Weak field limit and tests of a relativistic theory of gravity

Static spherically-symmetric solutions to the linearized field equations of a generalized scalartensor theory of gravity are derived. The gravitational potential outside such a source is determined; it is found that this potential can have an intermediate range variation. The question of whether such an intermediate range variation would manifest itself in two experiments is addressed.     

Group velocity correction to lunar laser ranging

The dispersive correction to the round trip lunar ranging distance is presented as a function of wavelength and humidity. For example, at 6943 Å (ruby laser line), 11. secz cm must be subtracted from the ‘refractive distance’. The refractive correction decreases with humidity whereas the dispersive correction increases.     

Computer applications to lunar and artificial satellite laser ranging

The University of Texas McDonald Observatory has long been a pioneer in acquiring laser ranging data, a data type which has substantially improved our knowledge of the dynamics of the earth-moon system as well as various aspects of geophysics and general relativity. (See Mulholland, 1980; Shelus, 1985; Shelus, 1987.) The McDonald Laser Ranging System (MLRS) is one of only 2 laser ranging stations world-wide having the capability of routine data acquisition on both lunar and artificial satellite targets (Shelus,IEEE, 1985). In this paper we discuss the current applications of modern computer technology to the problems of acquiring and reducing that ranging data. As technology continues to improve, the logical upgrade is the replacement of obsolescent station minicomputers with the resource-rich environment of micro-computers. The goal is to allow the automation of many station ranging functions as well as the enhancement of onsite data quality control, filtering, and analysis. Plans for such upgrades and their implications for dynamical astronomy are discussed.     

Project of the mission to Phobos

This article provides the main scientific objectives and characteristics of the Phobos-Soil project, intended to fly to the Martian satellite Phobos, deliver its soil samples to the Earth, as well as explore Phobos, Mars, and the Martian environment with onboard scientific instruments. We give the basic parameters of the ballistic scenario of the mission, spacecraft, and some scientific problems to be solved with the help of the scientific instruments installed on the spacecraft.     

Experiment on diffuse reflection laser ranging to space debris and data analysis

Space debris poses a serious threat to human space activities and needs to be measured and cataloged. As a new technology for space target surveillance, the measurement accuracy of diffuse reflection laser ranging(DRLR) is much higher than that of microwave radar and optoelectronic measurement. Based on the laser ranging data of space debris from the DRLR system at Shanghai Astronomical Observatory acquired in March-April, 2013, the characteristics and precision of the laser ranging data are analyzed and their applications in orbit determination of space debris are discussed, which is implemented for the first time in China. The experiment indicates that the precision of laser ranging data can reach 39 cm–228 cm. When the data are sufficient enough(four arcs measured over three days), the orbital accuracy of space debris can be up to 50 m.     

Seismology of Phobos: from geophysics to cosmogony

Several of the most fundamental and feasible geophysical problems partially related to the Phobos-Grunt mission have been analyzed based on the available works. The assumed results will form the informational basis for the development of the cosmogony of planets’ small satellites and asteroids. Correspondingly, the aims of the experiment are to study the internal structure and energy state of Phobos; to analyze the manifestation of pulsed effects and fields, including the registration of seismic signals and wave fields of Phobos; and to measure the long-period oscillations on the surface of Phobos in the range of 10⁻⁵–10 Hz. Studying Phobos gives an example of specific problems peculiar to small bodies of the Solar System: specific features of cratering, grooves, and morphological structures. The registration of gas-dust streams extends the knowledge of the space-time structure of the Solar System and its objects and processes and will confirm that stellar systems can constantly interact. The physical principles of the registration of seismic fields and signals are briefly described, and the instrumental basis for cosmogonic seismology is comparatively presented. It has been indicated that the piezoelectric and electrodynamic systems of the desired signal registration complete each other, and it is desirable to use both systems if 2- and 3-D registration systems are applied. The seismometric instrumentation of the Phobos spacecraft has been considered. The device’s physical characteristics, block diagrams, energy consumption, and information content are presented. The seismoacoustic (HF) device unit and its advantages during the registration of very weak signals owing to the use of the mechanical transformer effect are described in more detail. The seismic system created can ensure the solution of the scientific problems of the mission to Phobos, including the study of the internal structure, origin, depth structures, and external impacts of the field, corpuscular, and micrometeorite types.     

New consideration of atmospheric refraction in laser ranging data

In this paper we reconsider the formulae of tropospheric refraction correction for the Satellite Laser Range technique. From the expansion of the complementary error function, a new continued fraction form of the mapping function at optical frequencies is derived. The correction terms related to the operation frequency of the laser beam are considered in both the zenith delay and the mapping function. The correction for low-elevation satellites is briefly reviewed. The theoretical accuracy of the new mapping function has been analysed via the ray tracing integrals under the standard atmospheric profile. With respect to the radiosonde data, the deviations of the new mapping function are investigated in an elevation range down to near 1°, which is comparable with the results of the Marini–Murray formulae .     

