Milliseconds Of Arc Research Articles

Image motion and experimental study of a 0.1″ space pointing measuring instrument for micro-vibration conditions

There exists an increasing need for Milli-Arc-Seconds (MAS) accuracy pointing measurement for current and future space systems. To meet the 0.1″ space pointing measurement accuracy requirements of spacecraft in future, the influence of spacecraft micro-vibration on a 0.1″ Space Pointing Measuring Instrument (SPMI) is studied. A Quasi-Zero Stiffness Device (QZSD) with adaptive adjustment and variable stroke was proposed. Then, a series of micro-vibration experiments of the SPMI were carried out. The influence of the micro-vibration generated by Guidance Navigation Control (GNC) attitude control components under different attitudes on the SPMI was analyzed. Point spread function of image motion in micro-vibration was also derived. Further, the changes of image motion under the micro-vibration environment were evaluated by extracting the gray centroid of the images, and the experiment processes and results are deeply discussed. The results show that the first-order frequency of the QZSD system is 0.114 Hz, and it is induced by a double pendulum system; the image motion of single flywheel spinning reached 0.015 pixels; whilst the image motion reached 0.03 pixels when three flywheels are combined spinning. These latest findings provide a beneficial theoretical and technical support for the development of spacecraft with 0.1″ pointing accuracy.

Application of the radial basis function neural network to the short term prediction of the Earth’s polar motion

By a number of test cases using different sample numbers and sample lengths, we obtain a Radial Basis Function Neural Network (RBFNN) model that is suitable for the short-term forecast of polar motion, especially for the ultra-short-term forecast. By using the same data sample of Earth’s polar motion, this RBFNN model can achieve better short-term prediction accuracy than the least-squares+autoregressive (LS+AR) method, and better ultra-short-term prediction accuracy than the LS+AR+Kalman method. Using this model to forecast the polar motion data from January 1, 2002 to December 30, 2007 and from January 1, 2010 to December 30, 2016, respectively, experimental results show that the ultra-short-term forecast accuracy of this RBFNN model is within a precision of 3.15 and 3.08 milliseconds of arc (mas) in polar motion x direction, 2.02 and 2.04 mas in polar motion y direction; the short-term forecast accuracy of RBFNN model is within a precision of 8.83 and 8.69 mas in polar motion x direction, and 5.59 and 5.85 mas in polar motion y direction. As is stated above, this RBFNN model is well capable of forecasting the short-term of polar motion, especially the ultra-short-term.

The Physical Librations of the Moon Caused by its Tidal Deformation

The Moon, like Earth, is not completely solid, and experiences deformation changes, for example due to the tides, caused by the gravitational pull of the Earth's orbit in a complex and resonant nature of the motion of the Moon. It is shown that these deformations lead to temporary variations of Moon inertia tensor components and consequently to the variations in the movement of the poles of the Moon, as well as to the variations of axial rotation. The indicated variations module is in the order of 10--12 mas (millisecond of arc). There variations are important for the development of the high-precision theory of lunar physical libration, suitable for modern projects for the reclamation of the Moon, in particular the Japanese project ILOM, which contemplates installing the telescope on the lunar surface and determining its orientation accuracy of the order of 1--0.1 msd, as well as the Russian lunar program, providing the launch of five automatic stations to the Moon in 2019--2024

HD 202206: A Circumbinary Brown Dwarf System∗

Abstract Using Hubble Space Telescope Fine Guidance Sensor astrometry and previously published radial velocity measures, we explore the exoplanetary system HD 202206. Our modeling results in a parallax, milliseconds of arc, a mass for HD 202206 B of , and a mass for HD 202206 c of . HD 202206 is a nearly face-on G + M binary orbited by a brown dwarf. The system architecture that we determine supports past assertions that stability requires a 5:1 mean motion resonance (we find a period ratio, ) and coplanarity (we find a mutual inclination, ).

