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1.
The analyses have been made with the emphasis on four existing criteria for calibrating the azimuth of the photospheric transverse magnetic field measured with a heliomagnetograph. The results indicate that the potential criterion, Krall's criterion, i.e. Bt · Bz < 0 and Wu-Ai's criterion, i.e.

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, are applicable to different cases, and the criterion based on the assumption about azimuth continuity of the transverse field is unreliable for the magnetograms with discrete data. On the basis of these analyses, a synthesized method for determining the azimuth of the transverse magnetic field on solar photosphere has been suggested in this paper. The main points of the method are as follows:

The transverse magnetic field observed with a heliomagnetograph could be calibrated, respectively, by means of potential criterion and Krall's criterion, and two different results could be obtained. By comparing the both results with one another, we can find that the azimuth distributions of transverse field are the same in some areas, which are named as areas with certain transverse field (CA), and different in other areas, which are named as areas with uncertain transverse field(UA). In order to determine the transverse field in UA, we introduce an assumption that the values of (the factor of force-free magnetic field) at neighbouring points are close. According to this assumption, the distribution of in UA could be determined through extrapolating from the CA, and hence the azimuth distribution of the transverse field in UA could be determined as well.

An observational example shown in this paper preliminarily demonstrates the availability of the synthesized method.  相似文献   


2.
New photoelectric BVR light curves and radial velocity curves were obtained for the HIPPARCOS discovery DN Boo at the TÜBİTAK1 National Observatory of Turkey (TUG) and Dominion Astrophysical Observatory (DAO), respectively, to determine physical nature of the variable. The character of the obtained light curves and double-lined spectroscopic structures in the obtained spectra are revealed that DN Boo is a genuine EW type eclipsing binary. During the analysis of our new observations a simultaneous solution were derived for the photometric and spectroscopic data by using the Wilson–Devinney code and orbital parameters with absolute dimensions of the system were determined for the first time. Finally, the importance of very low mass-ratio contact binaries in the late stages of close binary evolution was discussed.  相似文献   

3.
A morphological analysis study of open clusters’ properties has been achieved for a sample of 160 UBVCCD open star clusters of approximately 128,000 stars near the galactic plane. The data was obtained and reduced from Tadross (2001) using the same reduction procedures, which makes this catalogue the largest homogeneous source of open clusters’ parameters.  相似文献   

4.
The DTM series of atmospheric density models (Barlier and Berger) have been developed for atmospheric constituent representation and precise orbit computation. They are based upon satellite drag total density data which are implicitly averaged over one or more days.

Our approach consists of refining the computation of the density model coefficients with more precise orbit computation, using the information contained in the tracking data. Satellite Laser Ranging (SLR) in case of Starlette (800 km) and GFZ-1 (380 km), Doppler-DORIS in case of SPOT2 (800 km).

This has been verified by comparison of the new density values to Dynamic Explorer 2 (DE-2) measurements, as well as by precise orbit computation. In both cases, an improvement of a few percent has been achieved, showing the interest of the method.

This study has been done in preparation for the new accelerometric mission CHAMP for which we prepare a new gravity field (GRIM5) using the orbit perturbation technique, as well as an improved density model, hence improving the drag modeling.  相似文献   


5.
《Astroparticle Physics》2008,29(4):257-281
The results of the measurements of the double-differential production cross-sections of pions, , in p–C and π±–C interactions using the forward spectrometer of the HARP experiment are presented. The incident particles are 12 GeV/c protons and charged pions directed onto a carbon target with a thickness of 5% of a nuclear interaction length. For p–C interactions the analysis is performed using 100,035 reconstructed secondary tracks, while the corresponding numbers of tracks for π-–C and π+–C analyses are 106,534 and 10,122, respectively. Cross-section results are presented in the kinematic range and in the laboratory frame. The measured cross-sections have a direct impact on the precise calculation of atmospheric neutrino fluxes and on the improved reliability of extensive air shower simulations by reducing the uncertainties of hadronic interaction models in the low energy range.  相似文献   

6.
If the photon possessed an electric charge or a magnetic moment, light waves propagating through magnetic fields would acquire new quantum mechanical phases. For a charged photon, this is an Aharonov–Bohm phase, and the fact that we can resolve distant galaxies using radio interferometry indicates that this phase must be small. This in turn constrains the photon charge to be smaller that if all photons have the same charge and smaller than if there are both positively and negatively charged photons. The best bound on the magnetic moment comes from the observed absence of wavelength-independent photon birefringence. Birefringence measurements, which compare the relative phases of right- and left-circularly polarized waves, restrict the magnetic moment to be less than . This is just a few orders of magnitude weaker than the experimental bounds on the electron and neutron electric dipole moments.  相似文献   

