P. Kenneth Seidelmann

Hubble Space Telescope Astrometric Observations and Orbital Mean Motion Corrections for the Inner Uranian Satellites

The 10 small inner satellites of Uranus were discovered in 1986 with Voyager 2 and not seen again until 1994, when eight were recovered with the Hubble Space Telescope Wide Field Planetary Camera 2 for astrometric, dynamical, and photometric studies. Thirty-three exposures were taken on 1994 August 14 with the PC1 chip in the BVRI filters. Measurable images of Ariel and Miranda were also obtained on the same CCD frames with those of the faint satellites. We present here the astrometric observations of these eight satellites relative to Miranda, as well as corrected orbital mean motions for them. For the full-well images of Ariel and Miranda, the astrometric limitation was due to an inadequate geometric distortion correction and distance from center. For the faint inner satellites, the astrometric precision varied from 50 mas for Bianca (V = 23 mag) to 9 mas for Puck (V = 20 mag) and was due primarily to a centroiding error caused by a low signal-to-noise ratio. The orbits of Owen & Synnott for the inner satellites were compared with these observations and corrections derived to their mean daily motions. While the orbits of Owen & Synnott proved to be better than their errors indicated, the new mean motions are 2 orders of magnitude more precise.

Stellar photometry with the Hubble Space Telescope Wide-Field/Planetary Camera: a progress report

We describe the prospects for the use of the Wide-Field/Planetary Camera (WFPC) for stellar photometry. The large halos of the point-spread function (PSF) resulting from spherical aberration and from spatial, temporal, and color variations of the PSF are the main limitations to accurate photometry. Degradations caused by crowding are exacerbated by the halos of the PSF. Here we attempt to quantify these effects and determine the current accuracy of stellar photometry with the WFPC. In realistic cases, the brighter stars in crowded fields have 0.09 mag errors; fainter stars have larger errors depending on the degree of crowding. We find that measuring Cepheids in Virgo Cluster galaxies is not currently possible without inordinate increases in exposure times.

HUBBLE SPACE TELESCOPE ASTROMETRIC OBSERVATIONS AND ORBITAL MEAN MOTION CORRECTIONS FOR THE INNER SATELLITES OF NEPTUNE

Six small inner satellites of Neptune were imaged in 1989 with Voyager 2. In 1997, we recovered the four outermost with the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 for astrometric, dynamical, and photometric studies. The ring arcs were not detected in our images. Thirteen exposures were taken in each of three HST orbits: two orbits on July 3 and one on July 6. Exposures were taken in the BVI filters. Measurable images of Neptune and Triton were also obtained on the same PC1 frames with those of the faint satellites. We present here the astrometric observations of these four satellites relative to Neptune, as well as corrected orbital mean motions for them. Field distortions in the PC1 chip were corrected with both the Trauger et al. and the Anderson & King distortion models. Calibration of the scale and orientation was accomplished by comparing the measured positions of Neptune and Triton with an accurate JPL J2000 ephemeris. Separate calibrations were made for both distortion models. Small differences were detected in the calibrations, dependent on wavelength, saturation, and filter, and a small difference was found between the calibrations resulting from both distortion correction models. The resulting separation and position angle observations for the inner satellites were compared with the orbits of Owen et al. and corrections derived to their mean daily motions. A small but significant discrepancy was found for Proteus between the correction derived from the observations of separation and that from the position angles. This was shown not to be due to calibrational errors but, apparently, to the need for improvement of other orbital elements—at least for Proteus. Despite this anomaly, the mean motion accuracies were improved by almost 2 orders of magnitude as a result of the longer baseline since the Voyager observations. More HST observations of these satellites are recommended in order to improve their orbits further and for the investigation of satellite-ring interactions.