A TECHNIQUE TO DERIVE IMPROVED PROPER MOTIONS FORKEPLEROBJECTS OF INTEREST

We outline an approach yielding proper motions with higher precision than exists in present catalogs for a sample of stars in the Kepler field. To increase proper motion precision we combine first moment centroids of Kepler pixel data from a single Season with existing catalog positions and proper motions. We use this astrometry to produce improved reduced proper motion diagrams, analogous to a Hertzsprung-Russell diagram, for stars identified as Kepler Objects of Interest. The more precise the relative proper motions, the better the discrimination between stellar luminosity classes. With UCAC4 and PPMXL epoch 2000 positions (and proper motions from those catalogs as quasi-bayesian priors) astrometry for a single test Channel (21) and Season (0) spanning two years yields proper motions with an average per-coordinate proper motion error of 1.0 millisecond of arc per year, over a factor of three better than existing catalogs. We apply a mapping between a reduced proper motion diagram and an HR diagram, both constructed using HST parallaxes and proper motions, to estimate Kepler Object of Interest K-band absolute magnitudes. The techniques discussed apply to any future small-field astrometry as well as the rest of the Kepler field.

Development of a digital zenith telescope for advanced astrometry

Like other optical astrometric techniques, the Photographic Zenith Tube (PZT) has played a key role in the past observations of the Earth rotation, and it also has a potential to be applied to several other observations by taking advantage of automatic observations with self compensation of tilt of the tube. We here propose In-situ Lunar Orientation Measurement (ILOM) to study lunar rotational dynamics by direct observations of the lunar rotation from the lunar surface by using a small telescope like PZT with an accuracy of 1 milli-seconds of arc (1 mas) in the post-SELENE mission. Our second application is to obtain local gravity field on the Earth by combining deflection of the vertical measured by PZT and the position measured by Global Positioning System (GPS) or Global Navigation Satellite System (GNSS). The accuracy required for this purpose is not as strict as ILOM. We have already developed a Bread Board Model (BBM) of the telescope for ILOM and made some experiments in order to know the performance of the driving mechanism under a similar condition to the lunar environment showing high vacuum, large temperature change and dusty condition. We have also shown that it is possible to correct the effects of uniform temperature change upon the optical system by using a simple model with an accuracy of better than 1 mas. This model has the potential to attain the accuracy of 1 mas, based on the results of the experiments and the simulations.

DISTANCE SCALE ZERO POINTS FROM GALACTIC RR LYRAE STAR PARALLAXES

We present new absolute trigonometric parallaxes and proper motions for seven Pop II variable stars: five RR Lyr variables; RZ Cep, XZ Cyg, SU Dra, RR Lyr, UV Oct; and two type 2 Cepheids; VY Pyx and {\kappa} Pav. We obtained these results with astrometric data from Fine Guidance Sensors, white-light interfer- ometers on Hubble Space Telescope. We find absolute parallaxes in milliseconds of arc: RZ Cep, 2.12\pm0.16 mas; XZ Cyg, 1.67\pm0.17 mas; SU Dra, 1.42\pm0.16 mas; RR Lyr, 3.77\pm0.13 mas; UV Oct, 1.71\pm0.10 mas; VY Pyx, 6.44\pm0.23 mas; and {\kappa} Pav, 5.57\pm0.28 mas; an average {\sigma}{\pi}/{\pi} = 5.4%. With these parallaxes we compute absolute magnitudes in V and K bandpasses corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Using these RRL absolute magnitudes, we then derive zero-points for MV -[Fe/H] and MK -[Fe/H]-Log P relations. The technique of reduced parallaxes corroborates these results. We employ our new results to determine distances and ages of several Galactic globular clusters and the dis- tance of the LMC. The latter is close to that previously derived from Classical Cepheids uncorrected for any metallicity effect, indicating that any such effect is small. We also discuss the somewhat puzzling results obtained for our two type 2 Cepheids.

