We use a Galerkin method to compute the eigenfunctions and eigenperiods of some of the Earths spheroidal and toroidal modes. The boundary conditions are treated using a Tau method. We show that for a realistic Earth model the difference between the computed and observed periods is less than 1.4%. We conclude that a Galerkin method may be an effective tool for the studies of the Earth's normal modes.

The understanding and modelling of the structure and evolution of stars is based on statistical physics as well as on hydrodynamics. Today, a precise identification and proper description of the physical processes at work in stellar interiors are still lacking (one key point being that of transport processes) while comparison of real stars to model predictions, which implies conversions from the theoretical space to the observational one, suffers from uncertainties in model atmospheres. This results in uncertainties on the prediction of stellar properties needed for galactic studies or cosmology (as stellar ages and masses). In the next decade, progress is expected from the theoretical, experimental and observational sides. I illustrate some of the problems we are facing when modelling stars and possible ways toward their solutions. I discuss how future observational ground-based or spatial programs (in particular those dedicated to micro-arc-second astrometry, asteroseismology and interferometry) will provide precise determinations of the stellar parameters and contribute to a better knowledge of stellar interiors and atmospheres in a wide range of stellar masses, chemical composition and evolution stages.

We describe the ongoing hardware and software developments that shall enable the ESO VLTI to perform narrow-angle differential delay astrometry in K-band with an accuracy of up to 10 μarcsec. The ultimate goal of these efforts is to perform an astrometric search for extrasolar planets around nearby stars.

We are entering the era of microarcsecond astrometric accuracy. Breaking the milliarcsecond barrier will lead to consequent leaps in astronomical understanding of diverse topics. Here we review some current ground-based trigonometric parallax efforts and their recent scientific results. We highlight the current status of nearby star research, including the RECONS census of stars within a 10 pc horizon, white dwarfs and cool subdwarfs, and the push to detect substellar objects via astrometry. We also provide details about recent improvements in the methodology that have permitted the determination of parallaxes with ~1 milliarcsecond accuracy, and what might be done to push routinely into the sub-millarcsecond regime.

We discuss the role of distances for understanding brown dwarfs and estimate the contribution expected by Gaia. We show that Gaia will only observe 25% of L and T dwarfs within 50pc which, at a conservative estimate, amounts to less than 400 objects. We discuss how Gaia results will nevertheless aid the ground-based programs providing reliable, bias free constraints for the calculation of parallaxes in an absolute system. We list the current ground-based programs underway and the possibilities for future all sky survey programs.

We review our work on Galactic open clusters in recent years, and introduce our proposed large program for the LOCS (LAMOST Open Cluster Survey). First, based on the most complete open clusters sample with metallicity, age and distance data as well as kinematic information, some preliminary statistical analysis regarding the spatial and metallicity distributions is presented. In particular, a radial abundance gradient of −0.058±0.006 dex kpc−1 is derived. By dividing clusters into the age groups we show that the disk abundance gradient was steeper in the past. Secondly, proper motions, membership probabilities, and velocity dispersions of stars in the regions of two very young open clusters are derived. Both clusters show clear evidence of mass segregation, which provides support for the “primordial” mass segregation scenario. Based on the advantages of the forthcoming LAMOST facility, we have proposed a detailed open cluster survey with LAMOST (the LOCS). The aim, feasibility, and the present development of the LOCS are briefly summarized.

As the oldest objects whose ages can be accurately determined, Galactic globular clusters can be used to establish the minimum age of the universe (and hence, to constrain cosmological models) and to study the early formation history of the Milky Way. The largest uncertainty in the determination of globular cluster ages is the distance scale. The current uncertainty in the distances to globular clusters is ~ 6%, which leads to a 13% uncertainty in the absolute ages of globular clusters. I am the PI on a SIM-Planetquest key project to determine the distances of 21 globular clusters with an accuracy of ranging from 1 to 4%. This will lead to age determinations accurate to 5 − 9%. The mean age of the oldest, most metal-poor globular clusters will be determined with an accuracy of ±3%.