Improvement of the numerical lunar ephemeris with laser ranging data

Analysis of lunar laser ranging data is underway at several institutions. We describe here our efforts at improving the numerical ephemeris of Moon, based on over three years' span of data. Orbit generation and correction procedures are discussed briefly. Comparisons of the new ephemeris with observations and with a widely available ephemeris are illustrated. The standard deviation of the observation residuals is 7 m.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Strong-field tests of gravity using pulsars and black holes

The sensitivity of the SKA enables a number of tests of theories of gravity. A Galactic Census of pulsars will discover most of the active pulsars in the Galaxy beamed toward us. In this census will almost certainly be pulsar–black hole binaries as well as pulsars orbiting the super-massive black hole in the Galactic centre. These systems are unique in their capability to probe the ultra-strong field limit of relativistic gravity. These measurements can be used to test the Cosmic Censorship Conjecture and the No-Hair theorem.The large number of millisecond pulsars discovered with the SKA will also provide a dense array of precision clocks on the sky. These clocks will act as the multiple arms of a huge gravitational wave detector, which can be used to detect and measure the stochastic cosmological gravitational wave background that is expected from a number of sources.     

Reduction of ephemeris error influence in determinations by lunar laser ranging

It has been shown in different previous papers that continuous or quasi continuous ranging at a lunar reflector from a terrestrial observatory will yield the distancew of that observatory to Earth instantaneous axis of rotation, and its longitudeL with respect to Ephemeris meridian. However it has been shown also that these determinations imply a very accurate knowledge of the geocentric range of the same reflector. By developing the difference: true minus computed geocentric ranges as a function of time, we establish relations between the first and second order terms of the above development and the errors entailing the longitude and distance to axis determinations, respectively.On the other hand, the different terms of that same development are related to the first, second, ... variations of true minus computed geocentric ranges of the reflector during lunar passage. Thus, the first two differences are finally related to errors committed onL andw determinations.The above properties have been extended to higher order variations. We show that, as could be expected, those with odd order correlate with longitude errors, and those with even order with distance to axis errors.Inasmuch as the magnitude of successive terms can be expected to decrease as their order increases, it appears thus that the most accurate determinations forL andw should rely on higher order variations, calling for range measurements in large number and evenly distributed during Moon passage.At the same time, comparison betweenw andL values resulting from variations of the same parity but different orders will provide a coherence test for such determinations.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Gas heating inside radio sources to mildly relativistic temperatures via induced compton scattering

The measured brightness temperatures of the low-frequency synchrotron radiation from intense extragalactic sources reach 10¹¹–10¹² K. If there is some amount of nonrelativistic ionized gas within such sources, it must be heated through induced Compton scattering of the radiation. If cooling via inverse Compton scattering of the same radio radiation counteracts this heating, then the plasma can be heated up to mildly relativistic temperatures kT～10–100 keV. In this case, the stationary electron velocity distribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several simple approximate expressions for the induced Compton heating rate of mildly relativistic electrons in an isotropic radiation field, as well as for the stationary electron distribution function and temperature. We give analytic expressions for the kernel of the integral kinetic equation (one as a function of the scattering angle, and the other for an isotropic radiation field), which describes the photon redistribution in frequency through induced Compton scattering in thermal plasma. These expressions can be used in the parameter range [in contrast to the formulas written out previously in Sazonov and Sunyaev (2000), which are less accurate].     

The secular acceleration of the Moon determined from lunar laser ranging data

Lunar Laser Ranging data covering the interval from August 1969 to December 1987 were used to determine the seculer acceleration in the mean longitude of the Moon (\.n). In our analysis, the DE200/LE200 planets and lunar ephemerides were adopted for calculating the theoretical distance between the observing station and reflector. The method of stepwise regression was used in the processing of the data and the value of –25.4 ± 0. 1/cy² was obtained by a weighted least squares fit.Our result is in good agreement with that derived by other authors using various methods. The uncertainty (\.n) estimated from LLR data would be decreasing rapidly with increasing the data span. The high precision obtained in this paper is mainly due to the longer span and higher measuring accuracy of data.     

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.     

Some results of investigating the stability of operation of the Ukrainian laser ranging stations

The stability of operation of the network of the Ukrainian laser ranging stations Simeiz, Katsyveli, Holosiiv-Kyiv, and L’viv is investigated by analyzing the Lageos-1 and Lageos-2 observations made over the period from January 5, 1989 through November 11, 2004. The coordinate determination stability is estimated for each station. Some factors which affect the network operation stability are pointed out.     

Manufacture of a hollow corner cube retroreflector for next generation of lunar laser ranging

Lunar laser ranging has made significant contributions to the study of gravitational physics and the Earth-Moon system. The best results for fundamental gravitational experiments have been achieved using lunar laser ranging data accumulated so far. However, corner cube retroreflector arrays placed on the Moon currently set a limit on the laser-ranging precision, which is approximately several centimeters for a single photon received. To achieve millimeter precision, next generation of lunar laser ranging using a single hollow retroreflector with a large aperture has been proposed. We developed a prototype hollow retroreflector with a 100-mm aperture using silicate bonding together with a new fabrication method. Dihedral angle offsets of 0.5′′, 0.8′′and 1.9′′were realized, which partly come close to meeting the requirements(offset of 0.6′′for each dihedral angle) for lunar laser ranging. Fluctuation of the wavefront is approximately 1.038λ at 633 nm. A thermal cycle test ranging from -40℃ to +75℃ was carried out for 18.5 periods(approximately 5 d). After this test, the dihedral angle offsets were measured to be 0.39′′, 1.00′′and 2.06′′. The results indicate the potential application of our method for manufacturing a hollow retroreflector with a large aperture to realize lunar laser ranging.     

Relation between classical and relativistic shock wave theories by means of shock tube tests

The author proposes a laboratory simulation of cosmic shock waves by means of the mathematical correlations between the shock equations in the classical and the relativistic fluid dynamics, respectively. In the present note only the normal shock is treated.