7.
Cosmic-ray induced neutrino backgrounds at the Moon are estimated using a semi-analytic approach. The analytic expressions are derived, flux estimates for and are given, and comparisons with the analogous backgrounds generated in the Earth’s atmosphere are presented. Suppression of the lunar fluxes relative to the terrestrial fluxes is found. At energies >10 GeV, the suppression approaches a maximum of order 10−4. The lower background environment suggests that the Moon may be advantageous for future particle astrophysics endeavors.  相似文献   

8.
In association with the large solar flare of April 15, 2001, the Chacaltaya neutron monitor observed a 3.6σ enhancement of the counting rate between 13:51 and 14:15 UT. Since the enhancement was observed beginning 11 min before the GLE, solar neutrons must be involved in this enhancement. The integral energy spectrum of solar neutrons can be expressed by a simple power law in energy with the index γ=-3.0±1.0. On the other hand, an integral energy spectrum of solar protons has been obtained in the energy range between 650 MeV and 12 GeV. The spectrum can also be expressed by a power law with the power index γ=-2.75±0.15. The flux of solar protons observed at Chacaltaya (at 12 GeV) was already one order less than the flux of the galactic cosmic rays. It may be the first simultaneous observation of the energy spectra of both high-energy protons and neutrons. Comparing the Yohkoh soft X-ray telescope images with the observed particle time profiles, an interesting picture of the particle acceleration mechanism has been deduced.  相似文献   

9.
We discuss the concept and the performance of a powerful future ground-based astronomical instrument, 5@5 – a 5 GeV energy threshold stereoscopic array of several large imaging atmospheric Cherenkov telescopes (IACTs) installed at a very high mountain elevation of about 5 km a.s.l. – for the study of the γ-ray sky at energies from approximately 5 to 100 GeV, where the capabilities of both the current space-based and ground-based γ-ray projects are quite limited. With its potential to detect the “standard” EGRET γ-ray sources with spectra extending beyond several GeV in exposure times from 1 to 103 s, such a detector may serve as an ideal “gamma-ray timing explorer” for the study of transient non-thermal phenomena like γ-radiation from AGN jets, synchrotron flares of microquasars, the high energy (GeV) counterparts of gamma ray bursts, etc. 5@5 also would allow detailed γ-ray spectroscopy of persistent nonthermal sources like pulsars, supernova remnants, plerions, radiogalaxies, and others, with unprecedented for γ-ray astronomy photon statistics. The existing technological achievements in the design and construction of multi(1000)-pixel, high resolution imagers, as well as of large, 20 m diameter class multi-mirror dishes with rather modest optical requirements, would allow the construction of such a detector in the foreseeable future, although in the longer terms from the point of view of ongoing projects of 100 GeV threshold IACT arrays like HESS which is in the build-up phase. An ideal site for such an instrument could be a high-altitude, 5 km a.s.l. or more, flat area with a linear scale of about 100 m in a very arid mountain region in the Atacama desert of Northern Chile.  相似文献   

10.
《Astroparticle Physics》2008,29(4):243-256
A method is developed to search for air showers initiated by photons using data recorded by the surface detector of the Auger Observatory. The approach is based on observables sensitive to the longitudinal shower development, the signal risetime and the curvature of the shower front. Applying this method to the data, upper limits on the flux of photons of 3.8×10-3, above , are derived, with corresponding limits on the fraction of photons being 2.0%, 5.1%, and 31% (all limits at 95% c.l.). These photon limits disfavor certain exotic models of sources of cosmic rays. The results also show that the approach adopted by the Auger Observatory to calibrate the shower energy is not strongly biased by a contamination from photons.  相似文献   

11.
《Astroparticle Physics》2009,31(6):399-406
From direct observations of the longitudinal development of ultra-high energy air showers performed with the Pierre Auger Observatory, upper limits of 3.8%, 2.4%, 3.5% and 11.7% (at 95% c.l.) are obtained on the fraction of cosmic-ray photons above 2, 3, 5 and 10 EeV , respectively. These are the first experimental limits on ultra-high energy photons at energies below 10 EeV. The results complement previous constraints on top–down models from array data and they reduce systematic uncertainties in the interpretation of shower data in terms of primary flux, nuclear composition and proton-air cross-section.  相似文献   

12.
In this paper we show the capabilities of the Large Volume Detector (INFN Gran Sasso National Laboratory) to identify a neutrino burst associated with a supernova explosion, in the absence of an “external trigger”, e.g., an optical observation. We describe how the detector trigger and event selection have been optimized for this purpose, and we detail the algorithm used for the on-line burst recognition. The on-line sensitivity of the detector is defined and discussed in terms of supernova distance and intensity at the source.  相似文献   

