Gravity-gradient stabilization of gyrostat satellites with rotor axes in principal planes

Three special classes of equilibrium orientations of gyrostat satellites subject to gravitational torques have been treated in the literature. Here we find the set of all equilibria for a restricted class of gyrostat configurations. Those configurations for which the internal angular momentum vector (or the rotor axis) is aligned with a principal axis have been treated in a separate work, where it is shown that at one, and only one, rotor speed there exists a continuum of equilibrium orientations. When the rotor axis is moved away from a principal axis in such a way that it is contained in a plane formed by two principal axes, it is shown that the continuum disappears, and we have a new set of eight equilibrium orientations which have not previously been described. The stability of these orientations is then investigated using the Hamiltonian as a Liapunov testing function. For properly chosen satellite inertia ratios some of these orientations are stable, and might be used in future gravitygradient stabilized satellites.This research is sponsored by the United States Air Force under Project RAND-Contract No. F44620-67-C-0045-monitored by the Directorate of Operational Requirements and Development Plans, Deputy Chief of Staff, Research and Development, Hq. USAF. Views or conclusions contained in this study should not be interpreted as representing the official opinion or policy of the United States Air Force. The material presented here was originally published in RAND Corporation Memorandum RM-5921-PR. The author wishes to acknowledge his indebtedness to Dr. R. E. Roberson for helpful discussions, and for suggesting a research area, part of which is treated here.     

Rocket-coronagraph photometry of the 7 March, 1970 corona from 3 to 8.5 R s

A rocket-borne coronagraph utilizing external occulting disks was used to photograph the solar corona from 3 to 9 R _s at 1931 UT on 7 March, 1970. Comparison of the rocket and ground-based observations shows a one-to-one correspondence between major streamers from the inner to the outer corona. In particular streamers over the poles are clearly visible against the background corona from 3 to 8 R _s. These rocket data had a scattered light level of 1.2 × 10^–10 B _s. The derived quiet equatorial and polar K + F corona was within 10% of the absolute brightness of standard coronal models and displayed identical radial gradients to those models. The photometric profiles of the NE limb streamer were analyzed assuming a model in which the core density follows a Gaussian distribution in directions perpendicular to the radius vector. This streamer was assumed to be rooted on the visible disk at 55 to 60° from the plane-of-the-sky as based on K-coronameter and XUV data. An uncertainty of as much as a factor of three still remains for the value of the axis density owing to uncertainty in the line-of-sight dimension of the streamer.     

Solar Cycle Predictions based on Solar Activity at Different Solar Latitudes

Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R _z(max) (the maximum in the 12-month running means of sunspot number R _z) with R _z(min) (the minimum in the 12-month running means of sunspot number R _z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86) for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation +0.78±0.11 with the sunspot number R _z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the sunspot number R _z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R _z(max )=129.7±16.3.     

The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

Towards a free–free template for CMB foregrounds

A full-sky template map of the Galactic free–free foreground emission component is increasingly important for high-sensitivity cosmic microwave background (CMB) experiments. We use the recently published Hα data of both the northern and southern skies as the basis for such a template.
The first step is to correct the Hα maps for dust absorption using the 100-μm dust maps of Schlegel, Finkbeiner & Davis. We show that for a range of longitudes, the Galactic latitude distribution of absorption suggests that it is 33 per cent of the full extragalactic absorption. A reliable absorption-corrected Hα map can be produced for ∼95 per cent of the sky; the area for which a template cannot be recovered is the Galactic plane area  | b | < 5°, l = 260°–0°–160°  and some isolated dense dust clouds at intermediate latitudes.
The second step is to convert the dust-corrected Hα data into a predicted radio surface brightness. The free–free emission formula is revised to give an accurate expression (1 per cent) for the radio emission covering the frequency range 100 MHz–100 GHz and the electron temperature range 3000–20 000 K. The main uncertainty when applying this expression is the variation of electron temperature across the sky. The emission formula is verified in several extended H  ii regions using data in the range 408–2326 MHz.
A full-sky free–free template map is presented at 30 GHz; the scaling to other frequencies is given. The Haslam et al. all-sky 408-MHz map of the sky can be corrected for this free–free component, which amounts to a  ≈6  per cent correction at intermediate and high latitudes, to provide a pure synchrotron all-sky template. The implications for CMB experiments are discussed.     

