Spectrum Disentangling and Orbital Solution for κ Dra

Based on a new set of electronic spectra in a relatively wide spectral range (3500–8300 Å) and using the methods of spectrum disentangling (code KOREL) and solution of RV curves (code FOTEL), we determined new orbital elements of the binary star κ Dra. The solution of the radial velocity curves for Balmer and some other strong metallic lines suggested a circular orbit and led to the following orbital elements: period P = 61.555 ± 0.029 days, epoch of periastron passage T _periast = 49980.22 ± 0.59, RV semi-amplitude K ₁ = 6.81 ± 0.24 km s^?1, and a mass function of f(m) = 0.002 M _⊙. Lines of the secondary were not detected. In addition, moving absorption bumps in the violet peaks of Hα and Hβ lines were found to be phase-locked with the orbital period. Their presence suggests some kind of interaction between the binary components.     

Research on Parallel Algorithms for uv-faceting Imaging

The uv-faceting imaging is one of the widely used large field of view imaging technologies, and will be adopted for the data processing of the low-frequency array in the first stage of the Square Kilometre Array (SKA1). Due to the scale of the raw data of SKA1 is unprecedentedly large, the efficiency of data processing directly using the original uv-faceting imaging will be very low. Therefore, a uv-faceting imaging algorithm based on the MPI (Message Passing Interface)+OpenMP (Open Multi-Processing) and a uv-faceting imaging algorithm based on the MPI+CUDA (Compute Unified Device Architecture) are proposed. The most time-consuming data reading and gridding in the algorithm are optimized in parallel. The verification results show that the results of the proposed two algorithms are basically consistent with that obtained by the current mainstream data processing software CASA (Common Astronomy Software Applications), which indicates that the proposed two algorithms are basically correct. Further analysis of the accuracy and total running time shows that the MPI+CUDA method is better than the MPI+OpenMP method in both the correctness rate and running speed. The performance test results show that the proposed algorithms are effective and have certain extensibility.     

Adaptive particle swarm optimization for optimal orbital elements of binary stars

The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.     

Giant planet migration through the action of disk torques and planet-planet scattering

This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.     

Space Event and Outlier Detection Based on Expectation Maximization Algorithm

The United States provide Element Sets (ELSET) database in Two-Line Element (TLE) format for public use, which plays an important role in the inversion of atmospheric density in the thermosphere, ballistic coefficient estimation, early-warning and so on. Due to large uncertainties existing in the TLE generation process, space environment changes, and space events, ELSET database contains a large number of abnormal TLE data to be filtered, such as corrected TLE, orbital element outlier, and Bstar outlier. The existing methods to filter out the outliers lack general applicability and are very complicated, which are only applicable to a few space targets in certain orbit regions. To overcome the shortcomings of the existing methods, a filtering method is proposed based on Expectation Maximization (EM) algorithm employing a sliding window and polynomial fitting method, which can detect outliers for different orbital elements and space events. The research shows that the algorithm can effectively single out the outliers in TLE sequences and is suitable for all orbital debris.     

Detection of Earth-mass and super-Earth Trojan planets using transit timing variation method

We have carried out an extensive study of the possibility of the detection of Earth-mass and super-Earth Trojan planets using transit timing variation method with the Kepler space telescope. We have considered a system consisting of a transiting Jovian-type planet in a short period orbit, and determined the induced variations in its transit timing due to an Earth-mass/super-Earth Trojan planet. We mapped a large section of the phase space around the 1:1 mean-motion resonance and identified regions corresponding to several other mean-motion resonances where the orbit of the planet would be stable. We calculated transit timing variations (TTVs) for different values of the mass and orbital elements of the transiting and perturbing bodies as well as the mass of central star, and identified orbital configurations of these objects (ranges of their orbital elements and masses) for which the resulted TTVs would be within the range of the variations of the transit timing of Kepler’s planetary candidates. Results of our study indicate that in general, the amplitudes of the TTVs fall within the detectable range of timing precision obtained from the Kepler’s long-cadence data, and depending on the parameters of the system, their magnitudes may become as large as a few hours. The probability of detection is higher for super-Earth Trojans with slightly eccentric orbits around short-period Jovian-type planets with masses slightly smaller than Jupiter. We present the details of our study and discuss the implications of its results.     

