A satellite relative motion model including $$J_2$$ and $$J_3$$J3 via Vinti’s intermediary

Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.     

Absorption of Photons from Distant Gamma-Ray Sources

Being the largest gravitationally bound structures in the Universe, galaxy clusters are huge reservoirs of photons generated by the bremsstrahlung of a hot cluster gas. We consider the absorption of high-energy photons from distant cosmological gamma-ray sources by the bremsstrahlung of galaxy clusters. The magnitude of this effect is the third in order of smallness after the effects of absorption by the cosmic microwave background and absorption by the extragalactic background light. Our calculations of the effect of absorption by the bremsstrahlung of galaxy clusters have shown that this effect manifests itself in the energy range ~1–100 GeV and can be τ ~ 10^?5 in optical depth.     

C-Band Radiometer for Continuum Observations at RATAN-600 Radio Telescope

We describe the development of the tools and methods of 4.7-GHz band observations on RATAN-600 radio telescope and present a new design solution—a radiometric unit, and the development of an uncooled tuned receiver based on this unit and meant for operating in the “total power” radiometer mode.We discuss the design of the radio unit and the specificities of the radiometer design.We demonstrate the possibility of conducting observations in the total power radiometer mode at the theoretical sensitivity on time scales up to 10 seconds. The sensitivity of such a radiometer remains higher than that of a Dicke radiometer on time scales up to 100 seconds.     

A model of Saturn inferred from its measured gravitational field

We present an interior model of Saturn with an ice-rock core,a metallic region,an outer molecular envelope and a thin transition layer between the metallic and molecular regions.The shape of Saturn’s 1 bar surface is irregular and determined fully self-consistently by the required equilibrium condition.While the ice-rock core is assumed to have a uniform density,three different equations of state are adopted for the metallic,molecular and transition regions.The Saturnian model is constrained by its known mass,its known equatorial and polar radii,and its known zonal gravitational coefficients,J_(2n),n=1,2,3.The model produces an ice-rock core with equatorial radius 0.203 R_S,where R_S is the equatorial radius of Saturn at the 1-bar pressure surface;the core densityρ_c=10388.1 kgm~(3)corresponding to 13.06 Earth masses;and an analytical expression describing the Saturnian irregular shape of the 1-bar pressure level.The model also predicts the values of the higher-order gravitational coefficients,J_8,J_10 and J_12,for the hydrostatic Saturn and suggests that Saturn’s convective dynamo operates in the metallic region approximately defined by 0.2 R_Sre0.7 R_S,where r_e denotes the equatorial radial distance from the Saturnian center of figure.     

Curvature Wavefront Sensor For Solar Adaptive Optics

Active or adaptive optics often require the ability to characterize wavefront aberrations using natural extended sources. The task becomes especially challenging when dealing with widely extended sources such as the solar granulation. We propose a new approach based on the processing of oppositely defocused images. This method, which is a generalization of a technique known as curvature sensing, derives the wavefront curvature from the difference between two oppositely defocused images and determines the second momenta of the point spread function. The proposed method measures the wavefront aberration from the images themselves, requires little computational resources, is fast enough to be used in a real-time adaptive optics system and is particularly adapted to random patterns such as solar granulation or spot penumbras whose morphology evolves during the observation. We envision the application of the method to real-time seeing compensation in solar astronomical telescopes, and to the correction of optical system aberrations in remote sensing instrumentation. This effort is directed towards building a curvature sensor for the real-time applications.     

X-ray emission from accretion disks in active galactic nuclei

We constructed a grid of relativistic models for standard high-relative-luminosity accretion α-disks around supermassive Kerr black holes (BHs) and computed X-ray spectra for their hot, effectively optically thin inner parts by taking into account general-relativity effects. They are known to be heated to high (～10⁶–10⁹ K) temperatures and to cool down through the Comptonization of intrinsic thermal radiation. Their spectra are power laws with an exponential cutoff at high energies; i.e., they have the same shape as those observed in active galactic nuclei (AGNs). Fitting the observed X-ray spectra of AGNs with computed spectra allowed us to estimate the fundamental parameters of BHs (their mass and Kerr parameter) and accretion disks (luminosity and inclination to the line of sight) in 28 AGNs. We show that the Kerr parameter for BHs in AGNs is close to unity and that the disk inclination correlates with the Seyfert type of AGN, in accordance with the unification model of activity. The estimated BH masses M_x are compared with the masses M_rev determined by the reverberation mapping technique. For AGNs with luminosities close to the Eddington limit, these masses agree and the model under consideration may be valid for them. For low-relative-luminosity AGNs, the differences in masses increase with decreasing relative luminosity and their X-ray emission cannot be explained by this model.     

