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Astrometric studies in the region of Algol

The distance and masses of the components of the triple star Algol (Beta Persei) are derived from photographic and electronic data collected with the two 0.76 m objectives of the Thaw Refractor at the University of Pittsburgh's Allegheny Observatory and with the 0.61 m visual refractor at Swarthmore College's Sproul Observatory. These datasets constitute the major narrow-field astrometric collections of this star. The newly derived weighted mean trigonometric parallax of Algol is now +0.0343 +/- 0.00085 corresponding to a distance modulus of 2.32 +/- 0.054 mag. The total mass of the Algol system is estimated at 6.05 +/- 0.45 solar mass. The photocentric semimajor axis of the AB/C orbit is determined in the blue, yellow, and red bandpasses of the three independent astrometric systems. The total mass for the A and B component stars is found to be 4.63 +/- 0.35 solar mass and the mass of the C component is determined to be 1.42 +/- 0.13 solar mass. Residuals to this solution showed no meaningful correlation to the orbital motion of A/B. Thus it is probable that the photocenter is located near the center of mass of the A/B subsystem. There is no evidence of a previously suggested 32 yr orbital motion and no significant acceleration is evident in the 60 yr photographic series. It is therefore unlikely that the system has a fourth stellar mass component. It is noted that the visual band interferometric studies of the Algol system have the AB and C components interchanged.

Gatewood, George↗

Coronal Structures in Cool Stars

Many papers have been published that further elucidate the structure of coronas in cool stars as determined from EUVE, HST, FUSE, Chandra, and XMM-Newton observations. In addition we are exploring the effects of coronas on the He I 1083081 transition that is observed in the infrared. Highlights of these are summarized below including publications during this reporting period and presentations. Ground-based magnetic Doppler imaging of cool stars suggests that active stars have active regions located at high latitudes on their surface. We have performed similar imaging in X-ray to locate the sites of enhanced activity using Chandra spectra. Chandra HETG observations of the bright eclipsing contact binary 44i Boo and Chandra LETG observations for the eclipsing binary VW Cep show X-ray line profiles that are Doppler-shifted by orbital motion. After careful analysis of the spectrum of each binary, a composite line-profile is constructed by adding the individual spectral lines. This high signal-to-noise ratio composite line-profile yields orbital velocities for these binaries that are accurate to 30 km/sec and allows their orbital motion to be studied at higher time resolutions. In conjunction with X-ray lightcurves, the phase-binned composite line-profiles constrain coronal structures to be small and located at high latitudes. These observations and techniques show the power of the Doppler Imaging Technique applied to X-ray line emission.

Oliversen, Ronald↗

Synthetic-aperture-radar imaging of the ocean surface using the slightly-rough facet model and a full surface-wave spectrum

A new model of synthetic-aperture-radar (SAR) imaging of ocean waves is described. The model is based on mapping individual, slightly-rough surface facets through the SAR processor into the image and responses of the facets in the image domain are added together coherently to give the composite image. A windowing technique allows both the orbital motion and the phase velocity of the long waves to be included. It is determined that the azimuthal cut-off is due to a smearing of the response of the facets in the image induced by the random orbital motion of the intermediate large-scale waves and that the focus adjustment that gives the greatest image contrast is half the phase velocity of the dominant long wave. The optimal processing technique, however, may consist of spatially offsetting the multiple looks on the image domain to compensate the propagation of long waves during the integration time of the SAR.

West, James C.↗

Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results

The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.

Eades, J. B., Jr.↗

Parabolic flight - Loss of sense of orientation

On the earth, or in level flight, a blindfolded subject being rotated at constant velocity about his recumbent long body axis experiences illusory orbital motion of his body in the opposite direction. By contrast, during comparable rotation in the free-fall phase of parabolic flight, no body motion is perceived and all sense of external orientation may be lost; when touch and pressure stimulation is applied to the body surface, a sense of orientation is reestablished immediately. The increased gravitoinertial force period of a parabola produces an exaggeration of the orbital motion experienced in level flight. These observations reveal an important influence of touch, pressure, and kinesthetic information on spatial orientation and provide a basis for understanding many of the postural illusions reported by astronauts in space flight.

Lackner, J. R.↗

Time Dependence of Collision Probabilities During Satellite Conjunctions

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

Hall, Doyle T.↗

General relativity and satellite orbits - The motion of a test particle in the Schwarzschild metric

The motion of a satellite of negligible mass about a massive spherically symmetric object in a space of Schwarzschild geometry is calculated by using ordinary Newtonian methods for an inverse-square gravitational field acted upon by an inverse-cube disturbing function. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted in the Lagrange planetary equations. The equations can be integrated to calculate the displacement in position of the satellite due to the relativistic potential. For example, the Beacon Explorer C satellite is found to be displaced by about 17.4 cm after one revolution. For Mercury the advance of the perihelion is about 85 km after one orbit, and the maximum periodic displacement is about 13 km.

