Effect of the high-order resonances on the orbital evolution of objects near geostationary orbit

The area-to-mass ratio of high-orbit space objects is estimated on the basis of positional observations from the SBG telescope at the Kourovka astronomical observatory of the Ural Federal University. The properties of regions where high-order resonances are located are analyzed. The position and sizes of the resonance zones depending on the area-to-mass ratio of objects are determined on the basis of numerical modeling. It is shown that a system transits through the high-order resonances due to secular perturbations of the semimajor axis under the Poynting-Robertson effect. The high-order resonances weakly influence the formation of the stochastic trajectories. The stochastic properties are mostly manifested in evolution of the semimajor axis of the orbit.     

Positional observations of small solar system bodies with the SBG telescope at the Astronomical Observatory of the Ural Federal University

The telescope SBG (D = 0.42 m, F = 0.76 m) at the Kourovka Astronomical Observatory of the Ural Federal University has undergone an upgrade in 2005–2006. A CCD camera (Apogee Alta U32) and a new drive system were installed, and a new system for telescope and observation control was implemented. This upgrade required verifying the astrometric quality of the telescope. The data processing approaches tested when searching for the optimum CCD image processing technique combined TYCHO2 and UCAC2 catalogues with various reduction models and methods for choosing reference stars. Lorentzian and Moffat profiles were used in the measurement of pixel coordinates. It was demonstrated that the accuracy of SBG observations of main-belt asteroids with precisely determined orbits depends on their brightness and varies from 0.06” (11.5 ^m ) to 0.4” (18.5 ^m ). Regular SBG observations of comets and asteroids (mostly near-Earth and potentially hazardous ones) have been performed since 2007. Coordinates of 8515 positions of 720 asteroids and more than 1000 positions of 40 comets were obtained. The RMS deviations of observed coordinates from their calculated values are typically smaller than 1”: the average deviations for asteroids are 0.33” (in right ascension) and 0.34” (in declination); the corresponding values for comets are 0.37” (in α) and 0.38” (in δ). The results of observations are sent to the Minor Planet Center and are used to determine orbits more accurately and solve other fundamental and applied problems.     

SBG camera of Kourovka Astronomical observatory

The set-up and principle of operation of the systems of the SBG telescope, which was upgraded in 2005–2006 at the Kourovka Astronomical observatory, are described in detail. The reduction of the field of view (photographic plates replaced by a CCD) is compensated by an increased operation speed, achieved by automating both the telescope drives and image processing procedure.     

The Resonance Region of Plutinos under the Perturbation of Outer Planets

Three resonances, the 3:2 exterior mean motion resonance with Neptune, Kozai resonance and 1:1 super resonance, are known to govern concurrently the stability of the motion of Pluto. We explore numerically the resonance zones in which the three resonance coexist. There might exist plutinos with relatively large masses in these zones. Considering that Pluto's perturbation is important to the long-term evolution of plutinos, the resonance zone is mainly explored in the mirror region of Pluto, which is a mirror image of the region around Pluto with respect to the invariant plane of the solar system. We find six resonance zones in the mirror region. The orbit elements at the centers of the six zones and the corresponding heliocentric distances, longitudes and latitudes on July 1, 2003 have been computed and listed for the reference of observation.     

Simulation of the detection zone of dangerous celestial bodies for space-based systems

The simulation results of zones of visibility of celestial bodies potentially dangerous for a wide-field orbital telescope taking into account the basic parameters of the detector, telescope, and movement of celestial bodies are presented. Visibility zones of 50–300 m of dangerous celestial bodies 7–60 days prior to their possible collision with the Earth are calculated using telescopes with apertures of 0.4, 0.75 (VT-77), and 1.5 m.     

ART-P/Granat observations of the X-ray pulsar 4U0115+634 during the outburst in February 1990

Observations of the transient X-ray pulsar 4U0115+634 with the ART-P telescope aboard the Granat Observatory during the outburst in February 1990 are presented. The source exhibited a strong, regular and irregular variability, including X-ray bursts of duration 300–500 s. Two absorption features were detected in the source's photon spectrum at ～12 and ～22 keV, which were interpreted as the lines of resonance scattering of its emission at the first and second cyclotron harmonics. The magnetic-field strength B on the neutron-star surface that corresponds to these lines is ～1.3 × 10¹² G. The ratio of the line energies slightly differs from the harmonic ratio 1: 2. Moreover, this ratio and the line energies themselves vary appreciably with phase on a time scale of one pulsation period. The dependence of other spectral parameters for 4U0115+634 on pulse phase is investigated.     