New estimates of the inertia tensor and rotation of the triaxial nonrigid Earth

The Earth's rotation is perturbed by mass redistributions and relative motions within the Earth system, as well as by the torques from both the internal Earth and celestial bodies. The present study aims to establish a theory to incorporate all these factors perturbing the rotation state of the triaxial Earth, just like the traditional rotation theory of the axial‐symmetric Earth. First of all, we reestimate the Earth's inertia tensor on the basis of two new gravity models, EIGEN‐GL05C and EGM2008. Then we formulate the dynamic equations and obtain their normal modes for an Earth model with a triaxial anelastic mantle, a triaxial fluid core, and dissipative oceans. The periods of the Chandler wobble and the free core nutation are successfully recovered, being ∼433 and ∼430 mean solar days, respectively. Further, the Liouville equations and their general solutions for that triaxial nonrigid Earth are deduced. The Liouville equations are characterized by the complex frequency‐dependent transfer functions, which incorporate the effects of triaxialities and deformations of both the mantle and the core, as well as the effects of the mantle anelasticity, the equilibrium, and dissipative ocean tides. Complex transfer functions just reflect the fact that decays and phase lags exist in the Earth's response to the periodic forcing. Our theory reduces to the traditional rotation theory of the axial‐symmetric Earth when assuming rotational symmetry of the inertia tensor. Finally, the present theory is applied to the case of atmospheric‐oceanic excitation. The effective atmospheric‐oceanic angular momentum function (AMF)χeff=χeff1+iχeff2for the present theory is compared with the AMFχeffsym=χeff1sym+iχeff2symfor the traditional theory and the observed AMFχobs=χ1obs+iχ2obs; we find that the difference betweenχeffandχeffsymis of a few milliseconds of arc (mas) and can sometimes exceed 10 mas. In addition, spectrum analyses indicate thatχeffis in good agreement withχeffsymand, further, show an increase of coherency withχobsespecially in the low‐frequency band. The obvious advantage ofχeffin the low‐frequency band with respect toχeffsymis the critical support of the present theory. However, still better performance of our theory can be expected if the models of the mantle anelasticity and oceanic dynamics were improved. Thus we conclude that the traditional Earth rotation theory should be revised and upgraded to include the effects of the Earth's triaxiality, the mantle anelasticity, and oceanic dynamics. The theory presented in this study might be more appropriate to describe the rotation of the triaxial Earth (or other triaxial celestial bodies such as Mars), though further studies are needed to incorporate the effects of the solid inner core and other possible influences.

Revised atmospheric excitation function series related to Earth's variable rotation under consideration of surface topography

The atmospheric angular momentum is closely related to variations in the Earth rotation. The atmospheric excitation function (AEF), known also as the atmospheric effective angular momentum function, is introduced in studying the atmospheric excitation of the Earth's variable rotation. It may be separated into two portions, i.e., the “wind” terms due to the atmospheric motion relative to the mantle and the “pressure” terms due to the variations of atmospheric mass distribution evident through surface pressure changes. The AEF wind terms during the period of 1948–2004 are reprocessed from the National Centers for Environmental Prediction‐National Center for Atmospheric Research (NCEP/NCAR) reanalysis 6‐hourly wind and pressure fields. Some previous calculations were approximate, in that the wind terms were integrated from an isobaric lower boundary of 1000 hPa. To consider the surface topography effect, however, the AEF is computed by integration using the winds from the Earth's surface to 10 hPa, the top atmospheric model level, instead of from 1000 hPa. For these two cases, only a minor difference, equivalent to ∼0.004 ms in length‐of‐day variation, exists with respect to the axial wind term. However, considerable differences, equivalent to 5∼6 milliseconds of arc in polar motion, are found regarding equatorial wind terms. We further compare the total equatorial AEF (with and without the topography effect) with the polar motion excitation function (PMEF) during the period of 1980–2003. The equatorial AEF gets generally closer to the PMEF, and improved coherences are found between them when the topography effect is included.