Time scales, their users, and leap seconds

Numerous time scales exist to address specific user requirements. Accurate dynamical time scales (barycentric, geocentric and terrestrial) have been developed based on the theory of relativity. A family of time scales has been developed based on the rotation of the Earth that includes Universal Time (specifically UT1), which serves as the traditional astronomical basis of civil time. International Atomic Time (TAI) is also maintained as a fundamental time scale based on the output of atomic frequency standards. Coordinated Universal Time (UTC) is an atomic scale for worldwide civil timekeeping, referenced to TAI, but with epoch adjustments via so-called leap seconds to remain within one second of UT1. A review of the development of the time scales, the status of the leap-second issue, and user considerations and perspectives are discussed. A description of some more recent applications for time usage is included.

The Future of Time: UTC and the Leap Second

Before atomic timekeeping, clocks were set to the skies. But starting in 1972, radio signals began broadcasting atomic seconds and leap seconds have occasionally been added to that stream of atomic seconds to keep the signals synchronized with the actual rotation of Earth. Such adjustments were considered necessary because Earths rotation is less regular than atomic timekeeping. In January 2012, a United Nations-affiliated organization could permanently break this link by redefining Coordinated Universal Time. To understand the importance of this potential change, its important to understand the history of human timekeeping.

The Full-Sky Astrometric Mapping Explorer – Distances and Photometry of 40 Million Stars

The Full-sky Astrometric Mapping Explorer (FAME) is designed to perform an all-sky, astrometric survey with unprecedented accuracy. It will create a rigid astrometric catalog of 4 × 10 7 stars with 5 m V m V μ as, with proper motion errors μ as/yr. For fainter stars, 9 m V μ as, with proper motion errors μ as/yr. It will also collect photometric data on these 4 × 10 7 stars in four Sloan Digital Sky Survey colors. NASA selected FAME to be one of five MIDEX missions funded for a concept study. In October 1999, NASA selected FAME for launch in 2004 as the MIDEX-4 mission in its Explorer program.

Mean Solar Time and Its Connection to Universal Time

Universal Time is the measure of Earth rotation that also serves as the astronomical basis of civil timekeeping. As the successor to Greenwich Mean Time (GMT), Universal Time intended to maintain uniform time as the angle between zero longitude and the mean sun—a fictitious point moving uniformly along the celestial equator that keeps pace with the Sun over the very long term. However, variability in the rotation rate of the Earth has caused Universal Time to diverge from the original geometric concept of mean solar time by approximately (1/365.2422) ΔT, where ΔT is the accumulated measure of nonuniform Earth rotation since 1900. After accounting for changes in the origin of the terrestrial and celestial reference systems since the end of the nineteenth century, simulated transits confirm that the Sun on average now crosses zero longitude at 12 h 00 m 00.2 s Universal Time, a result that is expected from theory.

How Gravity and Continuity in UT1 Moved the Greenwich Meridian

The concept of “Greenwich Mean Time,” and its modern equivalent, Universal Time, is based on the changing angle between a “prime meridian” and some point on the celestial sphere. In 1884, at the International Meridian Conference, it was recommended that the prime meridian “to be employed as a common zero of longitude and standard of time-reckoning throughout the globe” pass through the Airy “transit instrument at the Observatory of Greenwich.” Today, observatory visitors must walk approximately 102 m east before their satellite-navigation receivers indicate zero longitude. The need to maintain continuity in Universal Time by the Bureau International de l’Heure, in conjunction with a transition from astronomical to geodetic coordinates by 1984, when optical astronomical methods were replaced by modern techniques, is responsible for this offset. The difference between astronomical and geodetic longitudes is the deflection of the vertical in the east-west direction. Modern techniques enabled the establishment of a global reference frame centered at the center of mass of the Earth, through which the plane of the geodetic prime meridian passes. While the geodetic prime meridian does not intersect the Airy transit instrument at the surface of the Earth, its orientation with respect to the celestial sphere has remained intact.

The n-Body Problem

When going from two bodies to three, or more, bodies, the complexity increases significantly, due to their mutual attractions. The two-body problem can be mathematically formulated so a closed-form solution is possible. With more than two bodies, it is impossible to formulate such a solution. There are some special cases, however, that can be handled.

General Perturbations Theory

We have seen the complexity of the problem when more than two gravitating masses are involved. We have seen two methods of determining the orbits, Cowell’s and Encke’s methods . Now, let us look at the basic mathematical description of the perturbation problem.