13.
The MINOS experiment has observed a rise in the underground muon charge ratio rμ=μ+/μ-. This ratio can be related to the atmospheric production ratios of π+/π- and K+/K-. Our analysis indicates that the relevant variable for studying the charge ratio is , rather than . We compare a simple energy dependent parameterization of the rise in the charge ratio with more detailed previously published Monte Carlo simulations and an analytical calculation. We also estimate the size of two previously neglected effects in this context: the charge sign dependency of the dE/dx in rock, and the energy dependence of heavy primaries on the derived K+/K- ratio.  相似文献   

14.
The photo-coulomb neutrino process has been considered in the electro-weak theory and the influence of this process to the evolution of stars has been outlined. The scattering cross-section of this process is calculated in both low and high energy limit. The neutrino mass has been taken into account in this calculation. In the low-energy limit the neutrino luminosity is computed in the temperature range 108–109 K and is also compared to the previous result obtained according to the current-current coupling theory. The process may be significant for the evolution of stars in the later phases.  相似文献   

15.
From the volume-limited Main galaxy sample of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we construct three samples with g–r color bins , labeled S1–S3, to investigate how other properties of galaxies depend on environment at fixed color. For each sample, we measure the local three-dimensional galaxy density in a comoving sphere with radius equal to the distance to the 5th nearest galaxy for each galaxy, select about 5% galaxies and construct the two subsamples at both extremes of density. Our study suggests that the environmental dependence of luminosity is mainly due to the environmental dependence of galaxy color and the correlation between color and luminosity. In addition, we preferentially conclude that concentration index and morphologies are not strongly correlated with local density at fixed color, and that galaxy color is a galaxy property very predictive of the local environment. Because SDSS spectroscopy is incomplete for bright galaxies at very low redshifts, we also use a volume-limited Main galaxy sample with a lower redshift limit z = 0.05, which contains 94,954 galaxies at 0.05 < z < 0.089 with −22.40 < Mr < −20.16, and reach the same conclusions.Due to the bimodality of the u–r color distribution, we classify galaxies as ‘red’ and ‘blue’, respectively, and further subdivide the samples into star-forming galaxies and passive ones using Hα equivalent width, W0(Hα). Results show that color and star formation activity of galaxies are galaxy properties very predictive of the local environment.  相似文献   

16.
We present an overview of the low-frequency array (LOFAR) that will open a window on one of the last and most poorly explored regions of the electromagnetic spectrum. LOFAR will be a large (baselines up to 400 km), low-frequency aperture synthesis array with large collecting area ( at ) and high resolution (1.5″ at 100 MHz), and will provide sub-mJy sensitivity across much of its operating range. LOFAR will be a powerful instrument for solar system and planetary science applications as reviewed by papers in this monogram. Key astrophysical science drivers include acceleration, turbulence, and propagation in the galactic interstellar medium, exploring the high red-shift universe and transient phenomena, as well as searching for the red-shifted signature of neutral hydrogen from the cosmologically important epoch of re-ionization.  相似文献   

17.
Cosmic acceleration is investigated through a kink-like expression for the deceleration parameter (q). The new parametrization depends on the initial (qi) and final (qf) values of q, on the redshift of the transition from deceleration to acceleration (zt) and the width of such transition (τ). We show that although supernovae (SN) observations (Gold182 and SNLS data samples) indicate, at high confidence, that a transition occurred in the past (zt > 0) they do not, by themselves, impose strong constraints on the maximum value of zt. However, when we combine SN with the measurements of the ratio between the comoving distance to the last scattering surface and the SDSS + 2dfGRS BAO distance scale (Sk/Dv) we obtain, at 95.4% confidence level, and for (Sk/Dv+Gold182), and and for (Sk/Dv+SNLS), assuming qi = 0.5 and qf = −1. We also analyze the general case, qf  (−∞, 0) finding the constraints that the combined tests (Sk/Dv+SNLS) impose on the present value of the deceleration parameter (q0).  相似文献   