Atmospheric and oceanic contributions to Chandler wobble excitation determined by wavelet filtering

Fluctuations of Earth rotation are associated with the redistribution and motion of mass elements in the Earth system. On seasonal to interannual timescales, the largest effects are due to mass redistributions within atmosphere and oceans. In order to study the Earth's reaction on geophysical excitations, the dynamic Earth system model DyMEG has been developed. It is based on the balance of angular momentum in the Earth system. The model is forced by consistent atmospheric and oceanic angular momenta from reanalysis data and a global ocean circulation model. As rotational deformations of the Earth are regarded, forced variations of Earth rotation due to atmospheric and oceanic excitations influence the free polar motion (Chandler wobble) of DyMEG. The comparison of the numerical model results with geodetic observations reveals a good agreement in both the annual and the Chandler frequency band. In order to support the presumption that the excitation energy of atmospheric and oceanic angular momenta within a spectral band around the Chandler frequency is sufficient to reproduce the observed Chandler wobble, the excitation series are band‐pass filtered. For consistent filtering and signal analysis, wavelet techniques based on the Morlet function are applied. When DyMEG is forced with the filtered excitations, the resulting polar motion resembles the actually observed Chandler oscillation, which is determined from geodetic observations applying the same filtering method. Between 1980 and 2002 the correlation coefficient between the unconstrained model result and the observed Chandler wobble amounts to 0.99 and the root‐mean‐square difference is 16 milliarc seconds.

A spectral search for the inner core wobble in Earth's polar motion

The inner core wobble (ICW) is a normal mode of rotation of the inner core relative to the mantle predicted theoretically. While many papers have been devoted to its theoretical formulation, no attempt of its detection has been published in the literature. In this work, we first give a preliminary formulation for the variations of gravity and geopotential coefficients associated with the ICW that complements the formulation for the polar motion. The results show that the ICW is most likely detectable using polar motion data. Then we attempt to detect the ICW by comparing the spectrum of an Earth orientation parameter time series with that of the sum of an oceanic angular momentum time series and an atmospheric angular momentum time series. We found no firm evidence of the ICW using our approach to a resolvability of a few milliarc seconds. At such a low amplitude in polar motion, the ICW is far below the current detectability of the variations of gravity measured by absolute and superconducting gravimeters and of the variations of the geopotential coefficients obtained from the Gravity Recovery and Climate Experiment (GRACE).

Confirmation of Errors inHipparcosParallaxes fromHubble Space TelescopeFine Guidance Sensor Astrometry of the Pleiades

We present absolute trigonometric parallaxes and relative proper motions for three members of the Pleiades star cluster, obtained with HST's Fine Guidance Sensor 1r, a white-light interferometer. We estimate spectral types and luminosity classes of the stars comprising the astrometric reference frame from R \approx 2,000 spectra, VJHK photometry, and reduced proper motions. From these we derive estimates of absolute parallaxes and introduce them into our model as observations with error. We constrain the three cluster members to have a 1 sigma dispersion in distance less than 6.4 pc, and find an average pi_{abs}=7.43+-0.17+-0.20 milliseconds of arc, where the second error is systematic due to member placement within the cluster. This parallax corresponds to a distance of 134.6+-3.1 pc or a distance modulus of (m-M)=5.65+-0.05 for these three Pleiads, presuming a central location. This result agrees with three other independent determinations of the Pleiades distance. Presuming that the cluster depth systematic error can be significantly reduced because of the random placement of these many members within the cluster, these four independent measures yield a best-estimate Pleiades distance of pi_{abs}=7.49+-0.07 milliseconds of arc, corresponding to a distance of 133.5+-1.2 pc or a distance modulus of (m-M)=5.63+-0.02. This resolves the dispute between the main sequence fitting and the Hipparcos distance moduli in favor of main sequence fitting.

