Twenty years ago, there was disagreement at a level of a factor of two as regards the value of the expansion rate of the Universe. Ten years ago, a value that was good to 10% was established using the Hubble Space Telescope (HST), completing one of the primary missions that NASA designed and built the HST to undertake. Today, after confronting most of the systematic uncertainties listed at the end of the Key Project, we are looking at a value of the Hubble constant that is plausibly known to within 3%. In the near future, an independently determined value of H0 good to 1% is desirable to constrain the extraction of other cosmological parameters from the power spectrum of the cosmic microwave background in defining a concordance model of cosmology. We review recent progress and assess the future prospects for those tighter constraints on the Hubble constant, which were unimaginable just a decade ago.

Allan Sandage returned to the distance scale and the calibration of the Hubble constant again and again during his active life, experimenting with different distance indicators. In 1952 his proof of the high luminosity of Cepheids confirmed Baade's revision of the distance scale (H0 ~ 250 km s−1 Mpc−1). During the next 25 years, he lowered the value to 75 and 55. Upon the arrival of the Hubble Space Telescope, he observed Cepheids to calibrate the mean luminosity of nearby Type Ia supernovae (SNe Ia) which, used as standard candles, led to the cosmic value of H0 = 62.3 ± 1.3 ± 5.0 km s−1 Mpc−1. Eventually he turned to the tip of the red giant branch (TRGB) as a very powerful distance indicator. A compilation of 176 TRGB distances yielded a mean, very local value of H0 = 62.9 ± 1.6 km s−1 Mpc−1 and shed light on the streaming velocities in the Local Supercluster. Moreover, TRGB distances are now available for six SNe Ia; if their mean luminosity is applied to distant SNe Ia, one obtains H0 = 64.6 ± 1.6 ± 2.0 km s−1 Mpc−1. The weighted mean of the two independent large-scale calibrations yields H0 = 64.1 km s−1 Mpc−1 within 3.6%.

One of the Milky Way's fundamental parameters is the distance of the Sun from the Galactic Center, R0. This article reviews the various ways of estimating R0, placing special emphasis on methods that have become possible recently. In particular, we focus on the geometric distance estimate made possible thanks to observations of individual stellar orbits around the massive black hole at the center of the Galaxy. The specific issues of concern there are the degeneracies with other parameters, most importantly the mass of the black hole and the definition of the reference frame. The current uncertainty is nevertheless only a few percent, with error bars shrinking every year.

Very Long Baseline Interferometry (VLBI) observations can provide the positions of compact radio sources with an accuracy of order 50 micro-arcseconds. This is sufficient to measure the trigonometric parallax and proper motions of any object within 500 pc of the Sun to better than a few percent. Because they are magnetically active, young stars are often associated with compact radio emission detectable using VLBI techniques. Here we show how VLBI observations have already constrained the distance to the most often studied nearby regions of star formation (Taurus, Ophiuchus, Orion, etc.) and have started to provide information about their internal structure and kinematics. We will then briefly describe a large project, the ‘Gould's Belt Distances Survey,’ which has been designed to provide a detailed view of star formation in the solar neighborhood using VLBI observations.

The method of statistical-parallax determination is used to adjust the photometric distance-scale zero points and test the selection of several samples of old and intermediate-age tracer objects in the Milky Way, including RR Lyrae- and Mira-type variables, blue and red horizontal-branch stars, and red giants. We obtain reasonable and stable absolute-magnitude (and, hence, photometric distance-scale) corrections for all samples except for the red horizontal-branch stars, which appear to be significantly contaminated by main-sequence turn-off and subgiant stars.

We report on the parsec program, which observed 140 L and T dwarfs on a regular basis from 2007 to 2011, using the WIFI camera on the ESO/2.2 m telescope. Trigonometric parallaxes at 5 mas precision are derived for 49 objects, and mas yr−1-level proper motions are derived for approximately 200,000 objects in the same fields. We discuss image cleaning, object centroiding, and astrometric methods, in particular three different approaches for trigonometric parallax determination.

Determination of trigonometric parallaxes is one of the very few direct methods available for measuring cosmic distances, and the only one capable of reaching beyond the Solar System. It is fundamental both to determine the intrinsic properties of astrophysical objects and as the first step on the cosmic distance ladder. Steady improvements of instruments and techniques have extended the applicability of the parallax method to ever greater distances. However, it is not correct to say that the method is independent of physical assumptions. This review covers ground-based optical techniques, from Bessel's time to the present, as well as space observations and radio interferometry. Some emphasis is put on the physical limitations of the method, in particular its sensitivity to source structure and photocentric variability on different timescales.