Refinement of Near Earth Asteroids’ orbital elements via simultaneous measurements by two observers

The aspects of triangulation of Near Earth Asteroids by two arbitrarily positioned observers (one spaceborne and the other Earth-bound, as well as both spaceborne) are being investigated, and the resulting orbital elements are compared to those gained through common orbital determination and refinement techniques. The main advantages of the method proposed in this work are, that given the approximate position of an asteroid, high quality orbital elements can be acquired very rapidly using two observations only.     

Prediction of Solar Activity Based on Neuro-Fuzzy Modeling

This paper presents an application of the neuro-fuzzy modeling to analyze the time series of solar activity, as measured through the relative Wolf number. The neuro-fuzzy structure is optimized based on the linear adapted genetic algorithm with controlling population size (LAGA-POP). Initially, the dimension of the time series characteristic attractor is obtained based on the smallest regularity criterion (RC) and the neuro-fuzzy model. Then the performance of the proposed approach, in forecasting yearly sunspot numbers, is favorably compared to that of other published methods. Finally, a comparison predictions for the remaining part of the 22nd and the whole 23rd cycle of the solar activity are presented.     

The reality of comet groups and pairs

Although the common genetic origin of the Kreutz family of Sun-grazing comets has generally been accepted, there remains uncertainty with regard to genetic identity among other groups of comets whose orbital elements are nearly alike. Porter has listed a number of such grouds and Öpik has made a statistical study of the orbits of 472 comets with aphelion distance beyond Saturn. He lists 97 groups that show similarities among their three angular elements. He calculates an overall probability of some 10^?39 that these similarities could have occurred by chance, and thus concludes that 60% or more of such comets fall into genetic groups containing from two to seven members. This paper explores the statistical reality of Öpik's groups utilizing the Monte Carlo method of statistics as well as ordinary probability theory. The conclusion is reached that except for a few pairs the similarity among orbital elements within the groups is no greater than random expectation.     

Astrometric study of the triple star ADS 9173

An approximate orbit of the wide visual binary star ADS 9173 A(Bb) with a period of ～6000 yr has been determined for the first time by the method of apparent motion parameters. The orbit was computed using a short (1982–2004) arc of photographic observations obtained with the 26-inch Pulkovo Observatory refractor and the Hipparcos parallax. Agreement of the new orbit with the observations from the WDS catalog beginning in 1832 serves as a check. The errors in the orbital elements are large, but the orientation elements of the orbital plane (i and Ω) were estimated reliably. Component B has an invisible spectroscopic companion with a period of 4.9 yr. An astrometric orbit of Bb consistent with radial velocity measurements was determined from the residuals to the relative orbital motion of A(Bb). The orbital planes are nearly coplanar. If the mass of component B is taken in accordance with the mass—luminosity relation, 1.5 M _⊙, and the parallax is 0.″021, then the mass of the secondary component is no less than 0.5M _⊙. Component A may also be a long-period binary system.     

Lie-series for orbital elements: I. The planar case

Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor coefficients of the solution as a set of recurrence relations. In this paper, we present these recurrence formulae for orbital elements and other integrals of motion for the planar $N$ -body problem. We show that if the reference frame is fixed to one of the bodies—for instance to the Sun in the case of the Solar System—the higher order coefficients for all orbital elements and integrals of motion depend only on the mutual terms corresponding to the orbiting bodies.     

Structure of the 3:1 Jovian resonance: A comparison of numerical methods

The motion of asteroids near the 3:1 Jovian resonance in the restricted planar case is studied using three numerical methods: (a) integrating the full equations of motion, (b) integrating the averaged equations of motion, and (c) using an algebraic mapping recently developed by Wisdom (1982, Astron. J.87, 577–593). The relative merits of each method are investigated. It is concluded that in the regular regions of the phase space, methods b and c give excellent agreement with each other and that provided the maximum eccentricity e_max < 0.4 differences with the exact solution (method a) are <6% in e_max and <27% in the period of the oscillations. The additions of higher order terms in the expansion of the averaged Hamiltonian provides marginally better agreement with the full integration. This is probably due to the slow convergence of the expansion of the disturbing function at large eccentricities (e > 0.3). In chaotic regions of the phase there is little agreement between the orbital elements at any given time calculated by each method. However, all methods reflect the qualitative behavior of the chaotic trajectories and give good agreement on the bounds of the motion. Since the map is at least 200 times faster than solving the full equations of motion it is an efficient method of rapidly exploring accessible regions of the chaotic phase space.     

