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死在火星上

时间:2023-05-23  来源:  作者:天瑞说符

    the interval of the data output is 200 000 d  for the calculations of all nine planets , and about 8000 000 d  for the integration of the outer five planets .

    although no output filtering was done when the numerical integrations were in process, we applied a low-pass filter to the raw orbital data after we had completed all the calculations. see section 4.1 for more detail.

    2.4 error estimation

    2.4.1 relative errors in total energy and angular momentum

    according to one of the basic properties of symplectic integrators, which conserve the physically conservative quantities well , our long-term numerical integrations seem to have been performed with very small errors. the averaged relative errors of total energy  and of total angular momentum  have remained nearly constant throughout the integration period . the special startup procedure, warm start, would have reduced the averaged relative error in total energy by about one order of magnitude or more.

    relative numerical error of the total angular momentum δa/a0 and the total energy δe/e0 in our numerical integrationsn± 1,2,3, where δe and δa are the absolute change of the total energy and total angular momentum, respectively, ande0anda0are their initial values. the horizontal unit is gyr.

    note that different operating systems, different mathematical libraries, and different hardware architectures result in different numerical errors, through the variations in round-off error handling and numerical algorithms. in the upper panel of fig. 1, we can recognize this situation in the secular numerical error in the total angular momentum, which should be rigorously preserved up to machine-e precision.

    2.4.2 error in planetary longitudes

    since the symplectic maps preserve total energy and total angular momentum of n-body dynamical systems inherently well, the degree of their preservation may not be a good measure of the accuracy of numerical integrations, especially as a measure of the positional error of planets, i.e. the error in planetary longitudes. to estimate the numerical error in the planetary longitudes, we performed the following procedures. we compared the result of our main long-term integrations with some test integrations, which span much shorter periods but with much higher accuracy than the main integrations. for this purpose, we performed a much more accurate integration with a stepsize of 0.125 d  spanning 3 x 105 yr, starting with the same initial conditions as in the n?1 integration. we consider that this test integration provides us with a ‘pseudo-true’ solution of planetary orbital evolution. next, we compare the test integration with the main integration, n?1. for the period of 3 x 105 yr, we see a difference in mean anomalies of the earth between the two integrations of ?0.52°. 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 kino**a & nakai  where the difference is estimated as ?60°.

    3 numerical results – i. glance at the raw data

    in this section we briefly review the long-term stability of planetary orbital motion through some snapshots of raw numerical data. the orbital motion of planets indicates long-term stability in all of our numerical integrations: no orbital crossings nor close encounters between any pair of planets took place.

    3.1 general description of the stability of planetary orbits

    first, we briefly look at the general character of the long-term stability of planetary orbits. our interest here focuses particularly on the inner four terrestrial planets for which the orbital time-scales are much shorter than those of the outer five planets. as we can see clearly from the planar orbital configurations shown in figs 2 and 3, orbital positions of the terrestrial planets differ little between the initial and final part of each numerical integration, which spans several gyr. the solid lines denoting the present orbits of the planets lie almost within the swarm of dots even in the final part of integrations  and . this indicates that throughout the entire integration period the almost regular variations of planetary orbital motion remain nearly the same as they are at present.

    vertical view of the four inner planetary orbits  at the initial and final parts of the integrationsn±1. the axes units are au. the xy -plane is set to the invariant plane of solar system total angular momentum. the initial part ofn+1 . the final part ofn+1 . the initial part of n?1 . the final part ofn?1 . in each panel, a total of 23 684 points are plotted with an interval of about 2190 yr over 5.47 x 107 yr . solid lines in each panel denote the present orbits of the four terrestrial planets .

    the variation of eccentricities 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 elements does not differ significantly between the initial and final part of each integration, at least for venus, earth and mars. the elements of mercury, especially its eccentricity, seem to change to a significant extent. this is partly because the orbital time-scale of the planet is the shortest of all the planets, which leads to a more rapid orbital evolution than other planets; the