Construction of a celestial coordinate reference frame from VLBI data

A large number (∼2 million) of VLBI observations have been reduced in order to refine the measured coordinates of the observed radio sources. The data reduction was carried out in the OCCAM package using the least squares colocation method. Corrections to the coordinates of 642 objects were derived. The accuracy of the catalog is no worse than 0.2 milliseconds of arc for stable sources.

Parameter variability of the observed periodic oscillations of polar motion with smaller amplitudes

Compared to the Chandler and annual wobbles, the higher-frequency components of polar motion (PM) have substantially smaller amplitudes. Therefore, their study has had to wait until higher-quality time series with high temporal resolution, as measured by space geodetic techniques, have become available. Based on the combined Earth orientation series SPACE99 computed by the Jet Propulsion Laboratory (JPL) from 1976 to 2000 at daily intervals, the periodic PM terms, in particular at the quasi-biennial, 300-day, semi-Chandler, semi-annual, 4-month, 90-day, 2-month and 1.5-month periods, have been separated by band-pass filtering and it has been found that the persistence of oscillations becomes less with increasing frequency. In order to quantify and better describe the parameter variability of these PM components over time, the radii, direction angles and period lengths were computed from the periodic terms filtered out from the time series. The results clearly show the characteristics and time evolution of the periodic PM components. The largest elliptic oscillation is the semi-annual wobble with a maximum semi-major axis of up to 13 mas (milliarc seconds). The other wobbles are smaller. They have maximum semi-major axes of between 3 and 8 mas. If the oscillations have period lengths of 4 months and less, then they are elapsed not only progradly, but also retrogradly.

Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior

The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation‐wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high‐precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation‐precession data derived from an up‐to‐date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time‐dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity ef of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than ∼5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are ~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of ∼10%, constitutes the first firm detection of the resonance associated with this mode; the period found is ∼1025 days, double that with electromagnetic couplings ignored. (Throughout this work, “days,” referring to periods, stands for “mean solar days.”) A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better fit to the nutation data than any of the earlier series based on geophysical theory. In particular, the residuals in the out of phase amplitudes of the retrograde 18.6 year and annual nutations, which had long remained at ∼0.5 milliseconds of arc (mas), are now reduced to the level of the uncertainties in the observational estimates, thanks mainly to the role played by the electromagnetic couplings. The largest remaining discrepancy is that in the out of phase prograde 18.6 year nutation, of ∼72 micorseconds of arc (μas). The frequency dependence of the nutation amplitudes cannot be exactly represented through a resonance formula, nor may the resonance frequencies themselves be interpreted as the eigenfrequencies of free modes because of the presence of complex and frequency‐dependent system parameters. Nevertheless, we have constructed a new resonance formula which reproduces our nutation series accurately for almost all nutation frequencies; for the few remaining frequencies, a listing is given of the corrections to be applied in order to reproduce the exact results of the direct solution.

A cosmic double helix in the archetypical quasar 3C273.

Finding direct evidence for plasma instability in extragalactic jets is crucial for understanding the nature of relativistic outflows from active galactic nuclei. Our radio interferometric observations of the quasar 3C273 made with the orbiting radio telescope, HALCA, and an array of ground telescopes have yielded an image in which the emission across the jet is resolved, revealing two threadlike patterns that form a double helix inside the jet. This double helical structure is consistent with a Kelvin-Helmholtz instability, and at least five different instability modes can be identified and modeled by a light jet with a Lorentz factor of 2 and Mach number of 3.5. The model reproduces in detail the internal structure of the jet on scales of up to 30 milli-arc seconds ( approximately 300 parsecs) and is consistent with the general morphology of the jet on scales of up to 1 kiloparsec.

