Relativity in astrometry,Celestial mechanics and geodesy

Book review

Relativity in astrometry, Celestial mechanics and geodesySoffel, M. H.: 1989, Springer Verlag, DM 98. (Hardcover) (ISBN 3-540-18906-8)     

Earth,Moon, And Planets

Instructions for Authors

Earth, Moon, And Planets     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Physics of the earth and the solar system

Book Review

Physics of the earth and the solar systemB. Bertotti and P. Farinella, Kluwer Academic Publishers, (Volume 31 of Geophysics and Astrophysics Monographs) xv + 479 pp., subject index; price, £74.00, $99.00, Dfl 200 (hardcover); ISBN 0-7923-0535-3     

The large-number hypothesis and the Earth's expansion

The equation of state of the terrestrial material obtained from seismic data is adopted to construct three zone earth models under hypothesis of variable constant of gravityG as proposed by Dirac. Three hypotheses are investigated: variableG without creation, creation such thatm (mass) G ^–1, and multiplicative creation,mG ^–2. It is shown that, with the currently accepted value of the Hubble constant, , and for each hypothesis. On the multiplicative creation, the Earth radius would have been 5100 km, which is in agreement with estimate by some geophysicists.     

The intensity,velocity and magnetic structure of a sunspot region

The observational set-up for a detailed study of the velocity, intensity and magnetic-field fine structure in and around a sunspot is described. On highly resolved spectra we detected in the vicinity of a sunspot a large number of points with strong magnetic fields (magnetic knots). The magnetic field in these knots causes a striking decrease of the line depth (or a line gap after Sheeley, 1967). The properties of the magnetic knots are: (1) magnetic fields up to 1400 gauss; (2) diameter 1100 km; (3) coincidence with dark intergranular spaces; (4) generally downward material motion; (5) lifetime>30min; (6) estimated total number around an unipolar spot 2000; (7) combined magnetic flux comparable to the sunspot flux; (8) coincidence with Ca⁺ plages.For the smallest sunspots (pores) we obtained magnetic fields >1500 gauss. Hence a magnetic field of about 1400–1500 gauss appears to be a rather critical level for pore and spot formation.We found a large number of small areas producing line gaps without measurable magnetic field. These non-magnetic gap-regions coincide with bright continuum structures.Some aspects arising from the occurrence of hundreds of magnetic knots in an active region are discussed in the last section.Presently guest investigator at the Göttingen Observatory.Previously member of the High Altitude Observatory solar project at Sacramento Peak (Contract Nr. AF (628) - 4078).     

OBITUARY: Mukul Kundu (1930 – 2010)

Obituary

OBITUARY: Mukul Kundu (1930 – 2010)     

Determination of the equilibrium fO2 in bulk samples of H,L, and LL ordinary chondrites by solid‐state electrochemistry

High‐temperature solid‐state electrochemistry techniques (EMF method) were used to measure the oxygen fugacity (fO₂) of the ordinary chondrites Ochansk (H4), Savtschenskoje (LL4), Elenovka (L5), Vengerovo (H5), and Kharkov (L6). The fO₂ results are presented in the form of the following equations: It was found that fO₂ regularly increases from H chondrites to LL chondrites. Measured fO₂ are ~1.5 higher than those previously calculated from mineral assemblages. Kharkov (L6) is a little more oxidized than Elenovka (L5) in agreement with the progressive oxidation model. At the same time, Ochansk (H4) is more oxidized than Vengerovo (H5) and exhibits a slightly different slope compared to other chondrites and at T > 1200 K, becomes more reduced than Kharkov (L6) or Elenovka (L5). Measured oxygen fugacity values of meteorites fall within (0.1–1.0)·log fO₂ of one another. The possible explanation of discrepancies between measured and calculated values is discussed.     

Semi-detached binaries: The origin and present status of TU Mon,SX Cas,and DM Per

An attempt is made to trace back the possible progenitor systems of the Algol-type binaries TU Mon, SX Cas, and DM Per. The present characteristics are compared to the result of the evolution of 9M ₀+5.4M ₀. The position of the hot components in the HRD is discussed with regard to the theoretical models.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia 3–7 June, 1983.     

