arXiv subjects

James G. Williams

Publications and source records attributed to James G. Williams.

At least 19 recordsLinked to original sources

arXiv2024

Relativistic Time Transformations Between the Solar System Barycenter, Earth, and Moon

Relativistic corrections are essential for time transformations between geocentric, solar system barycentric, and luni-centric reference systems to account for differences in gravitational potential and relative motion. As the primary reference for Earth-based systems, Terrestrial Time (TT) provides the foundation for precise synchronization across spatial and temporal frameworks. To ensure consistency with TT, Barycentric Dynamical Time (TDB) must exhibit no average rate difference from TT. Although the International Astronomical Union (IAU) has established resolutions for transformations between TT and TDB, extending these frameworks to define a lunar surface time scale (TL) is essential for advancing lunar exploration. This paper derives the (TL - TT) transformation, quantifying a secular drift of 56.0256 us/day and periodic terms, with the largest amplitude of ~0.470 us at the mean anomalistic period. Additionally, the TT-compatible spatial scale and Lorentz contraction of Moon-centered positional coordinates are computed, achieving sub-nanosecond timing precision. These transformations, implemented in JPL ephemeris generation software, provide a robust framework for high-fidelity relativistic models of lunar timekeeping, enabling further refinements and supporting navigation, communication, and scientific operations in cis-lunar space.

astro-ph.EP↗

arXiv2020

Extending Science from Lunar Laser Ranging

The Lunar Laser Ranging (LLR) experiment has accumulated 50 years of range data of improving accuracy from ground stations to the laser retroreflector arrays (LRAs) on the lunar surface. The upcoming decade offers several opportunities to break new ground in data precision through the deployment of the next generation of single corner-cube lunar retroreflectors and active laser transponders. This is likely to expand the LLR station network. Lunar dynamical models and analysis tools have the potential to improve and fully exploit the long temporal baseline and precision allowed by millimetric LLR data. Some of the model limitations are outlined for future efforts. Differential observation techniques will help mitigate some of the primary limiting factors and reach unprecedented accuracy. Such observations and techniques may enable the detection of several subtle signatures required to understand the dynamics of the Earth-Moon system and the deep lunar interior. LLR model improvements would impact multi-disciplinary fields that include lunar and planetary science, Earth science, fundamental physics, celestial mechanics and ephemerides.

astro-ph.IM↗

arXiv2018

Determining parameters of Moon's orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from LLR observations made at different observatories in 1970-2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon's extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution. Solutions obtain accurate positions for the ranging stations and the 5 retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is -25.90 "/cy2, and the eccentricity is increasing by 1.48e-11 each year.

astro-ph.EP↗

arXiv2015

Historical Reflections on the Work of IAU Commission 4 (Ephemerides)

As part of a reorganization of the International Astronomical Union (IAU), Commission 4 (Ephemerides) went out of existence after the IAU General Assembly in August 2015. This paper presents brief discussions of some of the developments in fundamental astronomy that have influenced and been influenced by the work of Commission 4 over its 96-year history. The paper also presents notes about some of the publications of the national institutions that have played an essential role in the commission's mission. The contents of this paper were submitted for Commission 4's final report, to appear in IAU Transactions Vol. XXIX-A.

astro-ph.EP↗

arXiv2013

Bodily tides near the 1:1 spin-orbit resonance. Correction to Goldreich's dynamical model

Spin-orbit coupling is often described in the "MacDonald torque" approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2, 467), is combined with an assumption that the Q factor is frequency-independent (i.e., that the geometric lag angle is constant in time). This makes the approach unphysical because MacDonald's derivation of the said formula was implicitly based on keeping the time lag frequency-independent, which is equivalent to setting Q to scale as the inverse tidal frequency. The contradiction requires the MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky & Williams (2009; CMDA 104, 257), in application to spin modes distant from the major commensurabilities. We continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1:1 resonance. (For the original version of the model, see Goldreich 1966; AJ 71, 1.) We also study the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin rate larger than synchronous (pseudosynchronous spin). Which behaviour depends on the eccentricity, the triaxiality of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For small-amplitude librations, expressions are derived for the libration frequency, damping rate, and average orientation. However, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarov and Efroimsky (2012; arXiv:1209.1616) have found that a more realistic dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable.

