From Reference Frames to Relativistic Experiments: Absolute and Relative Radio Astrometry

Reference systems and frames are crucial for high precision absolute astrometric work, and their foundations must be well-defined. The current frame, the International Celestial Reference Frame, will be discussed: its history, the use of the group delay as the measured quantity, the positional accuracy of 0.3 milliarcsec, and possible future improvements. On the other hand, for the determination of the motion of celestial objects, accuracies approaching 0.01 milliarcsec can be obtained by measuring the differential position between the target object and nearby stationary sources. This astrometric technique uses phase referencing, and the current techniques and limitations are discussed, using the results from four experiments. Brief comments are included on the interpretation of the Jupiter gravity deflection experiment of September 2002.Comment: 25 pages, 7 figures--Presented at JENAM meeting in Budapest, 27-30 August 200

Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 millimeter. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth-Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core-mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton Univ., NJ, 2007

Relativistic scaling of astronomical quantities and the system of astronomical units

For relativistic modelling of high-accuracy astronomical data several time scales are used: barycentric and geocentric coordinate times, TCB and TCG, as well as two additional time scales, TDB and TT, that are defined as linear functions of TCB and TCG, respectively. The paper is devoted to a concise but still detailed explanation of the reasons and the implications of the relativistic scalings of astronomical quantities induced by the time scales TDB and TT. We consequently distinguish between quantities and their numerical values expressed in some units. It is argued that the scaled time scales, the scaled spatial coordinates and the scaled masses should be considered as distinct quantities which themselves can be expressed in any units, and not as numerical values of the same quantities expressed in some different, non-SI units (``TDB units'' and ``TT units''). Along the same lines of argumentation the system of astronomical units is discussed in the relativistic framework. The whole freedom in the definitions of the systems of astronomical units for TCB and TDB is demonstrated. A number of possible ways to freeze the freedom are shown and discussed. It is argued that in the future one should think about converting AU into a defined quantity by fixing its value in SI meters

The impact of the Kuiper Belt Objects and of the asteroid ring on future high-precision relativistic Solar System tests

We preliminarily investigate the impact of the Kuiper Belt Objects (KBOs) and of the asteroid ring on some proposed high-precision tests of Newtonian and post-Newtonian gravity to be performed in the Solar System by means of spacecraft in heliocentric \approx 1 AU orbits and accurate orbit determination of some of the inner planets. It turns out that the Classical KBOSs (CKBOS), which amount to \approx 70% of the observed population of Trans-Neptunian bodies, induce a systematic secular error of about 1 m after one year in the transverse direction T of the orbit of a test particle orbiting at 1 AU from the Sun. For Mercury the ratios of the secular perihelion precessions induced by CKBOs to the ones induced by the general relativity and the solar oblateness J_2 amount to 6 10^-7 and 8 10^-4, respectively. The secular transverse perturbation induced on a \approx 1 AU orbit by the asteroid ring, which globally accounts for the action of the minor asteroids whose mass is about 5 10^-10 solar masses, is 10 m yr^-1; the bias on the relativistic and J_2 Mercury perihelion precessions is 6.1 10^-6 and 1 10^-2, respectively. Given the very ambitious goals of many expensive and complex missions aimed to testing gravitational theories to unprecedented levels of accuracy, these notes may suggest further and more accurate investigations of such sources of potentially insidious systematic bias.Comment: Latex2e, Elsevier macros, 5 pages, no figures, 1 table. To appear in Planetary Space Science. Small change in table's captio

Gravitomagnetism and the Earth-Mercury range

We numerically work out the impact of the general relativistic Lense-Thirring effect on the Earth-Mercury range caused by the gravitomagnetic field of the rotating Sun. The peak-to peak nominal amplitude of the resulting time-varying signal amounts to 1.75 10^1 m over a temporal interval 2 yr. Future interplanetary laser ranging facilities should reach a cm-level in ranging to Mercury over comparable timescales; for example, the BepiColombo mission, to be launched in 2014, should reach a 4.5 - 10 cm level over 1 - 8 yr. We looked also at other Newtonian (solar quadrupole mass moment, ring of the minor asteroids, Ceres, Pallas, Vesta, Trans-Neptunian Objects) and post-Newtonian (gravitoelectric Schwarzschild solar field) dynamical effects on the Earth-Mercury range. They act as sources of systematic errors for the Lense-Thirring signal which, in turn, if not properly modeled, may bias the recovery of some key parameters of such other dynamical features of motion. Their nominal peak-to-peak amplitudes are as large as 4 10^5 m (Schwarzschild), 3 10^2 m (Sun's quadrupole), 8 10^1 m (Ceres, Pallas, Vesta), 4 m (ring of minor asteroids), 8 10^-1 m (Trans-Neptunian Objects). Their temporal patterns are different with respect to that of the gravitomagnetic signal.Comment: LaTex2e, 19 pages, 2 tables, 6 figures. Small typo in pag. 1406 of the published version fixe