The Pleiades is the best-studied open cluster in the sky. It is one of the primary open clusters used to define the ‘zero-age main sequence,' and hence it serves as a cornerstone for programs which use main-sequence fitting to derive distances. This role is called into question by the ‘Pleiades distance controversy:' the distance to the Pleiades from Hipparcos of approximately 120 pc is significantly different from the distance of 133 pc derived using other techniques. To resolve this issue, we plan to use Very Long Baseline Interferometry to derive a new, independent trigonometric parallax distance to the Pleiades. In these proceedings we present our observational program and report some preliminary results.

We present a new determination of the distance to the Pleiades using the moving-cluster method, allowing for inclusion of the effects of expansion and rotation of the cluster. While rotation appears neglegible, we find a slight expansion of the cluster with a maximum velocity of 0.15 km s−1 and a distance modulus of (m − M)0 = 5.50 ± 0.13 mag. This is larger but compatible with the new Hipparcos distance modulus of 5.40 ± 0.03 mag. On the other hand, various distance moduli for the Pleiades are found in the literature, many resulting from isochrone fitting. They scatter around a value of 5.63 mag. Our results are also compatible with these measurements, within the error bars.

Gaia's five-year observation baseline might naively lead to the expectation that it will be possible to fit the parallax of any sufficiently nearby object with the default five-parameter model (position at a reference epoch, parallax and proper motion). However, simulated Gaia observations of a ‘model Universe’ composed of nearly 107 objects, 50% of which turn out to be multiple stars, show that the single-star hypothesis can severely affect parallax estimation and that more sophisticated models must be adopted. In principle, screening these spurious single-star solutions is rather straightforward, for example by evaluating the quality of the fits. However, the simulated Gaia observations also reveal that some seemingly acceptable single-star solutions can nonetheless lead to erroneous distances. These solutions turn out to be binaries with an orbital period close to one year. Without auxiliary (e.g., spectroscopic) data, they will remain unnoticed.

In determining the distances to stars within the Milky Way galaxy, one often uses photometric or spectroscopic parallaxes. In these methods, the type of each individual star is determined, and the absolute magnitude of that star type is compared with the measured apparent magnitude to determine individual distances. In this paper, we define the term statistical photometric parallax, in which statistical knowledge of the absolute magnitudes of stellar populations is used to determine the underlying density distributions of those stars. This technique has been used to determine the density distribution of the Milky Way's stellar halo and its component tidal streams, using very large samples of stars from the Sloan Digital Sky Survey. Most recently, the volunteer computing platform MilkyWay@home has been used to find the best-fitting model parameters for the density of these halo stars.

Astrometric observations of neutron stars have been conducted with a variety of techniques and over a wide range of wavelengths, ranging from radio-pulse timing and Very Long Baseline Interferometry to optical and X-ray imaging. Here I review the techniques and scientific goals behind recent high-precision neutron-star astrometry. Such measurements can yield model-independent distances and velocities that can be exploited, for example, to locate neutron-star birth sites, establish reference-frame ties, model the Galactic electron-density distribution, and constrain the astrophysics of supernova explosions. Recently, the Fermi gamma-ray space telescope has identified several highly luminous recycled pulsars, and precise measurement of their distances is of paramount importance to understand their energetics and astrophysics. The ongoing science returns from precision astrometry will continue in the long term with improvements in technology such as focal-plane arrays and synergies with new telescopes such as Gaia and the Square Kilometer Array.

A common approach to determining distances to stars without astrometric information is to compare stellar evolution models with parameters obtained from spectroscopic techniques. This method is routinely applied in the context of large-scale stellar surveys out to distances of several kpc. However, systematic errors may arise because of inaccurate spectroscopic parameters. We explore the effects of non-local thermodynamic equilibrium (NLTE) on the determination of surface gravities and metallicities for a large sample of metal-poor stars within approximately 10 kpc of the Sun. Using the improved Teff scale, we then show that stellar parameters estimated based on the widely used method of 1D LTE excitation-ionization balance of Fe results in distances which are systematically in error. For metal-poor giants, [Fe/H] ~ −2 dex, the distances can be overestimated by up to 70%. We compare the results with those from the Radial Velocity Experiment Survey catalogue (rave) for the stars in common, and find similar offsets.

