Abstract. GaussFit is a new computer program for solving least squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.

We present an absolute parallax and relative proper motion for the fundamental distance scale calibrator, δ Cep. We obtain these with astrometric data from FGS 3, a white-light interferometer on HST. Utilizing spectrophotometric estimates of the absolute parallaxes of our astrometric reference stars and constraining δ Cep and reference star HD 213307 to belong to the same association (Cep OB6, de Zeeuw et al. 1999), we find π abs = 3.66 ± 0.15 mas. The larger than typical astrometric residuals for the nearby astrometric reference star HD 213307 are found to satisfy Keplerian motion with P = 1.07 ± 0.02 years, a perturbation and period that could be due to a F0V companion ∼ 7 mas distant from and ∼4 magnitudes fainter than the primary. Spectral classifications and VRIJHKT 2 M and DDO51 photometry of the astrometric reference frame surrounding δ Cep indicate that field extinction is high and variable along this line of sight. However the extinction suffered by the reference star nearest (in angular separation and distance) to δ Cep, HD 213307, is lower and nearly the same as for δ Cep. Correcting for color differences, we find = 0.23 ± 0.03 for δ Cep, hence, an absolute magnitude M V = −3.47 ± 0.10. Adopting an average V magnitude, = 15.03 ± 0.03, for Cepheids with log P = 0.73 in the LMC from Udalski et al. (1999), we find a V-band distance modulus for the LMC, m-M = 18.50 ± 0.13 or, 18.58 ± 0.15, where the latter value results from a highly uncertain metallicity correction (Freedman et al. 2001). These agree with our previous RR Lyr HST parallax-based determination of the distance modulus of the LMC.

We present an absolute parallax and relative proper motion for the fundamental distance scale calibrator, RR Lyr. We obtain these with astrometric data from FGS 3, a white-light interferometer on HST. We find π abs = 3.82 ± 0.2 mas. Spectral classifications and VRIJHKT 2 M and DDO51 photometry of the astrometric reference frame surrounding RR Lyr indicate that field extinction is low along this line of sight. We estimate = 0.07 ± 0.03 for these reference stars. The extinction suffered by RR Lyr becomes one of the dominant contributors to the uncertainty in its absolute magnitude. Adopting the average field absorption, =0.07 ± 0.03, we obtain M RR V = 0.61 −0.11 +0.10 . This provides a distance modulus for the LMC, m-M=18.38 -18.53 −0.11 +0.10 with the average extinction-corrected magnitude of RR Lyr variables in the LMC, , remaining a significant uncertainty. We compare this result to more than 80 other determinations of the distance modulus of the LMC.

We report the first astrometrically determined mass of an extrasolar planet, a companion previously detected by Doppler spectroscopy. Radial velocities first provided an ephemeris with which to schedule a significant fraction of the HST observations near companion peri-and apastron. The astrometry residuals at these orbital phases exhibit a systematic deviation consistent with a perturbation due to a planetary mass companion. Combining HST astrometry with radial velocities, we solve for the proper motion, parallax, perturbation size, inclination, and position angle of the line of nodes, while constraining period, velocity amplitude, longitude of periastron, and eccentricity to values determined from radial

We report on a sub-stellar companion search utilizing interferometric fringe-tracking astrometry acquired with Fine Guidance Sensor 3 (FGS 3) on the Hubble Space Telescope. Our targets were Proxima Centauri and Barnard's Star. We obtain absolute parallax values for Proxima Cen π abs = 0. ′′ 7687 ± 0. ′′ 0003 and for Barnard's Star π abs = 0. ′′ 5454 ± 0. ′′ 0003.Once low-amplitude instrumental systematic errors are identified and removed, our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 60 days for Proxima Cen. Between the astrometry and the Kürster et al. 1999 radial velocity results we exclude all companions with M > 0.8M Jup for the range of periods 1 < P < 1000 days. For Barnard's Star our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 150 days. Our null results for Barnard's Star are consistent with those of Gatewood (1995).