340 research outputs found
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
Post-Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits
The determination of velocities of stars from precise Doppler measurements is
described here using relativistic theory of astronomical reference frames so as
to determine the Keplerian and post-Keplerian parameters of binary systems. We
apply successive Lorentz transformations and the relativistic equation of light
propagation to establish the exact treatment of Doppler effect in binary
systems both in special and general relativity theories. As a result, the
Doppler shift is a sum of (1) linear in terms, which include the
ordinary Doppler effect and its variation due to the secular radial
acceleration of the binary with respect to observer; (2) terms proportional to
, which include the contributions from the quadratic Doppler effect
caused by the relative motion of binary star with respect to the Solar system,
motion of the particle emitting light and diurnal rotational motion of
observer, orbital motion of the star around the binary's barycenter, and
orbital motion of the Earth; and (3) terms proportional to , which
include the contributions from redshifts due to gravitational fields of the
star, star's companion, Galaxy, Solar system, and the Earth. After
parameterization of the binary's orbit we find that the presence of
periodically changing terms in the Doppler schift enables us disentangling
different terms and measuring, along with the well known Keplerian parameters
of the binary, four additional post-Keplerian parameters, including the
inclination angle of the binary's orbit, . We briefly discuss feasibility of
practical implementation of these theoretical results, which crucially depends
on further progress in the technique of precision Doppler measurements.Comment: Minor changes, 1 Figure included, submitted to Astrophys.
A generalized lens equation for light deflection in weak gravitational fields
A generalized lens equation for weak gravitational fields in Schwarzschild
metric and valid for finite distances of source and observer from the light
deflecting body is suggested. The magnitude of neglected terms in the
generalized lens equation is estimated to be smaller than or equal to 15 Pi/4
(m/d')^2, where m is the Schwarzschild radius of massive body and d' is
Chandrasekhar's impact parameter. The main applications of this generalized
lens equation are extreme astrometrical configurations, where 'Standard
post-Newtonian approach' as well as 'Classical lens equation' cannot be
applied. It is shown that in the appropriate limits the proposed lens equation
yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and
the Classical lens equation, thus provides a link between these both essential
approaches for determining the light deflection.Comment: 11 pages, 3 figure
Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
General relativistic deflection of light by mass, dipole, and quadrupole
moments of gravitational field of a moving massive planet in the Solar system
is derived. All terms of order 1 microarcsecond are taken into account,
parametrized, and classified in accordance with their physical origin. We
calculate the instantaneous patterns of the light-ray deflections caused by the
monopole, the dipole and the quadrupole moments, and derive equations
describing apparent motion of the deflected position of the star in the sky
plane as the impact parameter of the light ray with respect to the planet
changes due to its orbital motion. The present paper gives the physical
interpretation of the observed light-ray deflections and discusses the
observational capabilities of the near-future optical (SIM) and radio (SKA)
interferometers for detecting the Doppler modulation of the radial deflection,
and the dipolar and quadrupolar light-ray bendings by the Jupiter and the
Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.
Numerical versus analytical accuracy of the formulas for light propagation
Numerical integration of the differential equations of light propagation in
the Schwarzschild metric shows that in some situations relevant for practical
observations the well-known post-Newtonian solution for light propagation has
an error up to 16 microarcsecond. The aim of this work is to demonstrate this
fact, identify the reason for this error and to derive an analytical formula
accurate at the level of 1 microarcsecond as needed for high-accuracy
astrometric projects (e.g., Gaia).
An analytical post-post-Newtonian solution for the light propagation for both
Cauchy and boundary problems is given for the Schwarzschild metric augmented by
the PPN and post-linear parameters , and . Using
analytical upper estimates of each term we investigate which
post-post-Newtonian terms may play a role for an observer in the solar system
at the level of 1 microarcsecond and conclude that only one post-post-Newtonian
term remains important for this numerical accuracy. In this way, an analytical
solution for the boundary problem for light propagation is derived. That
solution contains terms of both post-Newtonian and post-post-Newtonian order,
but is valid for the given numerical level of 1 microarcsecond. The derived
analytical solution has been verified using the results of a high-accuracy
numerical integration of differential equations of light propagation and found
to be correct at the level well below 1 microarcsecond for arbitrary observer
situated within the solar system. Furthermore, the origin of the
post-post-Newtonian terms relevant for the microarcsecond accuracy is
elucidated. We demonstrate that these terms result from an inadequate choice of
the impact parameter in the standard post-Newtonian formulas
Experimental Tests of General Relativity
Einstein's general theory of relativity is the standard theory of gravity,
especially where the needs of astronomy, astrophysics, cosmology and
fundamental physics are concerned. As such, this theory is used for many
practical purposes involving spacecraft navigation, geodesy, and time transfer.
Here I review the foundations of general relativity, discuss recent progress in
the tests of relativistic gravity in the solar system, and present motivations
for the new generation of high-accuracy gravitational experiments. I discuss
the advances in our understanding of fundamental physics that are anticipated
in the near future and evaluate the discovery potential of the recently
proposed gravitational experiments.Comment: revtex4, 30 pages, 10 figure
Classification of intended phoneme production from chronic intracortical microelectrode recordings in speech-motor cortex
This is the published version, also available here: http://dx.doi.org/10.3389/fnins.2011.00065.We conducted a neurophysiological study of attempted speech production in a paralyzed human volunteer using chronic microelectrode recordings. The volunteer suffers from locked-in syndrome leaving him in a state of near-total paralysis, though he maintains good cognition and sensation. In this study, we investigated the feasibility of supervised classification techniques for prediction of intended phoneme production in the absence of any overt movements including speech. Such classification or decoding ability has the potential to greatly improve the quality-of-life of many people who are otherwise unable to speak by providing a direct communicative link to the general community. We examined the performance of three classifiers on a multi-class discrimination problem in which the items were 38 American English phonemes including monophthong and diphthong vowels and consonants. The three classifiers differed in performance, but averaged between 16 and 21% overall accuracy (chance-level is 1/38 or 2.6%). Further, the distribution of phonemes classified statistically above chance was non-uniform though 20 of 38 phonemes were classified with statistical significance for all three classifiers. These preliminary results suggest supervised classification techniques are capable of performing large scale multi-class discrimination for attempted speech production and may provide the basis for future communication prostheses
Parametrized Post-Newtonian Orbital Effects in Extrasolar Planets
Perturbative Post-Newtonian variations of the standard osculating orbital
elements are obtained by using the two-body equations of motion in the
Parameterized Post-Newtonian theoretical framework. The results obtained are
applied to the Einstein and. Brans - Dicke theories. As a results, the
semi-major axis and eccentricity exhibit periodic variation, but no secular
changes.. The longitude of periastron and mean longitude at epoch experience
both secular and periodic shifts. The Post-Newtonian effects are calculated and
discussed for six extrasolar planets.Comment: Accepted for publication in Astrophys. Space Sc
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
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