第一百日(2)囤积粪便发家致富
    唐跃坐在粪堆里,用剪刀剪开大便的真空包装,由于脱水和低温,袋中的粪便全部干燥而松脆,看上去坚硬,实际上轻轻一捣就会像沙子一样碎裂。

    他长这么大也没想过自己此生会有幸与大便亲密接触,以往唐跃都是拉完提裤冲水走人,相当无情,从来不会回头看一眼。

    唐跃把真空袋中的干燥粪便倒在铁盘子里,他甚至可以根据粪便中的食物残渣分辨出自己那天吃的是什么,许多富含粗纤维的食物在人的肠胃中得不到充分消化,会随着粪便一起排出来,唐跃有一阵子经常吃蔬菜罐头,那个时期的大便中就经常能看到未完全消化的植物纤维。

    唐跃戴着两层口罩,好在这些大便都已经干燥了很长时间,没什么气味。

    “粪便中的味道主要来自3-甲基吲哚,也就是粪臭素,这种东西如果沾在衣服上,那样你闻上去也会像一坨大便。”老猫坐在边上帮忙,它一边捣碎粪便一边碎碎念。

    唐跃觉得它更大的兴趣在于粪便本身。

    “唐跃,你看这坨翔,这里面有个长长的东西……是蛔虫吗啊不对,是未消化的纤维……”

    “唐跃,你这天吃的是不是蔬菜我看到了菜叶子残渣,这是食物浪费你知道么我觉得这些菜叶子挑出来还能吃。”

    “唐跃,你是不是肠胃功能和消化不太好呜呜呜呜呜……”

    唐跃拍了拍手,转过身来。

    他刚刚把一团卷起来的手套塞进了老猫的嘴里。

    总算消停了。

    “人畜粪便是一种非常传统的肥料,富含氮磷钾钙等元素,用来种植蔬菜非常合适,它们能给番茄提供足够的营养。”麦冬的声音在耳机响起,“唐跃,你需要把这些干燥的粪便进行复水,也就是加入水后充分搅拌,然后与取来的泥土进行混合。”

    进行复水……

    唐跃的额头上开始冒汗。

    虽然麦冬说得这么学术,但这个行为不就是……搅屎吗

    唐跃看了一眼自己手中的铁钎子,一根棍子的用途取决于它在什么人手中,如果是在哈利波特手上,那么它就是一支高大上的魔杖,如果在唐跃手上……它就只能是一根搅屎棍。

    出身决定一切。

    唐跃让老猫去把上次冷凝的水端了过来,淡水具体应该用多大的量麦冬没有说明,她只描述说“加入的水要让粪便足够软化稀释,黏稠程度介乎于稀汤和浓粥之间,应该像一锅水分稍稍过量的咖喱。”

    “接着再把粪便加在基质泥土中,就像把咖喱浇在米饭上那样。”

    这个比喻真是无敌了。

    唐跃这辈子都不想吃咖喱饭了。

    由于是初步实验性质的种植,麦冬和唐跃都不准备把所有的番茄种子全部用光,如果不慎失败,那就完蛋了。唐跃决定第一批只种十株左右的番茄,以此来验证方案的可行性,等到有了百分之百的把握,再把剩下的蔬菜种子撒下去也不迟。

    所以泥土和粪便都是按照十株番茄的用量而准备的,唐跃手中还有不少大便……在荒芜的火星上,大便确实是一种有价值的稀缺资源。

    唐跃想象着火星上如果有一个原始的农耕文明,那么大便必然是抢手货,或许有人会通过收集囤积大便来发家致富。

    老猫和唐跃一人头上套了一个头盔,如临大敌。

    老猫手里端着水槽,水槽中盛着冰水。

    唐跃手中紧握着一根铁扦子,面前摆着一个大烧杯,烧杯中是深棕色的神秘粉末与块状物。

    “准备好了么”老猫眼神坚毅。

    “准备好了。”唐跃点



第一百日(3)滑向深渊
    麦冬伸手按下面板上的按钮,电脑屏幕上弹出窗口“psychological test”。

    几秒钟后,屏幕上显示:please complete the following questions.
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