Rubincam, D. P.↗

An assessment of the impact of spacecraft glow on the Hubble space telescope. Summary of existing observations and theory

Visible spacecraft glow was first observed on the Atmospheric Explorer spacecraft (AE-E) and studied in some detail with the Visible Airglow Experiment (VAE). The AE-E was a spin-stabilized spacecraft without thrusters at an altitude of 140 to 280 km. The VAE contained six visible wavelength photometers that measured a glow spectrum which: (1) rose steeply in the red, (2) decreased with a cos cubed PH1 dependence from pointing into the ram direction of the spacecraft orbital motion, and (3) decreased in intensity with increasing altitude with the same dependence as the measured atomic oxygen number atmospheric density (O) and not with the measured molecular nitrogen density (N sub 2). It is proposed that the glow is produced by chemical reactions on the spacecraft surface as it sweeps through the atmospheric O, with roughly 5-8 eV per O atom available for excitation from the orbital motion of the spacecraft. This glow may in principal be produced by any of a number of species, including molecular band emission from OH, NO, and NO2. An attempt is made to scale the observed glow to the Hubble space telescope.

Clarke, J. T.↗

Gravity field determination for Mars Observer

Mars Observer will be the first near circular, low altitude and short-periodic orbiter of Mars. From previous Mars orbiters, such as Mariner 9 and Vikings 1 and 2, a large gravitational oblateness and in general a gravity field ten times stronger than the earth's field have been determined. Because of these, the gravity field will dominate the evolution of the spacecraft's orbital motion and is the principal error source for reconstructing the spacecraft's motion. Thus a gravity calibration (GC) period has been established prior to the mapping phase in order to refine the gravitational field model. This paper describes the plan being made by Navigation to implement the GC strategy. By analyzing simulated Doppler data acquired during the seven day GC period, we give (1) the expected improvement in the gravity field model and (2) the resulting improvement in reconstructed spacecraft orbital motion. In addition, we have developed a strategy for converging the GC gravity model.

Esposito, Pasquale B.↗

Experimental study of transient liquid motion in orbiting spacecraft

A test program was conducted involving forty-five drops of liquid propellant in instrumented tanks. Biaxial, low-g accelerations were applied to the model propellant tanks during free-fall testing, and forces exerted during liquid reorientation were measured and recorded. High speed photographic records of the liquid reorientation were also made. The test data was used to verify a mechanical analog which portrays the liquid as a point mass moving on an ellipsoidal constraint surface. The mechanical analog was coded into two FORTRAN 4 digital computer programs. Results showed excellent correlation between test data and analytical predictions of reorientation forces and liquid center of mass motion, verifying the basic analytical approach.

Berry, R. L.↗

Langmuir-Probe Measurements in Flowing-Afterglow Plasmas

The validity of the orbital-motion theory for cylindrical Langmuir probes immersed in flowing- afterglow plasmas is investigated experimentally. It is found that the probe currents scale linearly with probe area only for electron-collecting but not for ion-collecting probes. In general, no agreement is found between the ion and electron densities derived from the probe currents. Measurements in recombining plasmas support the conclusion that only the electron densities derived from probe measurements can be trusted to be of acceptable accuracy. This paper also includes a brief derivation of the orbital-motion theory, a discussion of perturbations of the plasma by the probe current, and the interpretation of plasma velocities obtained from probe measurements.

Johnsen, R.↗

Relative motion of near orbiting satellites.

The relative motion of two particles on adjacent orbits about the same primary has been investigated under the condition that both motions have the same period. The geometrical properties of the relative displacement and velocity traces, on representative planes, are studied. A complete state of the motion is given; and, the range and range-rate variations, over one or more orbits, are described. It has been found that cusps appear on some of the traces provided that a proper relationship exists between the eccentricity and inclination. (Here, one particle moves on a circular path while the second moves on an ellipse). The conditions for which cusps appear are given, and typical traces are shown.

Eades, J. B., Jr.↗

Elliptic motion

Newtonian theory, Keplerian law, and two-body problem applied to orbital motion

NEWTON THEORY↗

Unveiling the chemical fingerprint of phosphorus-rich stars: I. In the infrared region of APOGEE-2

