唐跃戴上口罩，并不想搭理老猫这个话痨。

老猫还在戳地上的大便，翻过来覆过去地戳。

“唐跃你看，这坨翔像不像一颗真空包装的茶叶蛋？你是怎么拉出这么圆的屎蛋蛋来的？能不能演示一下？”

“还有这个，这坨翔大，我估计一下，起码得有五两重吧……”

“这坨很有艺术气息，看上去像是梵高的星空。”

“哎唐跃！你来看这个，这坨翔长得很像你诶！简直就是一个模子里刻出来的，你们真是一对父子……”

唐跃恼怒地抄起一块干燥的大便砸了过去。

对火星轨道变化问题的最后解释

作者君在作品相关中其实已经解释过这个问题。

不过仍然有人质疑——“你说得太含糊了”，“火星轨道的变化比你想象要大得多！”

那好吧，既然作者君的简单解释不够有力，那咱们就看看严肃的东西，反正这本书写到现在，嚷嚷着本书bug一大堆，用初高中物理在书中挑刺的人也不少。

以下是文章内容：

long-terentricity of entricity or inclination in any orbital eleurs sourrence of any orbital crossing between either of a pair of planets takes place. this is because we know from experience that an orbital crossing is very likely to lead to a close encounter in planetary and protoplanetary systems (yoshinaga， kokubo & makino 1999). of course this statement cannot be simply applied to systems with stable orbital resonances such as the neptune–pluto system.

1.2previous studies and aims of this research

in addition to the vagueness of the concept of stability， the planets in our solar systeurate seentricities and inclinations of the terrestrial planets， especially of ess )， where we show raw orbital elements， their low-pass filtered results， variation of delaunay elements and angular momentum deficit， and results of our simple time–frequency analysis on all of our integrations.

in section 2 we briefly explain our dynamical model， numerical method and initial conditions used in our integrations. section 3 is devoted to a description of the quick results of the numerical integrations. very long-term stability of solar system planetary motion is apparent both in planetary positions and orbital elements. a rough estimation of numerical errors is also given. section 4 goes on to a discussion of the longest-term variation of planetary orbits using a low-pass filter and includes a discussion of angular momentum deficit. in section 5， we present a set of numerical integrations for the outer five planets that spans 5 1010 yr. in section 6 we also discuss the long-term stability of the planetary motion and its possible cause.

2 description of the nuuurate enough， which partly justifies our entricity of jupiter (～0.05) is ording to one of the basic properties of syuracy of nuuracy than the urate integration with a stepsize of 0.125 d (1/64 of the main integrations) spanning 3 105 yr， starting with the same initial conditions as in the n?1 integration. we consider that this test integration propare the test integration with the main integration， n?1. for the period of 3 105 yr， we see a difference in mean anomalies of the earth between the two integrations of ～0.52(in the case of the n?1 integration). this difference can be extrapolated to the value ～8700， about 25 rotations of earth after 5 gyr， since the error of longitudes increases linearly with time in the symplectic map. similarly， the longitude error of pluto can be estimated as ～12. this value for pluto is much better than the result in kinoshita & nakai (1996) where the difference is estimated as ～60.

3 nuentricities and orbital inclinations for the inner four planets in the initial and final part of the integration n+1 is shown in fig. 4. as expected， the character of the variation of planetary orbital eleentricity， seeentricities and inclinations of mercury on a time-scale of several 109 yr. however， the effect of the possible instability of the orbit of mercury may not fatally affect the global stability of the whole planetary system owing to the small mass of mercury. we will mention briefly the long-term orbital evolution of mercury later in section 4 using low-pass filtered orbital elements.

the orbital motion of the outer five planets seems rigorously stable and quite regular over this time-span (see also section 5).