Recent optical and near-infrared surveys have considerably improved our knowledge of galactic structure and galactic evolution. Two ways can be used to infer this knowledge from datasets: either inversing the data to get parameters describing the Galaxy, or using a synthetic approaches to test scenarios of formation and theoretical models for star and galaxy formation and evolution, both approaches being complementary. Using the synthetic approach the Besancon Galaxy model allows to test scenarios for the structure and evolution of the Galaxy by comparing simulations with the survey data. Examples are given using the 2MASS survey. Future uses of astrometric survey data are shown to be able to efficiently constrain the kinematics and dynamics of the Galaxy.

The concordance Cold Dark Matter model for the formation of structure in the Universe, while remarkably successful at describing observations on large scales, has a number of problems on galactic scales. The Milky Way and its satellite system provide a key laboratory for exploring dark matter (DM) in this regime, but some of the most definitive tests of local DM await microarcsecond astrometry, such as will be delivered by the Space Interferometry Mission (SIM Planetquest). I discuss several tests of Galactic DM enabled by future microarcsecond astrometry.

We study the transition between the thick and thick disks using solar neighbourhood data, focusing in particular on the status of local metal-poor thin disk stars ([Fe/H]<−0.3 dex, [α/Fe]<0.1 dex). The orbital properties of these stars, which are responsible for the hiatus in metallicity between the two disks, suggest that they most likely originate from the outer Galactic thin disk. It implies that the transition between the two stellar populations at a solar galactocentric distance must have occurred at a metallicity of about −0.3 dex. Transition stars at this metallicity are in fact present in local samples and fill the gap in α-element between the thick and thin disks. These results imply that, at least from the local data, there is a clear evolutionary link between the thick and thin disks.

Selecting 301 open clusters with complete spatial velocity measurements and ages, we are able to estimate the disk structure and kinematics of the Milky Way. Our analysis incorporates the disk scale height, the circular velocity of the Galactic rotation, the Galactocentric distance of the Sun and the ellipticity of the weak elliptical potential of the disk. We have derived the distance of the Sun to the Galactic center R0=8.03±0.70 kpc, that is in excellent agreement with the literature. From kinematic analysis, we found an age-dependent rotation of the Milky Way. The mean rotation velocity of the Milky Way is obtained as 235±10 km s−1. Using a dynamic model for an assumed elliptical disk, a clear weak elliptical potential of the disk with ellipticity of ε(R0) = 0.060±0.012 is detected, the Sun is found to be near the minor axis with a displacement of 30°±3°. The motion of clusters is suggested to be on elliptical orbits other than the circular rotation.

In 1992, we obtained the first observations of S2 a star close to the supermassive black hole at the Galactic Center. In 2002, S2 passed its periastron and in 2007, it completed a first fully observed revolution. This orbit allowed us to determine the mass of and the distance to the supermassive black hole with unprecedented accuracy. Here we present a re-analysis of the data set, enhancing the astrometric accuracy to 0.5 mas and increasing the number of well-determined stellar orbits to roughly 15. This allows to constrain the extended mass distribution around the massive black hole and will lead in the near future to the detection of post-Newtonian effects. We will also give an outlook on the potential of interferometric near-infrared astrometry with 10 microarcsecond accuracy from the VLTI.

We describe the efforts to understand our Milky Way Galaxy, from its center to outskirts, including (1) the measurements of the intrinsic size of the galactic center compact radio source Sgr A*; (2) the determination of the distance from the Sun to the Perseus spiral arm; and (3) the revealing of large scale global magnetic fields of the Galaxy.

With high-resolution millimeter-VLBI observations, Shen et al. (2005) have measured the intrinsic size of the radio-emitting region of the galactic center compact radio source Sgr A* to be only 1 AU in diameter at 3.5 mm. When combined with the lower limit on the mass of Sgr A*, this provides strong evidence for Sgr A* being a super-massive black hole. Comparison with the intrinsic size detection at 7 mm indicates a frequency-dependent source size, posing a tight constraint on various theoretical models.

With VLBI phase referencing observations, Xu et al. (2006) have measured the trigonometric parallax of W3OH in the Perseus spiral arm with an accuracy of 10 μas and also its absolute velocity with an accuracy of 1 km s−1. This demonstrates the capability of probing the structure and kinematics of the Milky Way by determining distances to 12 GHz methanol (CH3OH) masers in star forming regions of distant spiral arms and Milky Way's outskirts.