The origin of phosphorus, one of the essential elements for life on Earth, is currently unknown. Prevalent models of Galactic chemical evolution (GCE) systematically underestimate the amount of P compared to observations, especially at low metallicities. The recently discovered P-rich ([P/Fe] ≳ 1.2 dex) and metal-poor ([Fe/H] ≃ –1.0 dex) giants further challenge the GCE models, calling current theories on stellar nucleosynthesis into question. Since the observed low-mass giants are not expected to produce their high P contents themselves, our primary goal is to find clues on their progenitor or polluter. By increasing the number of known P-rich stars, we aim to narrow down a statistically reliable chemical abundance pattern that defines these peculiar stars. In this way, we place more robust constraints on the nucleosynthetic mechanism that causes the unusually high P abundances. In the long term, identifying the progenitor of the P-rich stars may contribute to the search for the source of P in our Galaxy. We performed a detailed chemical abundance analysis based on the high-resolution near-infrared (H band) spectra from the latest data release (DR17) of the APOGEE-2 survey. Employing the BACCHUS code, we measured the abundances of 13 elements in the inspected sample, which is mainly composed of a recent collection of Si-enhanced giants. We also analyzed the orbital motions and compared the abundance results to possible nucleosynthetic formation scenarios, and also to detailed GCE models. These models were produced with the OMEGA+ chemical evolution code, using four different massive star yield sets to investigate different scenarios for massive star evolution. We enlarged the sample of confirmed P-rich stars from 16 to a group of 78 giants, which represents the largest sample of P-rich stars to date. The sample includes the first detection of a P-rich star in a Galactic globular cluster. Significant enhancements in O, Al, Si, and Ce, as well as systematic correlations among the studied elements, unveil the unique chemical fingerprint of the P-rich stars. In contrast, the high [Mg/Fe] and [(C+N)/Fe] found in some of the P-rich stars with respect to P-normal stars is not confirmed over the full sample because of the current uncertainties. Strikingly, the strong overabundance in the α-element Si is accompanied by normal Ca and S abundances. This is at odds with current stellar nucleosynthesis models of massive stars. Our analysis of the orbital motion showed that the P-rich stars do not belong to a locally specific population in the Galaxy. In addition, we confirm that the majority of the sample stars are not part of binary systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Search for evidence of a clock related to the solar 154 day complex of periodicities

Evidence that has recently been compiled (Bai and Sturrock 1991) indicates that the enigmatic 154-day periodicity in solar activity may be viewed as part of a complex of periodicities that are approximate multiples of 25.8 days, suggesting that the Sun contains a 'clock' with frequency in the range 440 to 463 nano Hz. The clock may comprise either an oscillator or a rotator, each of which may be either real or virtual. We have reconsidered a previous spectrum analysis of the Zurich sunspot-number sequence by Knight, Schatten, and Sturrock (1979) which revealed a sharp, persistent and significant periodicity with a period of 12.072 days, corresponding to a frequency of about 958.8 nano Hz. This periodicity may be regarded as the (second) upper sideband of the second harmonic (2nu(sub R) + 2nu(sub E)) of a fundamental frequency of 447.7 nano Hz that is clearly within the search band. In this expression, nu(sub R) is the sidereal frequency of the hypothetical rotator and nu(sub E) is the frequency (31.69 nano Hz) of the Earth in its orbital motion around the Sun. In analyzing sunspot area data derived from the Greenwich data set, and on noting that any frequency is defined only to within the Nyquist frequency, we find clear evidence not only for the upper sideband of the second harmonic, but also for the second harmonic (2nu(sub R)) and the lower sideband of the second harmonic (2nu(sub R) - 2nu(sub E)). There is no strong peak at the fundamental frequency in the Greenwich data, but there is in the Zurich sunspot data. The effect of a linear oscillator is, to the lowest order in the amplitude, the same as the combined effect of two rotators of opposite polarities. A rotator that has arbitrary orientation with respect to the ecliptic may influence the outer layers of the Sun and thereby modulate the occurrence of solar activity such as sunspots. By analyzing a simple model, we find that such a rotator would influence surface activity in such a way that the spectrum of a 'signal' (such as the record of sunspots), as seen from the Earth, would contain components with frequencies that are certain integral combinations of nu(sub R) and nu(sub E). The amplitudes of the various components depend sensitively on theta, the angle between the axis of the rotator and the axis of the Earth's orbital motion. This simple model therefore offers a kinematical (but not dynamical) interpretation of the sunspot spectrum. The present analysis, while offering support of our conjectures that the Sun contains a clock that regulates the 154-day complex of periodicities, cannot distinguish between an osillator or a rotator (that might be a traveling wave), nor between a real rotator or a virtual rotator (that might be an apparent traveling wave due to the aliasing effect of an oscillator in a rotating system). Further analysis of sunspot and other data sets will be required to confirm the existence of such clock and (if it is real) to determine its physical nature.

Sturrock, P. A.↗

Physical Properties of Neptune and Triton Inferred from the Orbit of Triton

The orbital motion of Triton was redetermined from photographic data spanning the interval 1899-1981. The resulting ephemeris should provide Triton positions with respect to Neptune with an accuracy of plus or minus 500 km through the end of the century. The following physical results follow from the orbit solution. The inverse mass of Neptune + Triton is solar mass over (c sub N + m sub T) = 19490 plus or minus 40. No acceleration of the mean motion nor orbital eccentricity were detected, thus constraining the tidal dissipation factors of Neptune and Triton to O sub N less than or equal to 650 and QT less than or equal to 10,000. Tidal heating of Triton is presently insignificant. The gravitational harmonic J sub 2 of Neptune is 0.0043 plus or minus 0.0003 if Triton is as massive as m sub T/ M sub N = 0.00128, and if Neptune's spin is prograde with P approximately 18(h), or J sub 2 = 0.0037 plus or minus 0.0002 if Triton is much less massive. Triton undergoes extreme climatic variations due to the combined motion of it's orbit plane and Neptune's orbital motion. Approximately 10% of Triton's surface is presently hidden from diurnal insolation, which may provide a powerful cold trap for atmospheric voltatiles.

A W Harris↗