astro-ph.EP↗

arXiv2012

Corner-cube retro-reflector instrument for advanced lunar laser ranging

Lunar laser ranging (LLR) has made major contributions to our understanding of the Moon's internal structure and the dynamics of the Earth-Moon system. Because of the recent improvements of the ground-based laser ranging facilities, the present LLR measurement accuracy is limited by the retro-reflectors currently on the lunar surface, which are arrays of small corner-cubes. Because of lunar librations, the surfaces of these arrays do not, in general, point directly at the Earth. This effect results in a spread of arrival times, because each cube that comprises the retroreflector is at a slightly different distance from the Earth, leading to the reduced ranging accuracy. Thus, a single, wide aperture corner-cube could have a clear advantage. In addition, after nearly four decades of successful operations the retro-reflectors arrays currently on the Moon started to show performance degradation; as a result, they yield still useful, but much weaker return signals. Thus, fresh and bright instruments on the lunar surface are needed to continue precision LLR measurements. We have developed a new retro-reflector design to enable advanced LLR operations. It is based on a single, hollow corner cube with a large aperture for which preliminary thermal, mechanical, and optical design and analysis have been performed. The new instrument will be able to reach an Earth-Moon range precision of 1-mm in a single pulse while being subjected to significant thermal variations present on the lunar surface, and will have low mass to allow robotic deployment. Here we report on our design results and instrument development effort.

physics.ins-det↗

arXiv2012

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).

astro-ph↗

arXiv2012

Lunar Laser Ranging Tests of the Equivalence Principle

The Lunar Laser Ranging (LLR) experiment provides precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of highly accurate measurements of the distance between the Earth and Moon provide unique information that determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Analyses of precise laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-0.8 +/- 1.3) x 10^{-13} for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, (m_G/m_I)_E - (m_G/m_I)_M. Such an accurate result allows other tests of gravitational theories. Focusing on the tests of the EP, we discuss the existing data and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches to solutions. Additional high accuracy ranges and improvements in the LLR data analysis model will further advance the research of relativistic gravity in the solar system, and will continue to provide highly accurate tests of the Equivalence Principle.

gr-qc↗

arXiv2010

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 $10^7$, 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 hours, 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 years 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.

gr-qc↗

arXiv2009

Opportunities for Probing Fundamental Gravity with Solar System Experiments

The recent discovery of "dark energy" has challenged Einstein's general theory of relativity as a complete model for our macroscopic universe. From a theoretical view, the challenge is even stronger: general relativity clearly does not extend to the very small, where quantum mechanics holds sway. Fundamental physics models thus require some major revisions. We must explore deeper to both constrain and inspire this needed new physics. In the realm of the solar-system, we can effectively probe for small deviations from the predictions of general relativity: Technology now offers a wide range of opportunities to pursue experiments with accuracies orders of magnitude better than yet achieved. We describe both the relevant theoretical backgrounds and the opportunities for far more accurate solar system experiments.

gr-qc↗

arXiv2009

Lunar Laser Ranging Tests of the Equivalence Principle with the Earth and Moon

A primary objective of the Lunar Laser Ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. Time series of the highly accurate measurements of the distance between the Earth and Moon provide unique information used to determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Current LLR solutions give $(-1.0 \pm 1.4) \times 10^{-13}$ for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, $Δ(M_G/M_I)$. This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of $Δ(M_G/M_I)_{\tt SEP} = (-2.0 \pm 2.0) \times 10^{-13}$. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter $η$ of $(4.4 \pm 4.5)\times10^{-4}$, where $η= 4β-γ-3$ and both $γ$ and $β$ are parametrized post-Newtonian (PPN) parameters. The PPN parameter $β$ is determined to be $β- 1 = (1.2 \pm 1.1) \times 10^{-4}$. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR ranging accuracy will further advance the research of relativistic gravity in the solar system, and, most notably, will continue to provide highly accurate tests of the Equivalence Principle.

