have been observed for several decades using a 26-inch refractor at the Pulkovo Observatory. These stars are at a distance from 3.5 to 25 pc from the Sun. They belong to spectral classes F, G, K, and M. Their masses range from 0.3 to 1.5 solar masses. We have analyzed them as possible parent stars for exoplanets taking into account the physical characteristics of these stars. In view of dynamic parameters and orbital elements that we have obtained by Pulkovo observations, ephemerides of positions for the coming years are calculated. The boundaries of the habitable zones around these stars are calculated. The astrometric signal that depends on the gravitational influence of hypothetical planets is estimated. Space telescopes for astrometric observations with microsecond accuracy can be used to detect Earth-like planets near the closest stars of this program. This paper presents an overview of astrometric programs of searches for exoplanets.     

Astrometric detection of binary companions and planets: Acceleration of proper motion

Apparent acceleration of proper motion is one of the observable manifestations of orbital motion in binary stars. Owing to the increasing accuracy of astrometric measurements, it may also be a method to detect binarity of stars. This paper presents some analytical expressions for the effects of binary motion on proper motions when the orbital period is at least several times the span of observations. We estimate orbit dimensions and distances at which low‐mass companions and planets may be detected around main‐sequence stars, using preliminary estimates of precision for the AMEX, GAIA and SIM space missions.     

Advancing tests of relativistic gravity via laser ranging to Phobos

Phobos Laser Ranging (PLR) is a concept for a space mission designed to advance tests of relativistic gravity in the solar system. PLR’s primary objective is to measure the curvature of space around the Sun, represented by the Eddington parameter γ, with an accuracy of two parts in 10⁷, thereby improving today’s best result by two orders of magnitude. Other mission goals include measurements of the time-rate-of-change of the gravitational constant, G and of the gravitational inverse square law at 1.5-AU distances—with up to two orders-of-magnitude improvement for each. The science parameters will be estimated using laser ranging measurements of the distance between an Earth station and an active laser transponder on Phobos capable of reaching mm-level range resolution. A transponder on Phobos sending 0.25-mJ, 10-ps pulses at 1 kHz, and receiving asynchronous 1-kHz pulses from earth via a 12-cm aperture will permit links that even at maximum range will exceed a photon per second. A total measurement precision of 50 ps demands a few hundred photons to average to 1-mm (3.3 ps) range precision. Existing satellite laser ranging (SLR) facilities—with appropriate augmentation—may be able to participate in PLR. Since Phobos’ orbital period is about 8 h, each observatory is guaranteed visibility of the Phobos instrument every Earth day. Given the current technology readiness level, PLR could be started in 2011 for launch in 2016 for 3 yr of science operations. We discuss the PLR’s science objectives, instrument, and mission design. We also present the details of science simulations performed to support the mission’s primary objectives.     

Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation

From the analysis of all available radiometric measurements of distances between the Earth and the major planets (including observations of martian landers and orbiters over 1971–2003 with the errors of few meters) the positive secular trend in the Astronomical Unit AU is estimated as . The given uncertainty is the 10 times enlarged formal error of the least-squares estimate and so accounts for possible systematic errors of measurements and deficiencies of the mathematical model. The reliability of this estimate as well as its physical meaning are discussed. A priori most plausible attribution of this effect to the cosmological expansion of the Universe turns out inadequate. A model of the observables developed in the frame of the relativistic background metric of the uniform isotropic Universe shows that the corresponding dynamical perturbations in the major planet motions are completely canceled out by the Einstein effect of dependence of the rate of the observer’s clock (that keeps the proper time) on the gravitational field, though separately values of these two effects are quite large and attainable with the accuracy achieved. Another tentative source of the secular rate of AU is the loss of the solar mass due to the solar wind and electromagnetic radiation but it amounts in only to 0.3 m/cy. Excluding other explanations that seem exotic (such as secular decrease of the gravitational constant) at present there is no satisfactory explanation of the detected secular increase of AU, at least in the frame of the considered uniform models of the Universe.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

Mountains on neutron stars

The aim of this work is to compare a neutron star with an accreted crust and one with a non-accreted crust, and estimate which one is potentially a better source of gravitational waves (i.e. can sustain a larger “mountain”). To do this we present a new formalism, and find that a non-accreted crust can sustain a slightly larger “mountain”. We also discuss the importance of relativistic effects.      

Spectra of the spreading layers on the neutron star surface and constraints on the neutron star equation of state

Spectra of the spreading layers on the neutron star surface are calculated on the basis of the Inogamov–Sunyaev model taking into account general relativity correction to the surface gravity and considering various chemical composition of the accreting matter. Local (at a given latitude) spectra are similar to the X-ray burst spectra and are described by a diluted blackbody. Total spreading layer spectra are integrated accounting for the light bending, gravitational redshift and the relativistic Doppler effect and aberration. They depend slightly on the inclination angle and on the luminosity. These spectra also can be fitted by a diluted blackbody with the colour temperature depending mainly on a neutron star compactness. Owing to the fact that the flux from the spreading layer is close to the critical Eddington, we can put constraints on a neutron star radius without the need to know precisely the emitting region area or the distance to the source. The boundary layer spectra observed in the luminous low-mass X-ray binaries, and described by a blackbody of colour temperature   T _c= 2.4 ± 0.1 keV  , restrict the neutron star radii to   R = 14.8 ± 1.5 km  (for a  1.4-M_⊙  star and solar composition of the accreting matter), which corresponds to the hard equation of state.     