3.2 time–frequency maps

although the planetary motion exhibits very long-term stability defined as the non-existence of close encounter events， the chaotic nature of planetary dynamics can change the oscillatory period and amplitude of planetary orbital motion gradually over such long time-spans. even such slight fluctuations of orbital variation in the frequency domain， particularly in the case of earth， can potentially have a significant effect on its surface climate system through solar insolation variation (cf. berger 1988).

to give an overview of the long-term change in periodicity in planetary orbital motion， we performed many fast fourier transformations (ffts) along the time axis， and superposed the resulting periodgrams to draw two-dimensional time–frequency maps. the specific approach to drawing these time–frequency maps in this paper is very simple – much simpler than the wavelet analysis or laskars (1990， 1993) frequency analysis.

divide the low-pass filtered orbital data into many fragments of the same length. the length of each data segment should be a multiple of 2 in order to apply the fft.

each fragment of the data has a large overlapping part: for example， when the ith data begins from t=ti and ends at t=ti+t， the next data segment ranges from ti+δt≤ti+δt+t， where δt?t. we continue this division until we reach a certain number n by which tn+t reaches the total integration length.

we apply an fft to each of the data fragments， and obtain n frequency diagrams.

in each frequency diagram obtained above， the strength of periodicity can be replaced by a grey-scale (or colour) chart.

we perform the replacement， and connect all the grey-scale (or colour) charts into one graph for each integration. the horizontal axis of these new graphs should be the time， i.e. the starting times of each fragment of data (ti， where i= 1，…， n). the vertical axis represents the period (or frequency) of the oscillation of orbital elements.

we have adopted an fft because of its overwhelentricity and inclination of earth in n+2 integration. in fig. 5， the dark area shows that at the tientricity and inclination of earth only changes slightly over the entire period covered by the n+2 integration. this nearly regular trend is qualitatively the saaletti &ao 1998). this entricities of venus and earth can be disturbed easily by jupiter and saturn， which results in a positive correlation in the angular momentum exchange. on the other hand， the semimajor axes of venus and earth are less likely to be disturbed by the jovian planets. thus the energy exchange may be limited only within the venus–earth pair， which results in a negative correlation in the exchange of orbital energy in the pair.

as for the outer joes es 90 again. williams & benson (1971) anticipated this type of resonance， later confirmed by milani， nobili & carpino (1989).

an argument θ4=?p??n+ 3 (Ωp?Ωn) librates around 180 with a long period，～ 5.7 108 yr.

in our numerical integrations， the resonances (i)–(iii) are well maintained， and variation of the critical arguments θ1，θ2，θ3 remain similar during the whole integration period (figs 14–16 ). however， the fourth resonance (iv) appears to be different: the critical argument θ4 alternates libration and circulation over a 1010-yr time-scale (fig. 17). this is an interesting fact that kinoshita & nakais (1995， 1996) shorter integrations were not able to disclose.

6 discussion

what kind of dynamical mechanism maintains this long-term stability of the planetary 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 motion and secular) between any pair among the nine planets. jupiter and saturn are close to a 5:2 mean motion resonance (the famous ‘great inequality’)， but not just in the resonance zone. higher-order resonances may cause the chaotic nature of the planetary dynamical motion， but they are not so strong as to destroy the stable planetary motion within the lifetime of the real solar system. the second feature， which we think is more important for the long-term stability of our planetary system， is the difference in dynamical distance between terrestrial and jovian planetary subsystems (ito & tanikawa 1999， 2001). when we measure planetary separations by the mutual hill radii (r_)， separations among terrestrial planets are greater than 26rh， whereas those among jovian planets are less than 14rh. this difference is directly related to the difference between dynamical features of terrestrial and jovian planets. terrestrial planets have smaller masses， shorter orbital periods and wider dynamical separation. they are strongly perturbed by jovian planets that have larger masses， longer orbital periods and narrower dynamical separation. jovian planets are not perturbed by any other massive bodies.

the present terrestrial planetary systeentricity of jupiter)， since the disturbance caused by jovian planets is a forced oscillation having an aentricity， for example o(ej)～0.05， is far from sufficient to provoke instability in the terrestrial planets having such a wide separation as 26rh. thus we assume that the present wide dynamical separation among terrestrial planets (> 26rh) is probably one of the most significant conditions for maintaining the stability of the planetary system over a 109-yr time-span. our detailed analysis of the relationship between dynamical distance between planets and the instability time-scale of solar system planetary motion is now on-going.

although our numerical integrations span the lifetime of the solar system， the number of integrations is far from sufficient to fill the initial phase space. it is necessary to perform more and more numerical integrations to confirm and examine in detail the long-term stability of our planetary dynamics.

——以上文段引自 ito， t.& tanikawa， k. long-term integrations and stability of planetary orbits in our solar 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。