Our team was awarded 108 orbits of Hubble Space Telescope time to obtain parallaxes and photometry of nine metal-poor stars with [Fe/H] < −1.5 dex. The parallaxes are obtained from observations with the Fine Guidance Sensor (FGS 1r; 11 orbits per star) and photometry was obtained with the Advanced Camera for Surveys (one orbit per star). The first data were obtained in October 2008, and the data collection is ongoing. It is anticipated that the observations will be complete in June 2013. Preliminary data reduction has been completed for five of our target stars. The parallax errors vary from 0.12 to 0.16 milli-arcseconds, and the parallaxes are at least an order of magnitude more accurate than existing Hipparcos parallaxes for these stars. The errors in the true distance modulus range from 0.02 to 0.03 mag. Ground-based high-resolution spectra have been analyzed to obtain accurate abundances for three stars. The properties of the two stars with accurate abundances and parallaxes are in excellent agreement with those predicted by stellar evolution models.

We present a distance measurement to the semi-regular variable star RX Bootis (RX Boo). Using the VLBI Exploration of Radio Astrometry (VERA) telescope, we conducted astrometric observations of a water maser spot associated with RX Boo, as well as of the continuum reference source J1419+2706. Based on monitoring observations covering a full year, the annual parallax of RX Boo was measured at 7.31 ± 0.50 mas, corresponding to a distance of 136+10−9 pc. This distance uncertainty is smaller by a factor of two than those previously published, allowing us to determine the object's stellar properties more accurately. Using our distance, we can determine the absolute magnitude and discuss more precisely the locus of RX Boo on the period–luminosity (PL) relation. RX Boo exhibits two simultaneous pulsation periods and is located on the fundamental and first overtone Mira sequences of the PL relation. In addition, we calculated the radius and mass of the star.

We present a measurement of the trigonometric parallax of IRAS 05168+3634 with VERA. The parallax is 0.532 ± 0.053 milli-arcsec, corresponding to a distance of 1.88+0.21−0.17 kpc. This is significantly closer than the previous distance estimate of 6 kpc based on a kinematic distance measurement. This drastic change in the source distance implies the need for revised values of not only the physical parameters of IRAS 05168+3634, but it also impies a different location in the Galaxy, placing it in the Perseus arm rather than the Outer arm. We also measured the proper motion of the source. A combination of the distance and proper motion with the systemic velocity yields a rotation velocity Θ = 227+9−11 km s−1 at the source position, assuming Θ0 = 240 km s−1. Our result, combined with previous VLBI results for six sources in the Perseus arm, indicates that the sources rotate systematically more slowly than the Galactic rotation velocity at the local standard of rest. In fact, we derive peculiar motions in the disk averaged over the seven sources in the Perseus arm of (Umean, Vmean) = (11 ± 3, −17 ± 3) km s−1, which indicates that these seven sources are moving systematically toward the Galactic Center and lag behind the overall Galactic rotation.

RR Lyrae variables are the primary standard candles for old stellar populations, and the traditional first step in the definition of the distance scale. Their properties are known on the basis of well-established physical concepts and their calibration is based on several empirical methods. Both aspects are critically reviewed, and their application as distance indicators within the Galaxy and the Local Group are discussed, also in view of the observing facilities that will be available in the near future.

We review and discuss results of our survey of variable stars towards the Galactic Centre and their distances. In our near-infrared monitoring survey using IRSF/SIRIUS, we detected a number of Miras and Cepheids (both classical and type II) within 20 arcmin of the Galactic Centre. These distance indicators yield a distance to the Galactic Centre of between 7.5 and 8.5 kpc. A new calibration of the red clump also leads to a distance of ~ 8 kpc. For these indicators, which are luminosity-based, a large uncertainty resides in the correction for the foreground extinction, which depends on the reddening law. Nevertheless, our estimates are consistent with previous estimates based the kinematics of stars near the Galactic Centre, and this supports the reddening law we use.

We present new and independent estimates of the distances to the Magellanic Clouds (MCs) using near-infrared (NIR) and optical–NIR period–Wesenheit (PW) relations. The slopes of the PW relations are, within the dispersion, linear over the entire period range and independent of metal content. The absolute zero points were fixed using Galactic Cepheids with distances based on the infrared surface-brightness method. The true distance modulus we found for the Large Magellanic Cloud—(m − M)0 = 18.48 ± 0.01 ± 0.10 mag—and the Small Magellanic Cloud—(m − M)0 = 18.94 ± 0.01 ± 0.10 mag—agree quite well with similar distance determinations based on robust distance indicators. We also briefly discuss the evolutionary and pulsation properties of MC Cepheids.

We present a calibration of the metallicity and physical parameters (temperature, luminosity, gravity, mass, radius) for RR Lyrae stars using the ugrizsdss photometric system. Our work is based on calculations of synthetic horizontal branches (HBs), fully taking into account evolutionary effects for a wide range in metallicities and HB morphologies. We provide analytical fits that are able to provide all quantities mentioned with very high (internal) precision, based solely on mean sdss magnitudes and colors.