Determination of the area and mass distribution of orbital debris fragments

An important factor in modeling the orbital debris environment is the loss rate of debris due to atmospheric drag and luni/solar perturbations. An accurate knowledge of the area-to-mass ratio of debris fragments is required for the calculation of the effect of atmospheric drag. In general, this factor is unknown and assumed values are used. However, this ratio can be calculated for fragments for which changes in the orbital elements due to atmospheric drag as a function of time are known. This is the inverse of the technique used to determine the atmospheric density from the decay of satellites with accurately known area-to-mass ratios. These kinds of propagation programs are routinely used in predicting the decay of an orbiting vehicle. In this work the area-to-mass ratio of about 2600 fragments arising from the breakup of 24 artificial satellites have been determined. An analysis of the data on about 200 objects (rocket bodies, scientific satellites, etc.) with known mass, size, and shape has also been made. The value of the radar cross-section (RCS), as measured by the Eglin radar operating at 70 cm wavelength, has been correlated to the effective area of these objects. The measurements of the area-to-mass ratio of these objects then provide a calibration of the actual to the calculated mass. It has been shown that the debris mean mass, m, is related to the mean effective area, A, by a power law relation, m = k A ^1.86. However, for a given effective area the mass distribution is very broad. Moreover, the cumulative mass distribution, N(>m), can be expressed as N(>m) = D(m + b), where D, b, and c are constants. The asymptotic slope, c, of low intensity explosions is on the average lower than the slope for high intensity explosions, but there is considerable spread of this slope in each class. Part of the flattening, as indicated by the finite value of the parameter, b, can be understood as arising out of the spread in the RCS values due to the tumbling motion of the fragments and effects related to the detectability of the fragment by the Eglin radar. It has been established that the mass in a given breakup calculated using this technique is in good agreement with the expected mass value. These results can be used in modeling the breakups of other artificial earth satellites and safety analysis.     

图像移位堆叠方法用于暗天然卫星的天体测量

暗弱天然卫星与主带小行星相比,具有亮度低、速度变化快的特点.在观测这类天体时,不能简单地延长曝光时间来提高其信噪比.尝试观测多幅短曝光的CCD (chargecoupled device)图像,采用移位堆叠(shift-and-add)方法,希望提高目标成像的信噪比,获得暗弱天然卫星的精确测量结果.使用2018年4月9—12日夜间,中国科学院云南天文台1 m望远镜(1 m望远镜)拍摄的木星5颗暗卫星的229幅CCD图像,实施了移位堆叠试验.为了验证结果的正确性,与相近日期中国科学院云南天文台2.4 m望远镜(2.4 m望远镜)观测的相同木卫图像的测量结果进行了比较和分析.位置归算采用了JPL (Jet Propulsion Laboratory)历表.结果表明,对CCD图像使用移位堆叠方法,通过叠加约10幅曝光时间100 s的图像, 1 m望远镜能观测暗至19等星的不规则天然卫星,而且测量的准确度与2.4 m望远镜的测量结果有良好的一致性.     

Coupled orbit-attitude dynamics of high area-to-mass ratio (HAMR) objects: influence of solar radiation pressure, Earth’s shadow and the visibility in light curves

The orbital and attitude dynamics of uncontrolled Earth orbiting objects are perturbed by a variety of sources. In research, emphasis has been put on operational space vehicles. Operational satellites typically have a relatively compact shape, and hence, a low area-to-mass ratio (AMR), and are in most cases actively or passively attitude stabilized. This enables one to treat the orbit and attitude propagation as decoupled problems, and in many cases the attitude dynamics can be neglected completely. The situation is different for space debris objects, which are in an uncontrolled attitude state. Furthermore, the assumption that a steady-state attitude motion can be averaged over data reduction intervals may no longer be valid. Additionally, a subset of the debris objects have significantly high area-to-mass ratio (HAMR) values, resulting in highly perturbed orbits, e.g. by solar radiation pressure, even if a stable AMR value is assumed. Note, this assumption implies a steady-state attitude such that the average cross-sectional area exposed to the sun is close to constant. Time-varying solar radiation pressure accelerations due to attitude variations will result in un-modeled errors in the state propagation. This work investigates the evolution of the coupled attitude and orbit motion of HAMR objects. Standardized pieces of multilayer insulation (MLI) are simulated in a near geosynchronous orbits. It is assumed that the objects are rigid bodies and are in uncontrolled attitude states. The integrated effects of the Earth gravitational field and solar radiation pressure on the attitude motion are investigated. The light curves that represent the observed brightness variations over time in a specific viewing direction are extracted. A sensor model is utilized to generate light curves with visibility constraints and magnitude uncertainties as observed by a standard ground based telescope. The photometric models will be needed when combining photometric and astrometric observations for estimation of orbit and attitude dynamics of non-resolved space objects.     

