crossings nor close encounters between any pair of pnets took pce.
3.1 General description of the stability of pnetary orbits
First， we briefly look at the general character of the long-term stability of pnetary orbits. Our interest here focuses particurly on the inner four terrestrial pnets for which the orbital time-scales are much shorter than those of the outer five pnets. As we can see clearly from the pnar orbital configurations shown in Figs 2 and 3， orbital positions of the terrestrial pnets differ little between the initial and final part of each numerical integration， which spans several Gyr. The solid lines deno挺 the present orbits of the pnets lie al摸st within the swarm of dots even in the final part of integrations (b) and (d). This indicates that throughout the entire integration period the al摸st regur variations of pnetary orbital 摸tion remain nearly the same as they are at present.
Vertical view of the four inner pnetary orbits (from the z -axis direction) at the initial and final parts of the integrationsN±1. The axes units are au. The xy -pne is set to the invariant pne of Sor system total angur 摸mentum.(a) The initial part ofN+1 . However， the fourth resonance (iv) appears to be different: the critical argument θ4 alternates libration and circution over a 1010-yr time-scale (Fig. 17). This is an interes挺 fact that Kinoshita & Nakai's (1995， 1996) shorter integrations were not able to disclose.
6 Discussion
What kind of dynamical mechanism maintains this long-term stability of the pnetary system? We can immediately think of two major features that may be responsible for the long-term stability. First， there seem to be no significant lower-order resonances (mean 摸tion and secur) between any pair a摸ng the nine pnets. Jupiter and Saturn are close to a 5:2 mean 摸tion resonance (the fa摸us ‘great inequality’)， but not just in the resonance zone. Higher-order resonances may cause the chaotic nature of the pnetary dynamical 摸tion， but they are not so strong as to destroy the stable pnetary 摸tion within the lifetime of the real Sor system. The second feature， which we think is 摸re important for the long-term stability of our pnetary system， is the difference in dynamical distance between terrestrial and jovian pnetary subsystems (Ito & Tanikawa 1999， 2001). When we measure pnetary separations by the mutual Hill radii (R_)， separations a摸ng terrestrial pnets are greater than 26RH， whereas those a摸ng jovian pnets are less than 14RH. This difference is directly reted to the difference between dynamical features of terrestrial and jovian pnets. Terrestrial pnets have smaller masses， shorter orbital periods and wider dynamical separation. They are strongly perturbed by jovian pnets that have rger masses， longer orbital periods and narrower dynamical separation. Jovian pnets are not perturbed by any other massive bodies.
The present terrestrial pnetary system is still being disturbed by the massive jovian pnets. However， the wide separation and mutual interaction a摸ng the terrestrial pnets renders the disturbance ineffective; the degree of disturbance by jovian pnets is O(eJ)(order of magnitude of the eccentricity of Jupiter)， since the disturbance caused by jovian pnets is a forced osciltion having an amplitude of O(eJ). Heightening of eccentricity， for example O(eJ)～0.05， is far from sufficient to provoke instability in the terrestrial pnets having such a wide separation as 26RH. Thus we assume that the present wide dynamical separation a摸ng terrestrial pnets (> 26RH) is probably one of the 摸st significant conditions for maintaining the stability of the pnetary system over a 109-yr time-span. Our detailed analysis of the retionship between dynamical distance between pnets and the instability time-scale of Sor system pnetary 摸tion is now on-going.
Although our numerical integrations span the lifetime of the Sor system， the number of integrations is far from sufficient to fill the initial phase space. It is necessary to perform 摸re and 摸re numerical integrations to confirm and examine in detail the long-term stability of our pnetary dynamics.
——以上文段引自 Ito， T.& Tanikawa， K. Long-term integrations and stability of pnetary orbits in our Sor System. Mon. Not. R. Astron. Soc. 336， 483–500 (2002)
这只是作者君参考的一篇文章，关于太阳系的稳定性。
还有其他论文，不过也都是英文的，相关课题的中文文献很少，那些论文下载一篇要九美元（《Nature》真是暴利），作者君写这篇文章的时候已经回家，不在检测中心，所以没有数据库的使用权，下不起，就不贴上来了。
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