Astrometry and Celestial Mechanics have entered a new era with the advent of Micro-arcsecond positions, parallaxes and proper motions. Cutting-edge science topics will be addressed that were far beyond our grasp only a few years ago. It will be possible to determine definitive distances to Cepheid variables, the center of our Galaxy, the Magellanic Clouds and other Local Group members. We will measure the orbital parameters of dwarf galaxies that are merging with the Milky Way, define the kinematics, dynamics and structure of our Galaxy and search for evidence of the Dark Matter that makes up most of the mass in the universe. Stellar masses will be determined routinely to 1% accuracy and we will be able to make full orbit solutions and mass determinations for Extrasolar planetary systems. If we are to take advantage of Micro-arcsecond astrometry, we need to reformulate our study of reference frames, systems and the equations of motion in the context of special and general relativity. Methods also need to be developed to statistically analyze our data and calibrate our instruments to levels beyond current standards. As a consequence, our curricula must be drastically revised to meet the needs of students in the 21st Century. With the above considerations in mind, we developed a syllabus for an introductory one-semester course in Astrometry and Celestial Mechanics. This course gives broad introductions to most topics in our fields and a base of knowledge from which a student can elect areas for self-study or attendance at centers where advanced courses, workshops or internships are available.

The occultation of a 9.1 magnitude star by asteroid (22) Kalliope and its satellite Linus was successfully observed in Japan in 2006 November 7.826 UT. This was the first definite observation of an occultation of a satellite of an asteroid that was discovered previously by other means. As a result the position of the satellite relative to Kalliope was obtained to be d = 0.246 ± 0.011 (arcsec), and P = 313.8 ± 2.7 (deg), where d is the angular distance and P is the position angle. The derived size for Kalliope is (209 ± 40)km × (136 ± 26)km (with the major axis in position angle of (8 ± 17) deg), and that for Linus is (33 ± 3) km. From the observations, the occulted star is also found to be a close double star whose separation is about 0.7 mas in position angle of about 300 deg, and the magnitudes of the components are found to be almost the same (~9.9 mag).

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.

The extra-solar planet WASP-1b, discovered by SuperWASP consortium in 2006, was observed through R filter using the 1-meter telescope with CCD camera at Yunnan Observatory on November 11, 2006. The systematic errors in photometric data were reduced by means of Tamuz et al. (2005) and Collier Cameron et al. (2006)'s algorithms. In order to estimate the parameters of the system, the MCMC (Markov Chain Monte Carlo) analysis is applied to fit the observed light curve. The following parameters of the system are derived: Rp=1.44RJ, Mp=0.88MJ, R*=1.52R⊙, a=0.0396AU. The new parameters of the planet imply its low density, which agrees to the previous results.

The reconstruction of the Photographic Zenith Tube (PZT) at Ondřejov has been finished recently. The main improvement of the instrument consists in the replacement of the photographic plate with the CCD chip, and a completely new electronic control system. In addition to the astrometric use of the observations we intend to derive the variations of the local vertical and compare them with gravimetric observations of the nearby station Pecný.

We discuss astrometric capabilities of the future interferometer ALMA that will be located at a high altitude site (5000m) in Northern Chile to operate in the sub-millimeter range. In this paper, we estimate the astrometric precision of ALMA to be ~0.18 milliarcsecond at the optimum observing frequency of 345 GHz from an error budget including the thermal noise and the systematic errors caused by uncertainties in antenna coordinates, reference source coordinates, Earth orientation parameters, dry atmosphere parameter and by phase fluctuations due to moisture above the site. We briefly discuss three applications: first, astrometric search of exoplanets around 446 nearby stars detectable by ALMA; second, proper motions and parallaxes of pre-stellar cores and protostars; third, the rotation rate of the debris disk around ε Eri to test the theory of dust trapping in mean motion resonances with unseen planets.

Here we discuss the effects of type-I migration of protoplanetary embryos on mass and semimajor axis distributions of extrasolar planets. We summarize the results of Ida & Lin (2008a, 2008b), in which Monte Carlo simulations with a deterministic planet-formation model were carried out. The strength of type-I migration regulates the distribution of extrasolar gas giant planets as well as terrestrial planets. To be consistent with the existing observational data of extrasolar gas giants, the type-I migration speed has to be an order of magnitude slower than that given by the linear theory. The introduction of type-I migration inhibits in situ formation of gas giants in habitable zones (HZs) and reduces the probability of passage of gas giants through HZs, both of which facilitate retention of terrestrial planets in HZs. We also point out that the effect of magneto-rotational instability (MRI) could lead to trapping of migrating protoplanetary embryos in the regions near an ice line in the disk and it significantly enhances formation/retention probability of gas giants against type-I migration.

