老猫蹲下来，手中捏着一根不知道哪儿找来的棍子，饶有趣味地戳了戳地板上包装好的大便，“唐跃，我觉得你可能严重便秘且大便干燥，你看你拉的翔硬得跟大理石似的。”
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。
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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-terions and stability of plaary orbits in our Solar system
Abstract
We present the results of very long-terions of plaary orbital motions over 109 -yr tig all nine plas. A quick inspection of our numerical data shows that the plaary motion， at least in our simple dynamical model， seems to be quite stable even over this very long time-span. A closer look at the lowest-frequency oscillations using a low-pass filter shows us the potentially diffusive character of terrestrial plaary motion， especially that of Mercury. The behaviour of the eentricity of ions is qualitatively similar to the results from Jacques Laskar's secular perturbation theory (. emax～ over ～± 4 Gyr). However， there are no apparent secular increases of eentricity or inclination in any orbital eles， which may be revealed by still longer-terions. We have also perforions including motions of the outer five plas over the duration of ± 5 × 1010 yr. The result indicates that the three une–Pluto system have been maintained over the 1011-yr time-span.
1 Introduction
Definition of the problem
The question of the stability of our Solar systeed over several hundred years， since the era of Newton. The problem has attracted many fahe years and has played a central role in the development of non-linear dynad chaos theory. However， we do not yet have a definite answer to the question of whether our Solar system is stable or not. This is partly a result of the fact that the definition of the term ‘stability’ is vague when it is used in relation to the probleary motion in the Solar systeo give a clear， rigorous and physically meaningful definition of the stability of our Solar system.
Aions of stability， here we adopt the Hill definition (Gladman 1993): actually this is not a definition of stability， but of instability. We define a systeing unstable when a close encounter ours soem， starting frofiguration (Chambers， Wetherill & Boss 1996; Ito & Tanikawa 1999). A system is defined as experiencing a close encounter when two bodies approach one another within an area of the larger Hill radius. Otherwise the system is defined as being stable. Henceforward we state that our plaary system is dynamically stable if no close encounter happens during the age of our Solar systeally， this definition may be replaced by one in which an ourrence of any orbital crossing between either of a pair of plas takes place. This is because we know fro an orbital crossing is very likely to lead to a close encounter in plaary and protoplaary systems (Yoshinaga， Kokubo & Makino 1999). Of course this stateot be simply applied to systems with stable orbital resonances such as the Neptune–Pluto system.
Previous studies and aims of this research
In addition to the vagueness of the concept of stability， the plas in our Solar systeter typical of dynahaos (Sussman & Wisdom 1988， 1992). The cause of this chaotic behaviour is now partly understood as being a result of resonance overlapping (Murray & Holman 1999; Lecar， Franklin & Holman 2001). However， it would require integrating over an enseary systeg all nine plas for a period covering several 10 Gyr to thoroughly understand the long-terary orbits， since chaotic dynaterized by their strong dependence on initial conditions.
From that point of view， many of the previous long-terions included only the outer five plas (Sussman & Wisdom 1988; Kinoshita & Nakai 1996). This is because the orbital periods of the outer plas are so han those of the inner four plas that it is much easier to follow the systeion period. At present， the longest nuions published in journals are those of Duncan & Lissauer (1998). Although their main target was the effect of post-main-sequence solar ability of plaary orbits， they perforions covering up to ～1011 yr of the orbital motions of the four jovian plas. The initial orbital eles are the same as those of our Solar syste & Lissauer's paper， but they decrease the mass of the Sun gradually in their numerical experiments. This is because they consider the effect of post-ass loss in the paper. Consequently， they found that the crossing tiary orbits， which can be a typical indicator of the instability time-scale， is quite sensitive to the rate of he mass of the Sun is close to its present value， the jovian plas remain stable over 1010 yr， or perhaps longer. Duncan & Lissauer also performed four similar experiments on the orbital s (Venus to Neptune)， which cover a span of ～109 yr. Their experis are not yet co it seems that the terrestrial plas also reegration period， maintaining almost regular oscillations.
On the other hand， in his aurate semi-analytical secular perturbation theory (Laskar 1988)， Laskar finds that large and irregular variations can appear in the eentricities and inclinations of the terrestrial plas， especially of Mercury and Mars on a time-scale of several 109 yr (Laskar 1996). The results of Laskar's secular perturbation theory should be confirigated by fully nuions.
In this paper we present preliminary results of six long-terions on all nine plaary orbits， covering a span of several 109 yr， and of two other integrations covering a span of ± 5 × 1010 yr. The total elapsed tiions is more than 5 yr， using several dedicated PCs and workstations. One of the fundalusions of our long-terions is that Solar systeo be stable in terms of the Hill stability mentioned above， at least over a time-span of ± 4 Gyr. Actually， in our nuem was far more stable than what is defined by the Hill stability criterion: not only did no close encounter happen during the integration period， but also all the plaary orbital eleed in a narrow region both in time and frequency doary ochastic. Since the purpose of this paper is to exhibit and overview the results of our long-terions， we show typical exahe very long-term stability of Solar systeary motion. For readers who have and deeper interests in our numerical results， we have prepared a webpage (aess )， where we show raw orbital elements， their low-pass filtered results， variation of Delaunay elements and angular s of our sialysis on all of our integrations.
In Section 2 we briefly explain our dynamical model， numerical ditions used in our integrations. Section 3 is devoted to a description of the quick results of the nuions. Very long-term stability of Solar systeary motion is apparent both in plaary positions and orbital elements. A rough estimation of numerical errors is also given. Section 4 goes on to a discussion of the longest-terary orbits using a low-pass filter and includes a discussion of angular ion 5， we present a set of nuions for the outer five plas that spans ± 5 × 1010 yr. In Section 6 we also discuss the long-terary motion and its possible cause.
2 Description of the nuions
（本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了起点也不一定能成功显示。）
Numerical method
We utilize a second-order Wisdom–Holman syion method (Wisdom & Holman 1991; Kinoshita， Yoshida & Nakai 1991) with a special start-up procedure to reduce the truncation error of angle variables，‘warm start’(Saha & Tremaine 1992， 1994).
The stepsize for the nuions is 8 d throughout all integrations of the nine plas (N±1，2，3)， which is about 1/11 of the orbital period of the inner (Mercury). As for the determination of stepsize， we partly follow the previous nuion of all nine plas in Sussman & Wisdom (1988， d) and Saha & Tremaine (1994， 225/32 d). We rounded the decimal part of the their stepsizes to 8 to make the stepsize a o reduce the aumulation of round-off error in the coion to this， Wisdom & Holman (1991) perforions of the outer five plaary orbits using the sy map with a stepsize of 400 d， 1/ of the orbital period of Jupiter. Their result seeurate enough， which partly justifies our epsize. However， since the eentricity of Jupiter (～) is much smaller than that of Mercury (～)， we need sos simply in terms of stepsizes.
In the integration of the outer five plas (F±)， we fixed the stepsize at 400 d.
We adopt Gauss' f and g functions in the sy map together with the third-order Halley method (Danby 1992) as a solver for Kepler equations. The number of in Halley's method is 15， but they never reached the ions.
The interval of the data output is 200 000 d (～547 yr) for the calculations of all nine plas (N±1，2，3)， and about 8000 000 d (～21 903 yr) for the integration of the outer five plas (F±).
Although no output filtering was done when the nuions were in process， we applied a low-pass filter to the raw orbital data after we had coulations. See Section for more detail.
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