一种扩大FAST视场的方法

所有的大口径射电望远镜都存在这样一个问题：在其分辨率和灵敏度提高的同时，视场变小．而且口径越大，视场越小．这成为大口径望远镜不可回避的矛盾．要解决这个矛盾，可以在望远镜的焦平面上放置Ⅳ个分立馈源．让它们同时工作，这样可以看作把视场扩大了Ⅳ倍．望远镜的工作效率提高Ⅳ倍．但是这样做的缺点是——视场不连续．且馈源数目Ⅳ受到望远镜焦比(F／D)的限制．采用致密焦面阵(dense focal plane array)就可以很好地解决这个问题．致密焦面阵的单元不是喇叭口天线，而是无方向性的Vivaldi天线(Vivaldi antenna)．要把Vivaldi阵列应用到望远镜上，需要对单个Vivaldi天线和Vivaldi阵列的电性能有清楚的认识，并能根据需要来设计照明方向图．还要知道大望远镜的焦面上电磁场的分布情况，借此判断能否应用Vivaldi阵列，以及给出Vivaldi单元的分路赋权网络．主要给出了FAST的焦面场的分布情况．并说明应用Vivaldi阵列的可能性．     

Investigation of Light Pressure Influence on Dynamics of Near-Earth Objects in Resonant Orbits

The results of an analysis of changes in resonant orbital dynamics of near-Earth objects, which are caused by light pressure, are presented. We describe features of the orbital evolution of the objects subjected to the combined effect of secular resonances and light pressure. It was shown that the transfer of objects to highly elliptical and hyperbolic orbits is possible when the object’s area-to-mass ratio is large.     

The brightness distribution of the sun at 2.8cm wavelength

Maps of the Sun at 2.8 cm wavelength, observed with the 100-m telescope in Effelsberg, on 1972, October 31 and 1973, February 10, are discussed. The brightness distribution over the Sun is, with the exception of active regions, approximately constant and nearly sharp-edged. Regions of small enhancements in the radiation can be identified with zones of weak activity in the solar magnetograms. Optical filaments could also be seen in absorption at 2.8 cm wavelength, the optical depth being of the order of 0.2. Several active regions have been analysed with respect to their position relative to their optical counterparts and to their brightness temperature: The latter was found to reach almost 10⁶K in one case. No noticeable limb brightening could be observed; if any exists, it should be smaller than 5%. Likewise no noticeable elliptical deformation of the Sun's disk could be found. The geometrical thickness of the coronal layer, contributing to the undisturbed radiation at 2.8 cm was estimated to be a maximum of 4000 km.     

中等贫金属星高分辨率光谱分析 I.光谱数据与等值宽度

利用北京天文台兴隆观测基地2.16米望远镜的折轴阶梯光栅摄谱仪，获得了一批中等贫金属星的高分辨率，高信噪比光谱，通过MIDAS软件包对其中7颗中等贫金属星进行了光谱处理，得到了它们的等值宽度，最后给出院 样本恒星的等值宽度及误差分析。     

The impact of Earth’s shadow on the long-term evolution of space debris

Direct solar radiation pressure and Earth’s shadow crossings are known to be responsible for short-term variations of space debris orbital elements, the higher the area-to-mass ratio the larger the perturbation. Nevertheless, existing studies have always been performed on periods of time shorter than 150 years. Considering longer time scales of the order of a 1000 years, this paper focuses on the long-term periodic evolution of space debris trajectories caused by successive Earth’s shadow crossings. Other perturbations as the geopotential and third-body gravitational attractions obviously play a role and compete with the one which is described in this paper. Symplectic numerical propagations and new (semi-)analytical models are developed to identify a frequency associated to shadow entry and exit eccentric anomalies. It is shown that Earth’s shadow is responsible for large deviations from the initial orbital elements, even on shorter period of times, and that this effect increases along with the area-to-mass ratio.     