We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis with the shearing-sheet approximation and the analytic results are compared with numerical calculation. We investigate the cases where magneto-rotational instability (MRI) does not occur: either the disk is two-dimensional, or a very strong field is exerted. We derive formulae for torque exerted on the planet for both cases. We find that two-dimensional torque is suppressed when plasma beta is less than 1 and three-dimensional modes dominate, in contrast to unmagnetized case.

We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995-2007) and radial velocity (2000-2007) measurements from the W. M. Keck 10 meter telescopes, the Keplerian orbital parameters for the short period star S0-2 imply a distance of 8.3 ± 0.3 kpc, an enclosed mass of 4.8 ± 0.3 × 106M⊙, and a black hole position that is localized to within ± 1 mas and that is consistent with the position of SgrA*-IR. Astrometric bias from source confusion is identified as a significant source of systematic error and is accounted for in this study. Our black hole mass and distance are significantly higher than previous estimates. The higher mass estimate brings the Galaxy into better agreement with the relationship between the mass of the central black hole and the velocity dispersion of the host galaxy's bulge observed for nearby galaxies. It also raises the orbital period of the innermost stable orbit of a non-spinning black hole to 38 min and increases the Rauch-Tremaine resonant relaxation timescales for stars in the vicinity of the central black hole. Taking the black hole's distance as a measure of R0, which is a fundamental scale for our Galaxy, and other measurements of galactic constants, we infer a value of the Galaxy's local rotation speed (θ0) of 255 ± 13 km s−1. With the precisions of the astrometric and radial velocity measurements that are now possible with Laser Guide Star Adaptive Optics, we expect to be able to measure Ro to an accuracy of ~ 1% within the next ten years, which could considerably reduce the uncertainty in the cosmological distance ladder.

The Pan-STARRS pathfinding telescope PS1 will begin a major set of surveys starting in 2008, and lasting for 3.5 years. One of these, the PS1 3π Survey, will repeatedly observe the entire sky north of −30 degrees, visiting every position 12 times in each of 5 filters. With single-epoch astrometry of 10 milliarcseconds, these observations will yield parallaxes for stars within 100 pc and proper motions out to several hundred pc. The result will be an unprecedented view on nearby stellar populations and insight into the dynamical structure of the local portions of the Galaxy. One exciting science product will be a volume-limited sample of nearby low-mass objects including thousands of L dwarfs, hundreds of T dwarfs, and perhaps even cooler sub-stellar objects. Another project will use proper-motion measurements to improve the membership of nearby star forming regions.

A series of ground-based, dedicated astrometric, observational programs have been performed or are in preparation which provide a dense and accurate optical reference frame. Integral to all these programs are new observations to link the Hipparcos Celestial Reference Frame (HCRF) to the International Celestial Reference Frame (ICRF), based on compact, extragalactic radio sources.

The U.S. Naval Observatory CCD Astrograph Catalog (UCAC) 3rd release is in preparation. A pixel re-reduction is in progress to improve astrometric and photometric accuracy as well as completeness of this all-sky reference catalog to 16th magnitude. Optical counterparts of ICRF radio sources have been observed with 0.9-meter telescopes contemporaneously. Scanning of over 5000 early-epoch astrograph plates on StarScan has been completed. These data will improve the proper motions of stars in the 10 to 14 mag range for the UCAC3 release.

A 111 million-pixel CCD was successfully fabricated in 2006 and test observations at the USNO astrograph are underway. Four of such detectors will be used for the USNO Robotic Astrometric Telescope (URAT) focal plane assembly. Phase I of URAT will use the astrograph to reach 18th magnitude, while the new 0.85-meter telescope with a 4.5 deg diameter field of view will reach 21st magnitude. The URAT primary mirror has been fabricated.

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 in the approximation of the linearized Einstein equations. All terms of the order of 1 μas and larger are taken into account, parameterized, and classified in accordance with their physical origin. We discuss the observational capabilities of the near-future optical and radio interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bending by Jupiter and Saturn.

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.