With pulsar dispersion measures and rotation measures, Han et al. (2006) can directly measure the magnetic fields in a very large region of the Galactic disk. The results show that the large-scale magnetic fields are aligned with the spiral arms but reverse their directions many times from the most inner Norma arm to the outer Perseus arm.

Measuring the proper motions and geometric distances of galaxies within the Local Group is very important for our understanding of its history, present state and future. Currently, proper motion measurements using optical methods are limited only to the closest companions of the Milky Way. However, given that VLBI provides the best angular resolution in astronomy and phase-referencing techniques yield astrometric accuracies of ≈ 10 micro-arcseconds, measurements of proper motions and angular rotation rates of galaxies out to a distance of ~ 1 Mpc are feasible. This paper presents results of VLBI observations in regions of H2O maser activity of the Local Group galaxies M33 and IC 10. Two masing regions in M33 are on opposite sides of the galaxy. This allows a comparison of the angular rotation rate (as measured by the VLBI observations) with the known inclination and rotation speed of the Hi gas disk leading to a determination of a geometric distance of 730 ± 100 ± 135 kpc. The first error indicates the statistical error of the proper-motion measurements, while the second error is the systematic error of the rotation model. Within the errors, this distance is consistent with the most recent Cepheid distance to M33. Since all position measurements were made relative to an extragalactic background source, the proper motion of M33 has also been measured. This provides a three dimensional velocity vector of M33, showing that this galaxy is moving with a velocity of 190 ± 59 km s−1 relative to the Milky Way. For IC 10, we obtain a motion of 215 ± 42 km s−1 relative to the Milky Way. These measurements promise a new handle on dynamical models for the Local Group and the mass and dark matter halo of Andromeda and the Milky Way.

We derived proper motions and membership probabilities of stars in the regions of two very young (~ 2–4 Myr-old) open clusters NGC 2244 and NGC 6530. Both clusters show clear evidence of mass segregation, which provides strong support for the suggestion that the observed mass segregation is – at least partially – due to the way in which star formation has proceeded in these complex star-forming regions (“primordial” mass segregation).

We derived the luminosity function of thick disk using V/Vmax method for nearby sub-dwarf stars based on the sample stars of Carney et al. (1994). Hipparcos parallaxes and proper motions and Tycho2 proper motions were combined with radial velocities and metallicities from CLLA. We found that the luminosity function in the absolute magnitude range MV = 4–6 mag agree well with the luminosity function derived from the initial mass function (Reyle & Robin 2001).

We have studied the impact of long-term variability and surface brightness asymmetries on the parallaxes of long-period variable stars and red supergiants.

Utilization of sub-milliarcsecond trigonometric parallaxes shifts the classical problem of calibration of stellar parameters to a new level of complexity. Derivation of stellar luminosity from the parallaxes is not a straightforward task with a number of statistical effects, such as Malmquist bias, to be taken into account. Different methods are to be used in order to derive parameters of luminosity function depending on the nature of underlying stellar sample. It is emphasized that any combination of astrometric parameters (i.e. parallaxes) and astrophysical ones must be handled carefully to avoid or reduce statistical effects, which otherwise may seriously affect the astrophysical applications.

We present the results of a wide-field, high-precision UBVIc CCD photometric survey of the Galactic open cluster Blanco 1. Standardized photometry was acquired using the Y4Kcam on the SMARTS 1m telescope at CTIO. We have also determined new high-precision proper motions (σμ = 0.3 mas yr−1) over an eight square degree area down to V = 16.5. Combined with 1D kinematic data, our survey yields a complete list of cluster members down to ~ 0.5 M⊙ and new high-fidelity color-magnitude diagrams are presented for Blanco 1. Having established a bona fide membership catalog, astrophysical characteristics of solar-type cluster members such as X-ray activity and lithium abundance have been studied to gain more insights in the process of internal mixing and convection. Our new results should also help to better understand its peculiar location in the Milky Way and to unravel its dynamical history.

We present preliminary results from a proper motion study of the Carina dwarf spheroidal galaxy. Our proper motions show a scatter of ~1.1 mas yr−1 per Carina member star, and we determinate the mean ensemble motion to an accuracy of ~7 mas century−1. While this is a precise measurement of the relative proper motions of Carina members, our correction to an absolute frame is limited by the small number of measured QSOs in the field.