天文地球动力学中的相对论效应

天文地球动力学利用空间与地面观测手段 ,监测和研究地球整体与各圈层的物质运动以及它们间的相互作用 ,这都离不开广义相对论涉及的时间与空间。随着空间对地观测精度的提高 ,为了充分利用高精度观测提供的信息 ,在天文地球动力学的研究中必须考虑相对论效应。所涉及的相对论效应包括 :( 1 )相对论参考系的建立 ,( 2 )在恰当的参考系中对观测者和被观测对象的相对论运动方程 (平动和自转 )的描述 ,( 3 )观测者和被观测对象间的电磁信号传播 ,( 4 )依赖于坐标选择的结果与具有物理意义的可观测量间的转换 ,( 5)某些基本概念与定义在广义相对论框架下的重新确认。本文对天文地球动力学中的这些相对论效应作了简要的评述。     

Astronomical measurements and coordinate conditions in relativistic celestial mechanics

Determination of dynamical effects from the equations of motion and calculation of ephemerides in terms of measurable quantities on the basis of the equations of light should be performed in one and the same coordinate system. The choice of coordinate system is arbitrary. For illustration we consider coplanar circular motions of the Earth and one of the inner planets in the solar gravitational field described by the generalized three-parametric Schwarzschild metric. Specific values of the metric parameters characterize the adopted gravitational theory, as well as a definite coordinate system (for example, isotropic or standard coordinates). Coordinates of the planets and radii of the orbits are coordinate-dependent quantities and cannot be directly reconciled with measurable quantities such as the round-trip transit times of radar signals or the angular distance between the planet and the distant fixed source (quasar). These ephemeris data may be calculated in terms of the initial measured values independently of the employed coordinate system. Relativistic ephemeris corrections should be taken into account both in radar reflection measurements and astrometric observations.     

Tides and nutation of the earth: I. Models of an earth with an inelastic mantle and homogeneous,inviscid, liquid core

The use of very-long-baseline radio interferometers during the past 10–15 years has increased the accuracy of amplitude measurements of the Earths forced nutation by more than two orders of magnitude (from 3–5 arc ms to 20 arc s). At the same time, cryogenic gravimeters (which depend for their action on the repulsion of two superconductive rings in a gravitational field) have made it possible to also improve the accuracy of measurements of tidal variations in the gravitational force by two orders of magnitude. This opens up new avenues for the investigation of the mechanical properties of the Earths interior at ultralow frequencies. A brief review is given here of the basic results of interpreting astrometric data and measurements of tidal variations in the gravitational force. Problems suggested by the new observational techniques are formulated.Translated from Astronomicheskii Vestnik, Vol. 38, No. 6, 2004, pp. 542–558.Original Russian Text Copyright © 2004 by Molodensky.     

Acceleration of Relativistic Protons During the 20 January 2005 Flare and CME

The origin of relativistic solar protons during large flare/CME events has not been uniquely identified so far. We perform a detailed comparative analysis of the time profiles of relativistic protons detected by the worldwide network of neutron monitors at Earth with electromagnetic signatures of particle acceleration in the solar corona during the large particle event of 20 January 2005. The intensity – time profile of the relativistic protons derived from the neutron monitor data indicates two successive peaks. We show that microwave, hard X-ray, and γ-ray emissions display several episodes of particle acceleration within the impulsive flare phase. The first relativistic protons detected at Earth are accelerated together with relativistic electrons and with protons that produce pion-decay γ rays during the second episode. The second peak in the relativistic proton profile at Earth is accompanied by new signatures of particle acceleration in the corona within ≈1R _⊙ above the photosphere, revealed by hard X-ray and microwave emissions of low intensity and by the renewed radio emission of electron beams and of a coronal shock wave. We discuss the observations in terms of different scenarios of particle acceleration in the corona.     

A plea for better astrophysical and astrometric data in case of double stars of peculiar interest

Summary TheIAU Symposium No. 61 (Perth, 1973, “New Problems in Astrometry’) makes clear that radiosources will play an important role for astrometry in view of the linkage of reference systems. The purposes developed later were to link the various systems from the earth and the solar system to the most inertial possible one. Extragalactic radiosources are the most reliable objects but they are faint. So, intermediate objects are needed. Among them the radiostars, optical objects having radioemission at a certain level and for given frequencies have a fundamental and key position. Most of such radiostars are double or multiple ‘binaries’ as it can be seen from the list of reference stars issued by the Working Group of Commission 24, Working Group created in 1978. The last issue of the core list of radiostars was presented by Ch. de Vegt (Chairman of the WG) on the occasion of the last General Assembly of the IAU (November 1985). A recent study of the system α Scorpii (Antares) has shown that the data concerning the magnitude and the spectral type are not accurate enough, according to the accuracy obtained for the astrometric position (±0 _. ^s 003 for an astrolabe campaign in right ascension). There is also a need for better knowledge about the orbits. In the case of the astrolabe observations, if the distance between the components in <3″ the astrometric position concerns the photocenter and accurate physical properties are needed for comparison with the radio position. Better astrophysical properties are strongly needed for all radiostars to be used as references, during the time the astrometrists have to improve the accuracy of their measurements both in optical and radio fields. Presented by S. Débarbat.     

On the theory of the oblateness of the Sun

In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical harmonic coefficients (J ₂ and J ₄) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J ₂=−(6.13±2.52)×10⁻⁷ if all observed data are taken into account, and respectively, J ₂=−(6.84±3.75)×10⁻⁷ if only sunspot data are considered, and J ₂=−(3.49±1.86)×10⁻⁷ in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J ₄=(2.8±2.1)×10⁻¹². These values are compared to some others found in the literature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479