Evidence for short term changes in the intensity and spectrum of hard X-rays from Cyg X-1

The paper presents experimental evidence for the existence of fast intensity fluctuations with time scales of the order of a minute in the X-ray emission from Cyg X-1 at energies greater than 29 keV. Spectral variations over time intervals of 20–25 min are also observed in the same energy range. Whereas, similar intensity and spectral fluctuations have been reported earlier at lower energies the observations presented here is the first evidence for the existence of similar fluctuations at high energies.     

Variable stars in the field of open cluster NGC 6819

We report on the discovery of 25 variable stars plus 13 suspected variables found in the field of the open cluster NGC 6819. The stars were identified from time-series photometric data obtained on the Isaac Newton Telescope, La Palma, during two observing runs covering the 19 nights between 1999 June  22–30  and 1999 July  22–31  . The variables found include 12 eclipsing binaries with an additional three suspected, nine BY Draconis systems, plus four variables of other types, including one star believed to be a Cepheid. Three of the 15 eclipsing binaries are believed to be cluster members. Details of a further 10 suspected variable stars are also included.     

H2 in molecular shocks: observations from 2 to 12 microns

We present spectroscopy of the molecular shock in the supernova remnant IC 443. The H₂ level populations in IC 443 are nearly identical to Orion Peak 1 (Brand et al. 1988; Parmar et al. 1994) and are consistent with a partially dissociative J-shock. The similarity with Orion suggests the shock processes which dominate the emission in both regions are essentially identical.     

Late glacial and Holocene environmental change in the Lake Baikal region documented by oxygen isotopes from diatom silica

We investigate late glacial and Holocene climate change recorded in Lake Baikal using the oxygen isotope composition of diatom silica (δ¹⁸O_DIAT). Evaporation from the lake is minor, and the temperature fractionations of δ¹⁸O are unable to explain variations in the δ¹⁸O_DIAT record alone. Isotopically, low meltwater input from glaciers may have some influence on δ¹⁸O_DIAT, but the assumed periods of climatic warming and wastage do not coincide with large shifts in δ¹⁸O_DIAT. There is a gradual oxygen isotope lowering from 27.0‰ to 20.6‰ over the late glacial, while, during the Holocene, δ¹⁸O_DIAT values return to relatively high values. Previous studies of the modern oxygen and hydrogen isotope composition of Lake Baikal's inputs reveal that fluvial input to the lake's North Basin are isotopically lower than fluvial input from South Basin rivers. This north–south gradient of river δ¹⁸O and δD is mainly due to the greater input from isotopically low winter precipitation in the north and isotopically higher summer precipitation in the south. As a result, the δ¹⁸O_DIAT record from Lake Baikal can at least in part be explained by varying input from these sources related to seasonal changes in precipitation. Changes in atmospheric conditions may have a role in altering seasonality and the distribution of precipitation over Lake Baikal's catchment. A feedback mechanism is well known linking higher Eurasian spring snow cover extent (ESSC) to the development of anticyclonic conditions and low precipitation the following summer in the areas south of Lake Baikal. A simultaneous increase in the importance of depleted water (snowmelt) input from the north and decreased enriched summer precipitation in the south is needed to explain depletions in δ¹⁸O of lake water and subsequently δ¹⁸O_DIAT during colder periods. The opposite of this situation is required to enrich lake water during warmer periods. The analysis of δ¹⁸O from diatom silica is a useful proxy for environmental change, especially in lakes, like Lake Baikal, where carbonates are absent or diluted. However, analysis must be based on near pure diatom samples as even trace amounts of silt can have a dominating effect on δ¹⁸O_DIAT values.     

The Heliospheric Plasma Sheet Observed in situ by Three Spacecraft over Four Solar Rotations

Solar Physics - In this paper we present in&nbsp;situ observations of the heliospheric plasma sheet (HPS) from STEREO-A, Wind, and STEREO-B over four solar rotations in the declining phase of...