Magnetochemistry of the apollo landing sites

The magnetochemical synthesis, as presented, derives from an integration of the magnetic property systematics developed with corresponding bulk chemistry and petrology, and the results of mixing and reduction responses which feature in the production of the lunar regolith. Magnetochemical properties of the lunar soils are correlated with the Al/Si ratio and telescope spectral reflectivity curves. Magnetochemical diagrams utilizingχ _p(paramagnetic susceptibility ? FeO) andI _S(saturation magnetization ? Fe metal) serve to classify lunar samples, indicate the extent of mixing, and demonstrate that although reduction does take place in production of the regolith, the role of mixing is quite significant. The relative metal size distribution and magnetic stability for various rock types and soils of varying Al/Si values are reflected in theR _I(ratio of saturation isothermal remanence-I _R, to saturation magnetization -I _S) vsR _H(ratio of remanent coercive force -H _R, to coercive force -H _C) plot. All magnetic hysteresis loop parameters considered vary systematically according to the Al/Si values. All Apollo landing sites have distinct telescope curves correlated with petrology, chemistry, Al/Si values, and magnetic properties. Magnetic properties of sites not visited can now be reasonably estimated based on telescope reflectivity curves and orbital geochemical experiments.     

Stability of higher order resonances in the restricted three-body problem

Third and fourth order mean motion resonances are studied in the model of the restricted three-body problem by numerical methods for mass parameters corresponding approximately to the Sun?CJupiter and Sun?CNeptune systems. In the case of inner resonances, it is shown that there are two regions of libration in the 8:5 and 7:4 resonances, one at low, the other at high eccentricities. In the 9:5 and 7:3 resonances libration can exist only in one region at high eccentricities. The 5:2 and 4:1 resonances are very regular, with one librational zone existing for all eccentricities. There is no visible region of libration at any eccentricities in the 5:1 resonance, the transition between the regions of direct and retrograde circulation is very sharp. In the case of outer resonances, the 8:5 and 7:4 resonances have also two regions of libration, but the 9:5 resonance has three, the 7:3 resonance two librational zones. The 5:2 resonance is again very regular, but it is parted for two regions of libration at high eccentricities. Libration is possible in the 4:1 resonance only at high eccentricities. The 5:1 resonance is very symmetric. In the case of outer resonances, a comparison is made with trans-Neptunian objects (TNO) in higher order mean motion resonances. Several new librating TNOs are identified.     

Equivalent Widths of 15 Extrasolar-Planet Host Stars

We present the equivalent widths of 15 extrasolar-planet host stars. These data were based on the high-resolution, high signal-to-noise ratio spectra obtained with the 2.16m telescope at Xinglong station. The error in the Xinglong equivalent width is estimated by a comparison of these data with those given in previous studies of common stars.     

The development of the Schmidt telescope

Bernhard Schmidt (1879–1935) was born in Estonia. After a few years of studying engineering he ran an optical workshop in Mittweida, Saxonia, between 1901 and 1927. Astronomers appreciated the quality of his telescopes. Starting in 1925, on behalf of the Hamburg Observatory, he developed a short focal length optical system with a large field of view. For this purpose, Schmidt moved his workshop to the observatory. He succeeded in inventing the “Schmidt telescope” which allows the imaging of a large field of the sky without any distortions. Schmidt's first telescope (spherical mirror diameter 0.44 m, correction plate 0.36 m diameter, aperture ratio 1:1.75, and focal length 0.625 m) has been used since 1962 at the Boyden Observatory in Bloemfontein/South Africa. Apart from his 0.36m telescope, Schmidt produced a second larger one of 0.60m aperture. Shortly after Schmidt's death, the director of the observatory published details on the invention and production of the Schmidt telescope. After World War II, Schmidt telescopes have been widely used. The first large Schmidt telescope, the “Big Schmidt” (1.26 m), Mount Palomar, USA, was completed in 1948. The 0.80 m Schmidt telescope of Hamburg Observatory, planned since 1936, finished in 1954, is now on Calar Alto/Spain (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New challenges for adaptive optics: extremely large telescopes

The performance of an adaptive optics (AO) system on a 100-m diameter ground-based telescope working in the visible range of the spectrum is computed using an analytical approach. The target Strehl ratio of 60 per cent is achieved at 0.5 μm with a limiting magnitude of the AO guide source near R   magnitude~10, at the cost of an extremely low sky coverage. To alleviate this problem, the concept of tomographic wavefront sensing in a wider field of view using either natural guide stars (NGS) or laser guide stars (LGS) is investigated. These methods use three or four reference sources and up to three deformable mirrors, which increase up to 8-fold the corrected field size (up to 60 arcsec at 0.5 μm). Operation with multiple NGS is limited to the infrared (in the J band this approach yields a sky coverage of 50 per cent with a Strehl ratio of 0.2). The option of open-loop wavefront correction in the visible using several bright NGS is discussed. The LGS approach involves the use of a faint ( R ~22) NGS for low-order correction, which results in a sky coverage of 40 per cent at the Galactic poles in the visible.