The mid-infrared structure of the bipolar nebulae AFGL 915, AFGL 618, and AFGL 2688

We have obtained near diffraction-limited images of three bipolar PPN at UKIRT in October, 1993: AFGL 915 (the Red Rectangle), AFGL 618, and AFGL 2688 (the Egg Nebula). Images were taken at unidentified infrared (UIR) emission feature wavelengths and at several continuum wavelengths in the 10 and 20µm atmospheric windows. In all three PPN the emission is dominated by a central point source with fainter emission extending for several arcsec. In AFGL 2688, the mid-IR emission is extended in the same direction as the main optical lobes. In AFGL 915, the UIR feature emission is spatially separated from the central source. The spikes that have been observed at 2µm and give the nebula its rectangular appearance are also visible at 10µm.     

Fundamentals of Celestial Mechanics

Book review

Fundamentals of Celestial MechanicsDanby, J. M. A.: 1988, Willmann-Bell, Inc., US $19.95 (softbound)     

Dependence of DOLP on Coronal Electron Temperature,Speed, and Structure

We study the predictive capabilities of magnetic-feature properties (MF) generated by the Solar Monitor Active Region Tracker (SMART: Higgins et al. in Adv. Space Res. 47, 2105, 2011) for solar-flare forecasting from two datasets: the full dataset of SMART detections from 1996 to 2010 which has been previously studied by Ahmed et al. (Solar Phys. 283, 157, 2013) and a subset of that dataset that only includes detections that are NOAA active regions (ARs). The main contributions of this work are: we use marginal relevance as a filter feature selection method to identify the most useful SMART MF properties for separating flaring from non-flaring detections and logistic regression to derive classification rules to predict future observations. For comparison, we employ a Random Forest, Support Vector Machine, and a set of Deep Neural Network models, as well as lasso for feature selection. Using the linear model with three features we obtain significantly better results (True Skill Score: TSS = 0.84) than those reported by Ahmed et al. (Solar Phys. 283, 157, 2013) for the full dataset of SMART detections. The same model produced competitive results (TSS = 0.67) for the dataset of SMART detections that are NOAA ARs, which can be compared to a broader section of flare-forecasting literature. We show that more complex models are not required for this data.

     

Gravitational orbit-attitude coupling for very large spacecraft

Motion equations for the gravitationally coupled orbit-attitude motion of a spacecraft are presented. The gravitational force and torque are expanded in a Taylor series in the small ratio (spacecraft size/orbital radius). A recursive definition for higher moments of inertia is introduced which permits terms up tofourth order to be retained. The expressions are fully nonlinear in the attitude variables. A quasi-sunpointing (QSP) passive attitude-control mode is used to assess the effects of higher moments of inertia and gravitational coupling. The attitude motion is detectably coupled to the orbital motion. However, the higher moments of inertia influence only the attitude motion.Nomenclature f _G ,g _G ,f _Gi ,g _Gi total gravitational force and torque and their components of orderi in =/r ₀ - angular momentum of spacecraft about 0 and the spacecraft mass center - J ⁱ ,I ⁱ general moment of inertia about 0 and the spacecraft mass center - second (dyadic), third (triadic), and fourth (tetradic) moment of inertia about 0 and the spacecraft mass center - A andB (and related components) of the second, third and fourth moments of inertia about 0, see Equation (9) - M, m Earth's mass, spacecraft mass - Q ^ba rotation matrix taking _a into _b - position vector from attracting body's mass center to a general mass element, to 0 and to the spacecraft mass center - ₁, ₂, ₃ basis vectors of reference frame - , , _N misalignment angle betweenb ₃ and the (projected) true position of the Sun, its oscillatory component and nominal value - unit dyadic (-identity matrix) - ratio of characteristic spacecraft dimension to orbital radius - pitch angle (aboutb ₂ axis) - Earth's gravitational parameter - , position vector from 0 to a general mass element and the spacecraft mass center - , the (projected) true longitude of the Sun and the true longitude of the spacecraft - _/ angular velocity of reference frame with respect to - (·), (^*), (^o) d()/dt with respect to inertial space _I , and orbiting frame _O and a body-fixed spacecraft frame _b Presented at AAS/AIAA Astrodynamics Conference, Aug. 9–11, 1982.     

Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy². It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.     

