Marc A. Murison

On predicting long-term orbital instability : a relation between the Lyapunov time and sudden orbital transitions

In three examples representative of Solar System dynamics, we find that the Lyapunov time, T L (i.e., the inverse of the Lyapunov exponent) and the time for an orbit to make a sudden transition T C are strongly correlated. The relation between the two times is T C ∞T L b , with b≅1.8. The first example examines asteroid orbits interior to Jupiter; the sudden transition occurs when the asteroid makes a close approach to Jupiter, which occurs close to the time when the asteroids orbit crosses Jupiters orbit

STELLAR ASTROPHYSICS WITH A DISPERSED FOURIER TRANSFORM SPECTROGRAPH. I. INSTRUMENT DESCRIPTION AND ORBITS OF SINGLE-LINED SPECTROSCOPIC BINARIES

We have designed and constructed a second-generation version of the dispersed Fourier transform spectrograph, or dFTS. This instrument combines a spectral interferometer with a dispersive spectrograph to provide high-accuracy, high-resolution optical spectra of stellar targets. The new version, dFTS2, is based upon the design of our prototype, with several modifications to improve the system throughput and performance. We deployed dFTS2 to the Steward Observatory 2.3 m Bok Telescope from 2007 June to 2008 June, and undertook an observing program on spectroscopic binary stars, with the goal of constraining the velocity amplitude K of the binary orbits with 0.1% accuracy, a significant improvement over most of the orbits reported in the literature. We present results for radial velocity reference stars and orbit solutions for single-lined spectroscopic binaries.

Initial Results from the USNO Dispersed Fourier Transform Spectrograph

We have designed and constructed a ‘‘dispersed Fourier transform spectrometer’’ (dFTS), consisting of a conventionalFTSfollowedbyagratingspectrometer.Bycombiningthesetwodevices,wenegateasubstantialfraction of the sensitivity disadvantage of a conventional FTS for high-resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well suited to stellar spectroscopy, velocimetry,and extrasolar planet detection, which is competitive with existing high-resolution, high-accuracy stellar spectrometers. In this paper we describe the design of our prototype dFTS,explain the algorithmwe use to efficiently reconstruct a broadbandspectrum from a sequence of narrowband interferograms, and present initial observations and resulting velocimetry of stellar targets. Subject headingg binaries: spectroscopic — instrumentation: interferometers — instrumentation: spectrographs — planetary systems — techniques: interferometric

On an efficient and accurate method to integrate restricted three-body orbits

This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.

Full-sky Astrometric Mapping Explorer: an optical astrometric survey mission

The Full-sky Astrometric Mapping Explorer (FAME) is a MIDEX class Explorer mission designed to perform an all-sky, astrometric survey with unprecedented accuracy, determining the positions, parallaxes, proper motions, and photometry of 40 million stars. It will create a rigid, astrometric catalog of stars from an input catalog with 5 < mv < 15. For bright stars, 5 < mv < 9, FAMEs goal is to determine positions and parallaxes accurate to < 50 (mu) as, with proper motion errors < 50 (mu) as/year. For fainter stars, 9 < mv < 15, FAMEs goal is to determine positions and parallaxes accurate to < 500 (mu) as, with proper motion errors < 500 (mu) as/year. It will also collect photometric data on these 40 million stars in four Sloan DSS colors.

Chaotic orbits and long term stability: an example from asteroids of the Hilda group

This paper calculates Lyapunov times, T(L), for certain members of the Hilda minor planets, a group that librates at the 3:2 mean motion resonance with Jupiter. We find that many are definitely chaotic, but that the resulting escape times T(c), obtained from a relation that we recently published [Lecar et al., AJ, 104, 1230 (1992)] does not conflict with their being present today. On the other hand, we show that bodies with libration amplitudes 10 to 20 deg larger than the maximum currently found would have escaped during the lifetime of the solar system. We interpret this behavior as «observational» support for the relation between T(L) and T(c) that LFM inferred from numerical simulations. Consideration of T(L)s for real and hypothetical objects with low proper eccentricities at and near the Hilda group lends further support

POINTS: an astrometric spacecraft with multifarious applications

POINTS is a dual astrometric optical interferometer with nominal baseline length of 2 m and measurement accuracy of 5 microarcsecs for targets separated by about 90 degrees on the sky. If selected as the ASEPS-1 mission, it could perform a definite search for extra-solar planetary systems, either finding and characterizing a large number of them or showing that they are far less numerous than now believed. If selected as AIM, it could be a powerful new multidisciplinary research tool, opening new areas of astrophysical research and changing the nature of the questions being asked in some old areas. Based on a preliminary indication of the observational needs of the two missions, we find that a single POINTS mission lasting ten years would meet the science objectives of both ASEPS-1 and AIM. POINTS, which is small, agile, and mechanically simple, would be the first of a new class of powerful instruments in space and would prove the technology for the larger members of the class that are expected to follow. The instrument is designed around a metrology system that measures both the critical distances internal to the starlight interferometers and the angle between them. Rapid measurement leads to closure on the sky and the ability to detect and correct time-dependent measurement biases.

Optic-misalignment tolerances for the POINTS interferometers

We present the results of two parallel studies of the sensitivity of astrometric measurements to misalignment of each of the major optical assemblies in the POINTS instrument. Tilt and displacement of the optics lead to tilt, displacement, and defocussing of the starlight and metrology beams, giving rise to systematic errors. In one method, we derive analytic expressions for the lowest order dependence of the error on the misalignment, and evaluate them in the present interferometer design. In the second method, we use a commercial numerical ray tracing program to calculate the overall optical path travelled through the misaligned starlight and metrology paths; from those results, our own software determines the dependence of the residual error on the original misalignment. These sensitivities are compared to the analytic results for mutual verification. We also discuss the impact these results have had on the design of the instrument.

STELLAR ASTROPHYSICS WITH A DISPERSED FOURIER TRANSFORM SPECTROGRAPH. II. ORBITS OF DOUBLE-LINED SPECTROSCOPIC BINARIES

We present orbital parameters for six double-lined spectroscopic binaries (ι Pegasi, ω Draconis, 12 Bootis, V1143 Cygni, β Aurigae, and Mizar A) and two double-lined triple star systems (κ Pegasi and η Virginis). The orbital fits are based upon high-precision radial velocity (RV) observations made with a dispersed Fourier Transform Spectrograph, or dFTS, a new instrument that combines interferometric and dispersive elements. For some of the double-lined binaries with known inclination angles, the quality of our RV data permits us to determine the masses M 1 and M 2 of the stellar components with relative errors as small as 0.2%.

POINTS: the instrument and its mission

POINTS comprises a pair of independent Michelson stellar interferometers and a laser metrology system that measures both the critical starlight paths and the angle between the two baselines. The nominal design has baselines of 2 m, subapertures of 35 cm, and a single- measurement accuracy of 5 microarcseconds for targets separated by approximately equals 90 degree(s). In a five-year mission, POINTS could yield, e.g., a 1% Cepheid distance scale, galactic mass distribution, knowledge of cluster dynamics, and stellar masses and luminosities. In a ten-year mission, POINTS could perform a deep search for other planetary systems, using only 20% of the available observing time. POINTS does global astrometry, i.e., it measures widely separated targets, which yields closure calibration, numerous bright reference stars, and absolute parallax. The instrument has only three moving-part mechanisms, and only one of these must move with sub-milliradian accuracy. On each side of the interferometer, there are only three (interferometrically critical) optical surfaces preceding the beamsplitter or its fold flat. POINTS is small, agile, and mechanically simple. It would prove much of the technology for future imaging interferometers.