First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data

The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect. Indeed, corrections to the known perihelion rates of -0.0036 +/- 0.0050, -0.0002 +/- 0.0004 and 0.0001 +/- 0.0005 arcseconds per century were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on the basis of the EPM2004 ephemerides and a set of more than 317,000 observations of various kinds. The predicted relativistic Lense-Thirring precessions for these planets are -0.0020, -0.0001 and -3 10^-5 arcseconds per century, respectively and are compatible with the determined perihelia corrections. The relativistic predictions fit better than the zero-effect hypothesis, especially if a suitable linear combination of the perihelia of Mercury and the Earth, which a priori cancels out any possible bias due to the solar quadrupole mass moment, is considered. However, the experimental errors are still large. Also the latest data for Mercury processed independently by Fienga et al. with the INPOP ephemerides yield preliminary insights about the existence of the solar Lense-Thirring effect. The data from the forthcoming planetary mission BepiColombo will improve our knowledge of the orbital motion of this planet and, consequently, the precision of the measurement of the Lense-Thirring effect. As a by-product of the present analysis, it is also possible to constrain the strength of a Yukawa-like fifth force to a 10^-12-10^-13 level at scales of about one Astronomical Unit (10^11 m).Comment: LaTex, 22 pages, 1 figure, 5 tables, 62 references. To appear in Planetary and Space Scienc

Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy'

In a recent paper published in Classical and Quantum Gravity, 2004, vol. 21, p. 3803 Carlip used a vector-tensor theory of gravity to calculate the Shapiro time delay by a moving gravitational lens. He claimed that the relativistic correction of the order of v/c beyond the static part of the Shapiro delay depends on the speed of light c and, hence, the Fomalont-Kopeikin experiment is not sensitive to the speed of gravity c_g. In this letter we analyze Carlip's calculation and demonstrate that it implies a gravitodynamic (non-metric) system of units based on the principle of the constancy of the speed of gravity but it is disconnected from the practical method of measurement of astronomical distances based on the principle of the constancy of the speed of light and the SI metric (electrodynamic) system of units. Re-adjustment of theoretically-admissible but practically unmeasurable Carlip's coordinates to the SI metric system of units used in JPL ephemeris, reveals that the velocity-dependent correction to the static part of the Shapiro time delay does depend on the speed of gravity c_g as shown by Kopeikin in Classical and Quantum Gravity, 2004, vol. 21, p. 1. This analysis elucidates the importance of employing the metric system of units for physically meaningful interpretation of gravitational experiments.Comment: 8 pages, no figures, accepted to Classical and Quantum Gravit

Murphy et al. Reply to the Comment by Kopeikin on "Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit"

Lunar laser ranging analysis, as regularly performed in the solar system barycentric frame, requires the presence of the gravitomagnetic term in the equation of motion at the strength predicted by general relativity. The same term is responsible for the Lense Thirring effect. Any attempt to modify the strength of the gravitomagnetic interaction would have to do so in a way that does not destroy the fit to lunar ranging data and other observations.Comment: 1 page; accepted for publication in Physcal Review Letters; refers to gr-qc/070202

Role of plant functional traits in determining vegetation composition of abandoned grazing land in north-eastern Victoria, Australia

Question: In the Northern Hemisphere, species with dispersal limitations are typically absent from secondary forests. In Australia, little is known about dispersal mechanisms and other traits that drive species composition within post-agricultural, secondary forest. We asked whether mode of seed dispersal, nutrient uptake strategy, fire response, and life form in extant vegetation differ according to land-use history. We also asked whether functional traits of Australian species that confer tolerance to grazing and re-colonisation potential differ from those in the Northern Hemisphere. Location: Delatite Peninsula, NE Victoria, Australia. Methods: The vegetation of primary and secondary forests was surveyed using a paired-plot design. Eight traits were measured for all species recorded. ANOSIM tests and Non-metric Multi-dimensional Scaling were used to test differences in the abundance of plant attributes between land-use types. Results: Land-use history had a significant effect on vegetation composition. Specific leaf area (SLA) proved to be the best predictor of response to land-use change. Primary forest species were typically myrmecochorous phanerophytes with low SLA. In the secondary forest, species were typically therophytes with epizoochorous dispersal and high SLA. Conclusions: The attributes of species in secondary forests provide tolerance to grazing suggesting that disturbance caused by past grazing activity determined the composition of these forests. Myrmecochores were rare in secondary forests, suggesting that species had failed to re-colonise due to dispersal limitations. Functional traits that resulted in species loss through disturbance and prevented re-colonisation were different to those in the Northern Hemisphere and were attributable to the sclerophyllous nature of the primary forest