按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！
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…term integrations and stability of plaary orbits in our Solar system
Abstract
We present the results of very long…term numerical integrations of plaary orbital motions over 109 …yr time…spans including 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 eccentricity of Mercury in our integrations is qualitatively similar to the results from Jacques Laskar's secular perturbation theory （e。g。 emax～ 0。35 over ～± 4 Gyr）。 However， there are no apparent secular increases of eccentricity or inclination in any orbital elements of the plas， which may be revealed by still longer…term numerical integrations。 We have also performed a uple of trial integrations including motions of the outer five plas over the duration of ± 5 × 1010 yr。 The result indicates that the three major resonances in the Neptune–Pluto system have been maintained over the 1011…yr time…span。
1 Introduction
1。1Definition of the problem
The question of the stability of our Solar system has been debated over several hundred years， since the era of Newton。 The problem has attracted many famous mathematicians over the years and has played a central role in the development of non…linear dynamics and 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 problem of plaary motion in the Solar system。 Actually it is not easy to give a clear， rigorous and physically meaningful definition of the stability of our Solar system。
Among many definitions of stability， here we adopt the Hill definition （Gladman 1993）： actually this is not a definition of stability， but of instability。 We define a system as being unstable when a close enunter occurs somewhere in the system， starting from a certain initial nfiguration （Chambers， Wetherill &；amp； Boss 1996； Ito &；amp； Tanikawa 1999）。 A system is defined as experiencing a close enunter 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 enunter happens during the age of our Solar system， about ±5 Gyr。 Incidentally， this definition may be replaced by one in which an occurrence of any orbital crossing between either of a pair of plas takes place。 This is because we know from experience that an orbital crossing is very likely to lead to a close enunter in plaary and protoplaary systems （Yoshinaga， Kokubo &；amp； Makino 1999）。 Of urse 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 ncept of stability， the plas in our Solar system show a character typical of dynamical chaos （Sussman &；amp； Wisdom 1988， 1992）。 The cause of this chaotic behaviour is now partly understood as being a result of resonance overlapping （Murray &；amp； Holman 1999； Lecar， Franklin &；amp； Holman 2001）。 However， it would require integrating over an ensemble of plaary systems including all nine plas for a period vering several 10 Gyr to thoroughly understand the long…term evolution of plaary orbits， since chaotic dynamical systems are characterized by their strong dependence on initial nditions。
From that point of view， many of the previous long…term numerical integrations included only the outer five plas （Sussman &；amp； Wisdom 1988； Kinoshita &；amp； Nakai 1996）。 This is because the orbital periods of the outer plas are so much longer than those of the inner four plas that it is much easier to follow the system for a given integration period。 At present， the longest numerical integrations published in journals are those of Duncan &；amp； Lissauer （1998）。 Although their main target was the effect of post…main…sequence solar mass loss on the stability of plaary orbits， they performed many integrations vering up to ～1011 yr of the orbital motions of the four jovian plas。 The initial orbital elements and masses of plas are the same as those of our Solar system in Duncan &；amp； Lissauer's paper， but they decrease the mass of the Sun gradually in their numerical experiments。 This is because they nsider the effect of post…main…sequence solar mass loss in the paper。 nsequently， they found that the crossing time…scale of plaary orbits， which can be a typical indicator of the instability time…scale， is quite sensitive to the rate of mass decrease of the Sun。 When the mass of the Sun is close to its present value， the jovian plas remain stable over 1010 yr， or perhaps longer。 Duncan &；amp； Lissauer also performed four similar experiments on the orbital motion of seven plas （Venus to Neptune）， which ver a span of ～109 yr。 Their experiments on the seven plas are not yet prehensive， but it seems that the terrestrial plas also remain stable during the integration period， maintaining almost regular oscillations。
On the other hand， in his accurate semi…analytical secular perturbation theory （Laskar 1988）， Laskar finds that large and irregular variations can appear in the eccentricities 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 nfirmed and investigated by fully numerical integrations。
In this paper we present preliminary results of six long…term numerical integrations on all nine plaary orbits， vering a span of several 109 yr， and of two other integrations vering a span of ± 5 × 1010 yr。 The total elapsed time for all integrations is more than 5 yr， using several dedicated PCs and workstations。 One of the fundamental nclusions of our long…term integrations is that Solar system plaary motion seems to be stable in terms of the Hill stability mentioned above， at least over a time…span of ± 4 Gyr。 Actually， in our numerical integrations the system was far more stable than what is defined by the Hill stability criterion： not only did no close enunter happen during the integration period， but also all the plaary orbital elements have been nfined in a narrow region both in time and frequency domain， though plaary motions are stochastic。 Since the purpose of this paper is to exhibit and overview the results of our long…term numerical integrations， we show typical example figures as evidence of the very long…term stability of Solar system plaary motion。 For readers who have more specific and deeper interests in our numerical results， we have prepared a webpage （access ）， 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 nditions used in our integrations。 Section 3 is devoted to a description of the quick results of the nu