18.
In this article we present a theoretical method for the study of the general three-body problem by computer simulation developed in the Leningrad State University Astronomical Observatory (LSU AO). This method permits statistical methods to be used for studying the behaviour of triple systems. This is achieved by selecting a representative sample of initial conditions which then reveal general features of the evolution.The main results of numerical experiments on the three-body problem carried out at the LSU AO during the past 25 years have been summarized in the reviews by Anosova (1985), Anosova and Orlov (1985), and Anosova (1986).Systematic studies of about 3 × 104 triple systems with negative total energy (E < 0) have yielded the following main results. Most (93.4%) of the systems decay; the decay always occurs after a close triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (4.3%) of stable systems is formed if the angular momentum is non-zero. The qualitative evolution in three-dimensional cases is the same as for planar systems. Small changes in initial conditions sometimes lead to substantial differences in the final outcome. The decay of triple systems is a stochastic process similar to radioactive decay. The estimated mean lifetime is equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (107.1 ± 1.8) crossing times for equal-mass components. Thus, for solar mass components and a typical dimension d = 0.01 pc, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (1.6 ± 1.5) × 106 y, and for triple galaxies with M = 101° M 0 and d = 50 kpc, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (1.8 ± 1.7) × 1011 y. The value % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] decreases with increasing mass dispersion.In this article we also carry out a theoretical analysis of the changes of the integrals of motion in the general three-body problem used as the controls on the calculations. The following basic results have been found: (1) analytical functions of the changes of the integrals of motion during the integration time have been obtained; (2) changes in the integrals of the mass-centre of a triple system do not correlate with the cumulative integration errors; (3) the cumulative changes of the integral of energy are proportional to the sum of squares of the cumulative errors in the coordinates and the velocities of the bodies; (4) the cumulative changes of the square of the total angular momentum are proportional to the product of the square of these cumulative errors.The analysis of the accuracy of computer simulations conducted in LSU AO for the 3 × 104 triple systems with E < 0 is summarized by the following basic qualitative results: (1) the unstable triple systems decay after a mean lifetime % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] 100 or % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] 104 % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGObaaaaaa!3C6A!\[\overline h \]t where is a crossing time, and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGObaaaaaa!3C6A!\[\overline h \], is a mean integration step After this integration time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] the mean cumulative relative changes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamyraaaaaaa!3D10!\[\overline {DE} \] of the integrals of the energy of the triple systems are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamyraaaaaaa!3D10!\[\overline {DE} \] = (0.9±0.1) × 10–4, and the mean cumulative relative changes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamitaaaaaaa!3D17!\[\overline {DL} \] of the area integrals are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamitaaaaaaa!3D17!\[\overline {DL} \] = (1.0±0.1) × 10–6; the mean values of the cumulative errors % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaamiraiaadkhaaaa!3D2C!\[{Dr}\], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamOvaaaaaaa!3D21!\[\overline {Dv} \] in defining the coordinates (r) and velocities (v) of the bodies (during the total integration time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \]) are equal to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamOCaaaaaaa!3D3D!\[\overline {Dr} \] = 0.5 × 10–3 d, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGebGaamODaaaaaaa!3D41!\[\overline {Dv} \] = 0.5 × 10–2 v, where d is the unit of distance, and v is the unit of velocity; the mean local integration errors (of one integration step) are equal to r= 5 × 10–8 d, 6v = 5 × 10–7 v; (2) the process of accumulation of integration errors has a complicated character and correlates strongly with the process of dynamical evolution of the triple systems; (a) because of the strong gravitational interplays of the bodies, the process of the accumulation of the integration errors is very intensive; however, the triple systems with these interplays of the bodies have, as a rule, a small escape time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] t, and the cumulative calculation errors are small too; (b) in the stable triple systems the local integration errors are practically constant during the numerical study of their evolution, and the calculations can be carried out (if it is necessary) during the time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa0aaaeaacaWGubaaaaaa!3C56!\[\overline T \] = (2–3) × 103 without disturbing the periodical motions of the bodies; (3) thus, in the general three-body problem with different initial conditions, it is not necessary to carry out the computer simulations over long times, as most of the triple systems decay and do not have very long lifetimes; (4) the mean level of the cumulative errors Dr and Dv of the definitions of the coordinates and velocities of bodies in the different triple systems is practically equal.  相似文献   

19.
We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t).  相似文献   

20.
We presents the results of our study of new spectroscopic components in the visual binaries ADS 10683 (HD 160 239=BD?154 635=HIP 86412; G6/G8V; \(V = 9\mathop .\limits^m 08\); \(B - V = 0\mathop .\limits^m 76\); 2000: 17h39m24s, ?15°46′) and ADS 11791 (HD 175039=BD?054 798=HIP 92726; G5; \(V = 8\mathop .\limits^m 78\); \(B - V = 0\mathop .\limits^m 72\); 2000: 18h53m42s, ?05°33′). ADS 10683B and ADS 11791A are single-lined spectroscopic binaries; their orbital periods are \(6\mathop .\limits^d 9171 \pm 0\mathop .\limits^d 0002\) and \(50\mathop .\limits^d 514 \pm 0\mathop .\limits^d 004\), respectively. We constructed their radial velocity curves and computed their spectroscopic orbital elements.  相似文献   

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