Precise Masses for Wolf 1062 AB from [ITAL]HUBBLE SPACE TELESCOPE[/ITAL][ITAL]Hubble Space Telescope[/ITAL] Interferometric Astrometry and M[CLC]c[/CLC]Donald Observatory Radial Velocities

We present an analysis of astrometric data from FGS 3, a white-light interferometer on {\it HST}, and of radial velocity data from two ground-based campaigns. We model the astrometric and radial velocity measurements simultaneously to obtain parallax, proper motion and component masses for Wolf 1062 = Gl 748 AB (M3.5V). To derive the mass fraction, we relate FGS 3 fringe scanning observations of the science target to a reference frame provided by fringe tracking observations of a surrounding star field. We obtain an absolute parallax $\pi_{abs} = 98.0 \pm 0.4$ milliseconds of arc, yielding ${\cal M}_A = 0.379 \pm 0.005{\cal M}_{\sun}$ and ${\cal M}_B= 0.192 \pm 0.003 {\cal M}_{\sun}$, high quality component masses with errors of only 1.5%.

Diameters of δ Cephei and η Aquilae Measured with the Navy Prototype Optical Interferometer

We have measured the diameters of the Cepheid variables δ Cephei (18 nights) and η Aquilae (11 nights) with the Navy Prototype Optical Interferometer. The primary results of these observations are the mean angular diameters ⟨θLD⟩ of these Cepheids: 1.520 ± 0.014 milliseconds of arc (mas) for δ Cep and 1.69 ± 0.04 mas for η Aql. We also report limb-darkened diameters for the check stars in this program: for β Lac, θLD = 1.909 ± 0.011 mas and for 12 Aql, θLD = 2.418 ± 0.010 mas. When combined with radius estimates from period-radius relations in the literature, the Cepheid angular diameters suggest distances slightly smaller than, but still consistent with, the Hipparcos distances. Pulsations are weakly detected at a level of ∼1.5 to 2 σ for both Cepheids.

Coupling of long oceanic waves in the Pacific Ocean and the rotating elastic Earth during the 1986–1987 El Niño

We investigate interannual coupling between the rotating elastic Earth and the ocean during the 1986–1987 El Niño. We find the E‐W component of the ground tilt at the Esashi Earth Tides Station up toward the east about 50 milliarc seconds (mas), a rise of sea level about 5 cm at Chichijima and Oshima in the northwestern Pacific Ocean, and an increase of ∼1 cm in the very long baseline interferometry (VLBI) baseline distance between Kashima (Japan) and Kauai (Hawaiian Islands) as well as the residual length of day (LOD) changes of ∼50 μs during the 1986–1987 El Niño. The residual LOD is derived from elimination of changes in atmospheric angular momentum. Our discussions are based on the coupling between torsional motions of the elastic Earth and reflection of the eastward traveling equatorial Kelvin waves at the eastern boundary of the Pacific Ocean. These equatorial waves exchange the momentum and the axial and zonal component of vorticity with the elastic Earth. During the 1986–1987 El Niño, reflection of the Kelvin wave is expected to excite torsional motions and to couple with differential zonal rotation in the elastic Earth and to generate anomalies of ∼1.6 μs in LOD. The differential zonal rotation due to the torsional motion can produce the same order of the magnitude of changes in the VLBI baseline distance between Kashima and Kauai. Variations of the E‐W component of the tilt cannot be explained by torsional motion. We infer that the midlatitude Rossby waves are generated in the central Pacific Ocean. This conclusion is consistent with sea level changes at Chichijima and Oshima and changes of the tilt at Esashi.

Hipparcos Astrometric Results

AbstractThe astrometric results of Hipparcos include the positions at epoch (1991.25), the proper motion in the new IAU extragalactic reference system (ICRS), and parallaxes for about 118 000 stars. One dimensional positions are also given for 48 asteroids and 3 satellites. Due to the non-isotropy of the scanning law, the uncertainties are position dependent. Some indications of the remaining correlations are given. Various tests and comparisons show that systematic errors in parallax, if any, are not larger than 0.1 millisecond of arc.