We present observational results on the red supergiant VY Canis Majoris with VERA. We have observed 22 GHz H2O masers and 43 GHz SiO masers (v=1 and 2 J=1-0) around VY CMa for 13 months. We succesfully detected a parallax of 0.87 ± 0.08 mas, corresponding to the distance of 1.15 +0.10−0.09 kpc using H2O masers. As the result of phase-referencing analyses, we have measured absolute positions for both H2O masers and SiO masers. The H2O maser features show rapid expansion off the central star.

Using phase-referenced multi-epoch Very Long Baseline Array observations, we have measured the trigonometric parallax of several young stars in the Taurus and Ophiuchus star-forming regions with unprecedented accuracy. The mean distance to the Taurus complex was found to be about 140 pc, and its depth around 20 pc, comparable to the linear extent of Taurus on the sky. In Ophiuchus, 4 sources have been observed so far. Two of them were found to be at about 160 pc (the distance traditionally attributed to Ophiuchus), while the other 2 are at about 120 pc. Since the entire Ophiuchus complex is only a few parsecs across, this difference is unlikely to reflect the depth of the region. Instead, we argue that two physically unrelated sites of star-formation are located along the line of sight toward Ophiuchus.

The Astrometric Data-Reduction Software (ADRS) processes fringe, delay, environmental, and calibration data for PRIMA narrow-angle astrometry. It is automated software designed to provide fully-calibrated differential delays and separation angles. The ADRS is divided into on-line and off-line processing. The former deals with calibration and data compression, while the latter applies corrections and calculates science quantities. PRIMA is the first VLTI instrument that may require removal of long-term environmental trends. The trend identification and fitting routines are not part of the distributed on-line and off-line processing software. Instead, files containing fit parameters will be updated regularly. Coding is presently underway. The PRIMA error budget summarizes the principal sources of error in PRIMA astrometric observations.

Deep-space laser ranging will be ideal for testing relativistic gravity, and mapping the solar-system to an unprecedented accuracy. ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I are such missions. ASTROD I is a mission with a single spacecraft; it is the first step of ASTROD with 3 spacecraft. In this talk, after a brief review of ASTROD and ASTROD I, we concentrate on the precision of solar astrodynamics that can be achieved together with implications on astrometry and reference frame ties. The precise planetary ephemeris derived from these missions together with second post-Newtonian test of relativistic gravity will serve as a foundation for future precise astrometry observations. Relativistic frameworks are discussed from these considerations.

The ESA astrometric mission Gaia will be able to put to test General Relativity thanks to differential astrometric measurements. The differential experiment, GAREX, implemented in the form of repeated Eddington-like measurement, aims at measuring the quadrupole light bending due to an oblate planet by comparing the evolution of relative distances in stellar fields in the vicinity of it. Simulations which utilize (i) selected fields extracted from the GSCII data base, (ii) a realistic error model as function of the star's magnitude and distance from Jupiter's edge, show the real best scenarios and how to improve the Gaia ability to detect this relativistic effect.

Although late stage gap formation reduces the surface density in the vicinity of protoplanets, simulations suggest gas may continue to leak through the protoplanets tidal barrier, replenishing the gas supply and allowing protoplanets to acquire masses comparable to or larger than that of Jupiter. Global gas depletion is a possible explanation for gaseous planets with lower masses in weak-line T-Tauri disks and ice giants in our own solar system, but it is unlikely to have stalled the growth of multiple systems around nearby stars that contain relatively low-mass, close-in planets along with more massive and longer period companions. Here, we suggest a potential solution. We show that supersonic infall of surrounding gas onto a protoplanet is only possible interior to both its Bondi and Roche radii. Although the initial Bondi radius is much smaller than its Roche radius, the former overtakes the latter during its growth. Thereafter, a positive pressure gradient is required to induce the gas to enter the Roche lobe of the protoplanet and flow is significantly reduced. We present the results of analysis and numerical simulations to show that the accretion rate increases rapidly with the ratio of the protoplanets Roche to Bondi radii. Based on these results we suggest that in regions with low geometric aspect ratios gas accretion is quenched, resulting in relatively low protoplanetary masses.

A compiled catalogue consisting of more than 22000 reference stars in the range of 10m – 16m obtained with 235 fields of δ from −17° to +80° around extragalactic radio sources (ERS) selected from the ICRF list. Initial catalogues were obtained from photographic (PG) and CCD observations.