gr-qc↗

arXiv2006

Williams et al. Reply (to the Comment by Dumin on "Progress in Lunar Laser Ranging Tests of Relativistic Gravity")

A decreasing gravitational constant, G, coupled with angular momentum conservation is expected to increrase a planetary semimajor axis, a, as \dot a/a=-\dot G/G. Analysis of lunar laser ranging data strongly limits such temporal variations and constrains a local (~1 AU) scale expansion of the solar system as \dot a/a=-\dot G/G =-(4\pm9)\times10^{-13} yr^{-1}, including that due to cosmological effects.

gr-qc↗

arXiv2006

Space-based tests of gravity with laser ranging

Existing capabilities in laser ranging, optical interferometry and metrology, in combination with precision frequency standards, atom-based quantum sensors, and drag-free technologies, are critical for the space-based tests of fundamental physics; as a result, of the recent progress in these disciplines, the entire area is poised for major advances. Thus, accurate ranging to the Moon and Mars will provide significant improvements in several gravity tests, namely the equivalence principle, geodetic precession, PPN parameters $β$ and $γ$, and possible variation of the gravitational constant $G$. Other tests will become possible with development of an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances. Motivated by anticipated accuracy gains, we discuss the recent renaissance in lunar laser ranging and consider future relativistic gravity experiments with precision laser ranging over interplanetary distances.

gr-qc↗

arXiv2005

Potential Capabilities of Lunar Laser Ranging for Geodesy and Relativity

Lunar Laser Ranging (LLR), which has been carried out for more than 35 years, is used to determine many parameters within the Earth-Moon system. This includes coordinates of terrestrial ranging stations and that of lunar retro-reflectors, as well as lunar orbit, gravity field, and its tidal acceleration. LLR data analysis also performs a number of gravitational physics experiments such as test of the equivalence principle, search for time variation of the gravitational constant, and determines value of several metric gravity parameters. These gravitational physics parameters cause both secular and periodic effects on the lunar orbit that are detectable with LLR. Furthermore, LLR contributes to the determination of Earth orientation parameters (EOP) such as nutation, precession (including relativistic precession), polar motion, and UT1. The corresponding LLR EOP series is three decades long. LLR can be used for the realization of both the terrestrial and selenocentric reference frames. The realization of a dynamically defined inertial reference frame, in contrast to the kinematically realized frame of VLBI, offers new possibilities for mutual cross-checking and confirmation. Finally, LLR also investigates the processes related to the Moon's interior dynamics. Here, we review the LLR technique focusing on its impact on Geodesy and Relativity. We discuss the modern observational accuracy and the level of existing LLR modeling. We present the near-term objectives and emphasize improvements needed to fully utilize the scientific potential of LLR.

gr-qc↗

arXiv2005

Lunar Laser Ranging Contributions to Relativity and Geodesy

Lunar laser ranging (LLR) is used to conduct high-precision measurements of ranges between an observatory on Earth and a laser retro-reflector on the lunar surface. Over the years, LLR has benefited from a number of improvements both in observing technology and data modeling, which led to the current accuracy of post-fit residuals of ~2 cm. Today LLR is a primary technique to study the dynamics of the Earth-Moon system and is especially important for gravitational physics, geodesy and studies of the lunar interior. LLR is used to perform high-accuracy tests of the equivalence principle, to search for a time-variation in the gravitational constant, and to test predictions of various alternative theories of gravity. On the geodesy front, LLR contributes to the determination of Earth orientation parameters, such as nutation, precession (including relativistic precession), polar motion, and UT1, i.e. especially to the long-term variation of these effects. LLR contributes to the realization of both the terrestrial and selenocentric reference frames. The realization of a dynamically defined inertial reference frame, in contrast to the kinematically realized frame of VLBI, offers new possibilities for mutual cross-checking and confirmation. Finally, LLR also investigates the processes related to the Moon's interior dynamics. Here, we review the LLR technique focusing on its impact on relativity and give an outlook to further applications, e.g. in geodesy. We present results of our dedicated studies to investigate the sensitivity of LLR data with respect to the relativistic quantities. We discuss the current observational situation and the level of LLR modeling implemented to date. We also address improvements needed to fully utilize the scientific potential of LLR.

