Symplectic Mappings of Co-orbital Motion in the Restricted Problem of Three Bodies

The dynamics of co-orbital motion in the restricted three-body problem are investigated by symplectic mappings. Analytical and semi-numerical mappings have been developed and studied in detail. The mappings have been tested by numerical integration of the equations of motion. These mappings have been proved to be useful for a quick determination of the phase space structure reflecting the main characteristics of the dynamics of the co-orbital problem.     

Lithium Abundances in the Atmospheres of SLR C-Giants WZ Cas and WX Cyg from Resonance and Subordinate Li I Lines

Lithium abundances in the atmospheres of the super Li-rich C-giants WZ Cas and WX Cyg are derived by the spectral synthesis technique using the Li I resonance line at λ670.8 nm and three subordinate lines at λλ 812.6, 610.4 and 497.2 nm. The differences between the Li abundances derived from the λ670.8 nm line and the λλ 497.2, 812.6 nm lines do not exceed ±0.5 dex. The lithium line at λ610.4 nm provides typically lower abundances than the resonance line (by ≈ 1 dex). The mean LTE and NLTE Li abundances from three Li I lines (excluding λ610.4 nm) are 4.7, 4.9 for WZ Cas, and 4.6, 4.8 for WX Cyg, respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

HD 82943行星系统的2:1共振与稳定性

用直接数值积分方法通过模拟不同的行星构型探讨了HD82943行星系统(由两颗共振的巨行星组成)的长期动力演化,同时,还研究了在相空间的轨道运动.在对系统长达107年数值积分中,发现所有的稳定轨道均与2:1共振相关联.典型地,在相同的时标内,两个共振幅角θ1和θ2同时(或其中之一)存在秤动.由于共振幅角在一定范围内的秤动,因而使两颗行星轨道半长径被约束而表现为规则运动模式.另外,利用分析模型(包含了外行星偏心率e2的因素),还讨论了对于不同取值的e2和相对近星点经度θ时,内行星在相空间的运动,并发现2:1轨道共振对于相对较小的e2以及当θ=0°时易于保持.此外,适中的e2将导致系统的两颗行星进入深度共振状态.再者,分析模型和数值计算的结果吻合得很好,两者都揭示了行星系统的2:1共振结构.     

Analysis of mapping coverage obtained from spacecraft

An exact analysis of the coverage obtained by spacecraft using cross-track scanning and nadir-centered conical imaging, under imposed viewing obliqueness and resolution requirements, is presented. In addition to exact expressions for the area acquired and the area acquisition rate, envelope theory is introduced to obtain the boundary of the imaged area. These expressions are relatively compact, allowing rapid machine computation. The effects of the sun phase angle, and of imaging system limitations are also examined. The Galileo mission encounter with Callisto is used as a numerical example, from which certain general conclusions are drawn regarding optimal imaging trajectories.     

Final tidal evolution of orbit-orbit resonances

In this paper we describe a model for the tidal evolution of an orbit-orbit resonance between two satellites of the same planet. We let the system evolve till infinity or until the resonance is destroyed. We find that there are asymptotic values for the eccentricities and inclinations. We list the possible final stages that a resonance can achieve, we give a few examples, and finally we discuss the limitations of the model and its possible applications to real systems.     

Aspects of the zero level problem of solar magnetographs

The zero level problem of solar magnetographs is particularly important for observations of large-scale magnetic fields on the Sun. Experiments conducted at the STOP telescope of the Sayan observatory show that, in addition to adjustment errors of the polarization analyzer and the spectrograph focusing, spurious signals of the magnetograph are caused by polarization effects in optical components preceding the polarization analyzer and aberration errors of the spectrograph.     

Transforming observational data and theoretical isochrones into the ACS/WFC Vega-mag system

We propose a zero-point photometric calibration of the data from the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) on board the Hubble Space Telescope , based on a spectrum of Vega and the most up-to-date in-flight transmission curves of the camera. This calibration is accurate at the level of a few hundredths of a magnitude. The main purpose of this effort is to transform the entire set of evolutionary models into a simple observational photometric system for ACS/WFC data, and to make them available to the astronomical community. We provide the zero-points for the most used ACS/WFC bands, and give basic recipes for calibrating both the observed data and the models. We also present the colour–magnitude diagram from ACS data of five Galactic globular clusters, spanning the metallicity range  −2.2 <[Fe/H] < −0.04  , and we provide fiducial points representing their sequences from several magnitudes below the turn-off to the red giant branch tip. The observed sequences are compared with the models in the newly defined photometric system.     

Chaotic Diffusion And Effective Stability of Jupiter Trojans

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.