Units of relativistic time scales and associated quantities

This note suggests nomenclature for dealing with the units of various astronomical quantities that are used with the relativistic time scales TT, TDB, TCB and TCG. It is suggested to avoid wordings like "TDB units" and "TT units" and avoid contrasting them to "SI units". The quantities intended for use with TCG, TCB, TT or TDB should be called "TCG-compatible", "TCB-compatible", "TT-compatible" or "TDB-compatible", respectively. The names of the units second and meter for numerical values of all these quantities should be used with out any adjectives. This suggestion comes from a special discussion forum created within IAU Commission 52 "Relativity in Fundamental Astronomy"

How Well Do We Know the Orbits of the Outer Planets?

This paper deals with the problem of astrometric determination of the orbital elements of the outer planets, in particular by assessing the ability of astrometric observations to detect perturbations of the sort expected from the Pioneer effect or other small perturbations to gravity. We also show that while using simplified models of the dynamics can lead to some insights, one must be careful to not over-simplify the issues involved lest one be misled by the analysis onto false paths. Specifically, we show that the current ephemeris of Pluto does not preclude the existence of the Pioneer effect. We show that the orbit of Pluto is simply not well enough characterized at present to make such an assertion. A number of misunderstandings related to these topics have now propagated through the literature and have been used as a basis for drawing conclusions about the dynamics of the solar system. Thus, the objective of this paper is to address these issues. Finally, we offer some comments dealing with the complex topic of model selection and comparison.Comment: Accepted for publication in the Ap

About the various contributions in Venus rotation rate and LOD

% context heading (optional) {Thanks to the Venus Express Mission, new data on the properties of Venus could be obtained in particular concerning its rotation.} % aims heading (mandatory) {In view of these upcoming results, the purpose of this paper is to determine and compare the major physical processes influencing the rotation of Venus, and more particularly the angular rotation rate.} % methods heading (mandatory) {Applying models already used for the Earth, the effect of the triaxiality of a rigid Venus on its period of rotation are computed. Then the variations of Venus rotation caused by the elasticity, the atmosphere and the core of the planet are evaluated.} % results heading (mandatory) {Although the largest irregularities of the rotation rate of the Earth at short time scales are caused by its atmosphere and elastic deformations, we show that the Venus ones are dominated by the tidal torque exerted by the Sun on its solid body. Indeed, as Venus has a slow rotation, these effects have a large amplitude of 2 minutes of time (mn). These variations of the rotation rate are larger than the one induced by atmospheric wind variations that can reach 25-50 seconds of time (s), depending on the simulation used. The variations due to the core effects which vary with its size between 3 and 20s are smaller. Compared to these effects, the influence of the elastic deformation cause by the zonal tidal potential is negligible.} % conclusions heading (optional), leave it empty if necessary {As the variations of the rotation of Venus reported here are of the order 3mn peak to peak, they should influence past, present and future observations providing further constraints on the planet internal structure and atmosphere.}Comment: 12 pages, 10 figures, Accepted in A&

The Full-sky Astrometric Mapping Explorer -- Astrometry for the New Millennium

FAME is designed to perform an all-sky, astrometric survey with unprecedented accuracy. It will create a rigid astrometric catalog of 4x10^7 stars with 5 < m_V < 15. For bright stars, 5 < m_V < 9, FAME will determine positions and parallaxes accurate to < 50 microarcseconds, with proper motion errors < 50 microarcseconds/year. For fainter stars, 9 < m_V < 15, FAME will determine positions and parallaxes accurate to < 500 microarcseconds, with proper motion errors < 500 microarcseconds/year. It will also collect photometric data on these 4 x 10^7 stars in four Sloan DSS colors.Comment: 6 pages, 4 figures, to appear in "Working on the Fringe

Relativistic Celestial Mechanics with PPN Parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.Comment: 71 page

Plantar fasciitis and calcaneal spur formation are associated with abductor digiti minimi atrophy on MRI of the foot

Objective To determine the association of atrophy of the abductor digiti minimi muscle (ADMA), an MRI manifestation of chronic compression of the inferior calcaneal nerve suggesting the clinical diagnosis of Baxter’s neuropathy, with MRI markers of potential etiologies, including calcaneal spur formation, plantar fasciitis, calcaneal edema, Achilles tendinosis and posterior tibial tendon dysfunction (PTTD). Materials and methods Prevalence of calcaneal spur formation, plantar fasciitis, calcaneal edema, Achilles tendinosis and PTTD was assessed retrospectively on 100 MRI studies with ADMA and 100 MRI studies without ADMA. Patients ranged in age from 10–92 years. Pearson chi-square analyses and Fisher’s exact test were used to compare prevalence of the above findings in patients with and without ADMA. Logistic regression was used to determine which variables were significantly associated with ADMA. Results Among patients with ADMA, there was significantly greater age (57.2 years vs 40.8 years, p \u3c 0.001), presence of Achilles tendinosis (22.0% vs 3.0%, P \u3c 0.001), calcaneal edema (15.0% vs 3.0%, P = 0.005), calcaneal spur (48.0% vs 7.0%, P \u3c 0.001), plantar fasciitis (52.5% vs 11.0%, P \u3c 0.001), and PTTD (32.0% vs 11.0%, P \u3c 0.001). After multivariate logistic regression analysis, only age [odds ratio (OR) 1.06, 95% confidence interval (CI) 1.03, 1.09], calcaneal spur (OR 3.60, 95% CI 1.28, 10.17), and plantar fasciitis (OR 3.35, 95% CI 1.31, 8.56) remained significant. Conclusion Advancing age, calcaneal spur, and plantar fasciitis are significantly associated with ADMA. Their high odds ratios support the notion of a possible etiologic role for calcaneal spur and plantar fasciitis in the progression to Baxter’s neuropathy