Isovortical orbits of autonomous,conservative, two degree-of-freedom dynamical systems

For an autonomous, conservative, two degree-of-freedom dynamical system, vorticity (the curl of velocity) is constant along the orbit if the velocity field is divergence-free such that: $$u\left( {x, v} \right) - \psi _y , v\left( {x, y} \right) = - \psi _x .$$ Isovortical orbits in configuration space are level curves of a scalar autonomous function Ψ (x, v) satisfying a second-order, non-linear partial differential equation of the Monge-Ampere type: $$2\left( {\psi _{xx} \psi _{yy} - \psi _{xy}^2 } \right) + U_{xx} + U_{yy} = 0,$$ where U(x. y) is the autonomous potential function. The solution Soc the time variable is reduced to a quadrature following determinatio of Ψ. Self-similar solutions of the Monge-Ampere equation under Birkhoff's one-parameter transformation group are derived for homogeneous (power-law) potential functions. It is shown that Keplerian orbits belong to the class of planar isovortical flows.     

Die offenen sternhaufen M36, M38 und NGC 2477

The open star clusters M36, M38 and NGC 2477 were investigated by the strip method on charts of photographs taken with the Schmidt-Spiegel of the German Observatory Hoher List (M36/38) and the Curtis-Schmidt Telescope of the Cerro Tololo Interamerican Observatory (NGC 2477). The results are — Masses: 830, 2350, 4400 ; radii: 6.4, 10.0, 10.0 pc; central densities: 9.9, 15.3, 32.5 pc^–3; density laws: Gaussian (M36), generalized law of Schuster withn=3.00, 2.79; mean velocities of the stars 0.74, 1.01, 1.38 km s^–1.

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Mitteilungen Serie A.     

Balloon observations of solar protons on September 29–30, 1968, over Iceland

On September 29, 1968 a proton event has been recorded during three balloon flights performed at Reykjavik, Iceland (64.2 N, 21.7 W) with GM telescopes and scintillation detector. Solar X-rays have been recorded at 1620 UT when a flare of Importance 2B occurred at N 16, W 52. A comparison between X-rays and microwave emissions is made; the time of the maximum of X-ray intensity is taken as the time of the acceleration and ejection of the particles. The beginning of the proton event is at 1650 UT, and particles were observed for almost 24 h. The spectrum of solar protons E>120 MeV is given for several periods between 7 and 20 h after the flare using three independent methods. The solar particle source spectrum is found as: 321-01 (particles/MeV ster), which implies that (1.2±0.1) × 10³¹ protons (E>120 MeV)/ster have been ejected by the Sun.The time behaviour of the event fits well with Krimigis' model for solar particles diffusion in the interplanetary space. Comparison with other events shows that the radial dependence of the diffusion coefficient is the same (1) on September 28, 1961, July 7, 1966 and September 29, 1968. The diffusion mean free path at 1 AU is 0.11 AU for 1966, period of low solar activity, and decreases with solar activity (0.08 AU for 1961 and 1968). The fit of the time behaviour of the event with Burlaga's ADB model is also discussed.     

Solar proton events during solar cycles 19, 20, and 21

Solar proton events have been studied for over thirty years and a great deal of lore has grown around them. It is the purpose of this paper to test some of this lore against the actual data. Data on solar proton events now exist for the period from 1956 to 1985 during which time 140 events took place in which the event integrated fluxes for protons of energy > 30 MeV was larger than 10⁵ particles cm^-2. We have studied statistical properties of event integrated fluxes for particles with energy > 10 MeV and for particles with energy > 30 MeV. Earlier studies based on a single solar cycle had resulted in a sharp division of events into ordinary and anomalously large events.Two such entirely separate distributions imply two entirely separate acceleration mechanisms, one common and the other very rare. We find that the sharp division is neither required nor justified by this larger sample. Instead the event intensity forms a smooth distribution for intensities up to the largest observed implying that any second acceleration mechanism cannot be rare. We have also studied the relation of event sizes to the sunspot number and the solar cycle phase. We find a clear bimodal variation of annual integrated flux with solar cycle phase but no statistically significant tendency for the large events to avoid sunspot maximum. We show there is almost no relation between the maximum sunspot number in a solar cycle and the solar cycle integrated flux. We also find that for annual sunspot numbers greater than 35 (i.e., non-minimum solar cycle conditions) there is no relation whatsoever between the annual sunspot numbers and annual integrated flux.