gr-qc↗

arXiv2004

Progress in Lunar Laser Ranging Tests of Relativistic Gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the Equivalence Principle (EP); they also enable several very accurate tests of relativistic gravity. We report the results of our recent analysis of Lunar Laser Ranging (LLR) data giving an EP test of Δ(M_G/M_I)_{EP} =(-1.0 +/- 1.4) x 10^{-13}. This result yields a Strong Equivalence Principle (SEP) test of Δ(M_G/M_I)_{SEP} =(-2.0 +/- 2.0) x 10^{-13}. Also, the corresponding SEP violation parameter ηis (4.4 +/- 4.5) x 10^{-4}, where η=4β-γ-3 and both βand γare parametrized post-Newtonian (PPN) parameters. Using the recent Cassini result for the parameter γ, PPN parameter βis determined to be β-1=(1.2 +/- 1.1) x 10^{-4}. The geodetic precession test, expressed as a relative deviation from general relativity, is K_{gp}=-0.0019 +/- 0.0064. The search for a time variation in the gravitational constant results in \dot G/G=(4 +/- 9) x 10^{-13} yr^{-1}, consequently there is no evidence for local (~1AU) scale expansion of the solar system.

gr-qc↗

arXiv2004

Lunar Laser Ranging Science: Gravitational Physics and Lunar Interior and Geodesy

Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q=33 \pm 4 at a month and a weak dependence on period. Lunar rotation depends on interior properties; a fluid core is indicated with radius ~20% that of the Moon. Tests of relativistic gravity verify the equivalence principle to \pm 1.4 x 10^{-13}, limit deviations from Einstein's general relativity, and show no rate for the gravitational constant $\dot{G}/G$ with uncertainty 9 x 10^{-13} 1/yr.

gr-qc↗

arXiv2004

Lunar Laser Ranging Science

Analysis of Lunar Laser Ranging (LLR) data provides science results: gravitational physics and ephemeris information from the orbit, lunar science from rotation and solid-body tides, and Earth science. Sensitive tests of gravitational physics include the Equivalence Principle, limits on the time variation of the gravitational constant G, and geodetic precession. The equivalence principle test is used for an accurate determination of the parametrized post-Newtonian (PPN) parameter β. Lunar ephemerides are a product of the LLR analysis used by current and future spacecraft missions. The analysis is sensitive to astronomical parameters such as orbit, masses and obliquity. The dissipation-caused semimajor axis rate is 37.9 mm/yr and the associated acceleration in orbital longitude is -25.7 ''/cent^2, dominated by tides on Earth with a 1% lunar contribution. Lunar rotational variation has sensitivity to interior structure, physical properties, and energy dissipation. The second-degree lunar Love numbers are detected; k_2 has an accuracy of 11%. Lunar tidal dissipation is strong and its Q has a weak dependence on tidal frequency. A fluid core of about 20% the Moon's radius is indicated by the dissipation data. Evidence for the oblateness of the lunar fluid-core/solid-mantle boundary is getting stronger. This would be independent evidence for a fluid lunar core. Moon-centered coordinates of four retroreflectors are determined. Station positions and motion, Earth rotation variations, nutation, and precession are determined from analyses. Extending the data span and improving range accuracy will yield improved and new scientific results. Adding either new retroreflectors or precise active transponders on the Moon would improve the accuracy of the science results.

gr-qc↗