Increase of the Magnetic Flux From Polar Zones of the sun in the Last 120 Years

Lockwood, Stamper, and Wild (1999) argued that the average strength of the magnetic field of the Sun has doubled in the last 100 years. They used an analysis of the geomagnetic index aa. We calculated the area of polar zones of the Sun, A _pz, occupied by unipolar magnetic field on H synoptic magnetic charts, following Makarov (1994), from 1878 to 2000. We found a gradual decrease of the annual minimum latitude of the high-latitude zone boundaries, _2m, of the global magnetic field of the Sun at the minimum of activity from 53° in 1878 down to 38° in 1996, yielding an average decrease of 1.2° per cycle. Consequently the area of polar zones A _pz of the Sun, occupied by unipolar magnetic field at the minimum activity, has risen by a factor of 2 during 1878–1996. This means that the behavior of the index aa and consequently the magnetic flux from the Sun may be explained by an increase of the area of polar caps with roughly the same value of the magnetic field in this period. The area of the unipolar magnetic field at the poles (A _pz) may be used as a new index of magnetic activity of the Sun. We compared A _pz with the aa, the Wolf number W and A^* -index (Makarov and Tlatov, 2000). Correlations based on `11-year' averages are discussed. A temperature difference of about 1° between the Maunder Minimum and the present time was deduced. We have found that the highest latitude of the polar zone boundaries of the large-scale magnetic field during very low solar activity reaches about 60°, cf., the Maunder Minimum. It is supposed that the _2m-latitude coincides with the latitude where _r=0, with (r,) being the angular frequency of the solar rotation. The causes of the waxing and waning of the Sun's activity in conditions like Maunder Minimum are discussed.     

New magnetic chemically peculiar stars

Our observations with the 6-m telescope revealed six new magnetic chemically peculiar (CP) stars among objects with large depressions in the continuum: HDE 293764, BD+17°3622, HD 169887, HDE 231054, HDE 338226, and HDE 343872. The presence of a magnetic field is suspected in several other CP stars. The maximum longitudinal field component B _e exceeds 1.5 kG for all six stars; in HDE 293764 and HDE 343872, it reaches 3.8 kG. For each object, we present our magnetic-field measurements and published data on previous studies. The method of searching for magnetic stars based on an analysis of spectrophotometry shows its efficiency.     

Wave Beams in an Inhomogeneous Plasma in a Transverse Magnetic Field

The propagation of axisymmetric magnetohydrodynamic waves near the equatorial plane of the crust of a neutron star in a transverse magnetic field is considered. The magnetic field is perpendicular to the equatorial plane. The magnetic fields and electric currents excited by this wave beam at the stellar surface are determined.     

RAGLAND,AN LL3.4 CHONDRITE FIND FROM NEW MEXICO

The Ragland, New Mexico chondrite was found in 1978, and consists of a single stone of 12.16 kg that broke into three pieces. The stone is moderately weathered and has a pronounced chondritic texture. Bulk composition favors an LL classification, and modal analysis and oxygen isotopic composition are consistent with this. The thermoluminescence sensitivity of 0.056 ± 0.020 normalized to Dhajala, compositional variability of olivine (mean Fa 18.3, σ = 10.1) and low-Ca pyroxene (mean Fs 14.6, σ = 6.7), and Ca concentrations in olivine indicate metamorphic subtype 3.4 ± 0.1. The isotopically heavy oxygen composition, which is characteristic of subtypes 3.0–3.1, may be a primary characteristic and not a result of weathering. Low concentrations of radiogenic ⁴⁰Ar and planetary ³⁶Ar suggest noble gas loss.