Radar detectability of asteroids: A survey of opportunities for 1977 through 1987

The capability of Earth-based radar to study asteroids is assessed with respect to determining the number of detectible objects and the number of detectable events during the next 10 years. Bar graphs have been prepared showing the number of events and objects falling into 5-db detectability slots based both on estimates of minimum distance and on direct calculations using known orbital elements. These indicate that the Goldstone radar system operating at 3.5-cm wavelength should be able to detect roughly 18 different asteroids at 34 favorable opportunities during the next 10 years. The Arecibo radar system operating at 12.5-cm wavelength may be able to detect 60 asteroids at approximately 97 favorable opportunities in the 10-year period. This sample is sufficiently large that classification of types and correlation with optical data should be possible. The detectability margin for many objects should be large enough to permit more refined analysis of the radar spectrograms. Estimates of the average surface roughness, rotation rate, and direction of the polar axis, as well as estimates of range and Doppler frequency offsets, which can be used to refine the orbital elements, should be otainable for many objects. Equations are given which indicate the variances expected for measurements of cross section, center frequency, and bandwidth measured either singly or jointly. These are functions of the noise-to-signal ratio and other physical parameters such as the backscattering law. Curves are given based on backscattering functions of the form cosⁿθ.     

Orbital correlation of space objects based on orbital elements

Orbital correlation of space objects is one of the most important elements in space object identification. Using the orbital elements, we provide correlation criteria to determine if objects are coplanar,co-orbital or the same. We analyze the prediction error of the correlation parameters for different orbital types and propose an orbital correlation method for space objects. The method is validated using two line elements and multisatellite launching data. The experimental results show that the proposed method is effective, especially for space objects in near-circular orbits.     

New methods for large dynamic range problems in planetary formation

Modern N -body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the time-step for all objects to be set to a small fraction of the orbital period of the innermost body. This computational expense can be prohibitive for even moderate particle number for many physically interesting scenarios, such as recent models of the formation of hot exoplanets, in which the semimajor axis of possible progenitors can vary by orders of magnitude. We present new methods which retain most of the benefits of the standard symplectic integrators but allow for radial zones with distinct time-steps. These approaches should make simulations of planetary accretion with large dynamic range tractable. As proof-of-concept, we present preliminary science results from an implementation of the algorithm as applied to an oligarchic migration scenario for forming hot Neptunes.     

Equivalence for lie transforms

The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions.     

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 1: The orbits

Orbital parameters of the satellite NIMBUS 1 ROCKET (1964-52B) have been determined at 285 epochs using about 14,500 optical and radar observations during the last 2233 days of its life. 1964-52B was in an orbit inclined at about 98.7° to the Equator and it decayed on 13 August 1974. The orbital elements were found using the RAE orbit refinement program PROP 6 giving average orbital accuracies in perigee height and inclination at 110 m and 0.002° respectively.     

Simulated Annealing and Bayesian Posterior Distribution Analysis Applied to Spectral Emission Line Fitting

Spectral-line fitting problems are extremely common in all remote-sensing disciplines, solar physics included. Spectra in solar physics are frequently parameterized by using a model for the background and the emission lines, and various computational techniques are used to find values to the parameters given the data. However, the most commonly-used techniques, such as least-squares fitting, are highly dependent on the initial parameter values used and are therefore biased. In addition, these routines occasionally fail because of ill-conditioning. Simulated annealing and Bayesian posterior distribution analysis offer different approaches to finding parameter values through a directed, but random, search of the parameter space. The algorithms proposed here easily incorporate any other available information about the emission spectrum, which is shown to improve the fit. Example algorithms are given and their performance is compared to a least-squares algorithm for test data – a single emission line, a blended line, and very low signal-to-noise-ratio data. It is found that the algorithms proposed here perform at least as well or better than standard fitting practices, particularly in the case of very low signal-to-noise ratio data. A hybrid simulated annealing and Bayesian posterior algorithm is used to analyze a Mg x line contaminated by an O IV triplet, as observed by the Coronal Diagnostic Spectrometer onboard SOHO. The benefits of these algorithms are also discussed.