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
nns and starr syste
abstract
e resent the results of very loner nurical tegrations of ary orver 109 yr tisans cdg all ne s a quick section of our nurical data shos that the ary otion， at leastnur sile dynaical odel， sees to ver this very long tisan a closer lk at the loestfrequency osciltions g a loass filter shosntentially diffive character of terrestrial ary otion， esecially that of rcury the f the eentricity of rcurynns is qualitatively siir to the results fro jacques skar039s secur erturry eg eax～ 035never， there are no aarent secur creases of eentricity or ctionnrf the s， hich ay erter nurical tegrations e have al erford a ule of trial tegrations cdg otions of the outer five snn of ± 5 x 1010 yr the result dicates that the three ajor renances n syste have ver the 1011yr tisan
nn
nble
nf the star syste has ver several hundred years， sce the era of on the roble has attracted any fao atheaticians the years and has yed a central rolennt of nonlear dynaics and chaos theory hoever， e do not yet have a defite anser to the question of hether our r syste is stat this is artly a result of the fact that the defition of the ter ‘staue hen it is edn the ronnr syste actually it is not easy to give a clear， riro and hysically angful defition of the star syste
nf stat the hill defition gdan 1993: actually this is not a defition of staf stability e defe a syste as nurs here n fro a certa itial nfiguration chabers， etherill aaaaaa aaaaaa tanikaa 1999 a syste is defed as exeriencg a close enunter hen o ne another ith an area of the rr hill radi otherise the syste is defed as rard e state that our ary syste is dynaically stase enunter haens durg the a of our r syste， aut ±5 gyr cidentally， this defition ay nenurrence of any orssg f a air of s takes ce this is exerience that an orssg is very likely to lead to a close enunternary systes yoshaga， koku aaaaaa ako 1999 of urse this statent cannot systes ith stanances such as the une–to syste
n studies and ais of this research
nf the ncet of stability， the snr syste sho a character tyical of dynaical chaos ssan aaaaaa isdo 1988， 1992 the cae of this chaotic artly understd as nance g urray aaaaaa hon 1999 lecar， frankl aaaaaa hon 2001 hoever， it ould require tegratg an ensef ary systes cdg all ne s for a eriod verg several 10 gyr to thoroughly understand the loner evotion of ary ortic dynaical systes are characterized ng deendence on itial nditions
nf vie， any of the revio loner nurical tegrations cded only the outer five s ssan aaaaaa isdo 1988 koa aaaaaa nakai 1996 this is ruter s arennr than those of the ner four s that it is uch easier to follo the syste for a given tegration eriod at resent， the lonst nurical tegrations uurnals are those of duncan aaaaaa lissauer 1998 although their a tart as the effect of ostasequence r ass loss on the starrd any tegrations verg u to ～1011 yr of the orur jovian s the itial orbital elents and asses of s are the sa as those of our r syste duncan aaaaaa lissauer039s aer， but they decrease the ass of the sun gradually their nurical exerts this is becae they nsider the effect of ostasequence r ass loss the aer nsequently， they found that the crossg tiscale of ary orbits， hich can f the stability tiscale， is quite sensitive to the rate of ass decrease of the sun hen the ass of the sun is close to its resent vae， the jovian s rea star erhas lonr duncan aaaaaa lissauer al erford four siir exerts on the orf seven s ven to une， hich ver a san of ～109 yr their exerts on the seven s are not yet rehensive， but it sees that the terrestrial s al rea stan eriod， atag alost regur osciltions
nther hand， his aurate seianalytical secur erturry skar 1988， skar fds that r and irregur variations can aear the eentricities and ctions of the terrestrial s， esecially of rcury and ars on a tiscale of several 109 yr skar 1996 the results of skar039s secur erturuld ated rations
this aer e resent reliary results of six loner nurical tegrations on all ne ary orf several 109 yr， and of o other tegrations verg a san of ± 5 x 1010 yr the total esed ti for all tegrations is ore than 5 yr， g several dedicated cs and orkstations one of the fundantal ncsions of our loner tegrations is that r syste ary otion sees to be staf the hill stave， at leastnf ± 4 gyr actually，nur nurical tegrations the syste as far ore stable than hat is defed nly did no close enunter haen durg the tegration eriod， nrn th ti and frequency doa， though ary otions are stochastic sce the urose of this aer is to exhivervie the results of our loner nurical tegrations， e sho tyical exale figures as evidence of the very loner star syste ary otion for readers ho have ore secific and deeer terestsnur nurical results， e have reared a ee aess ， here e sho ra orass filtered results， variation of deunay elents and angur ontu deficit， and results of our sile ti–frequency analysis on all of our tegrations
nn 2 e ur dynaical odel， nurical thod and itial nditions ednns section 3 is devoted to a descrition of the quick results of the nurical tegrations very loner star syste ary otion is aarent thnns and orugh estiation of nurical errors is al given section 4 es on to a discsion of the lonstter variation of ary orass filter and cdes a discsion of angur ontu deficitnn 5， e resent a set of nurical tegrations for the outer five s that sans ± 5 x 1010 yrnn 6 e al discs the loner station and its ossible cae
nf the nurical tegrations
（本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了也不一定能成功显示。）
nd
nrder isdo–hon sylectic a as our a tegration thod isdo aaaaaa hon 1991 koa， yoshida aaaaaa nakai 1991 ith a secial startu rocedure to reduce the truncation error of angle variables，‘ar start’saha aaaaaa treae 1992， 1994
nrations is 8 d throughout all tegrations of the ne s n±1，2，3， hich is arf the nerostnr the deteration of stesize， e artly follo the revio nurical tegration of all ne s n 1988， 72 d and saha aaaaaa treae 1994， 22532 d e rounded the decial art of the their stesizes to 8 to ake the stesize a ultile of 2n reduce the auution of roundoff errornn rocessesn this， isdo aaaaaa hon 1991 erford nurical tegrations of the outer five ary or the sylectic a ith a stesize of 400 d， 11083 of the orf juiter their result sees to ugh， hich artly jtifies our thod of deterg the stesize hoever， sce the eentricity of juiter ～005 is uch saller than that of rcury ～02， e need care hen e are these tegrations silynf stesizes
nf the outer five s f±， e fixed the stesize at 400 d
n functions nther ith the thirdorder halley thod danlver for keler equations the nuns e set nd is 15， but they never reached the axiunur tegrations
nutut is 200 000 d ～547 yr for the calcutions of all ne s n±1，2，3， and aut 0 000 d ～21 903 yr for the tegration of the outer five s f±
n as done hen the nurical tegrations erencess， e alied a loass filter to the ra orbital data after e had leted all the calcutions see section 41 for ore detail
nn
nntu
nne of the f sylectic tegrators， hich nserve the hysically nservative quantities ell total orur ontu， our loner nurical tegrations see to have rd ith very sall errors the averad retive errors of total energy ～10?9 and of total angur ontu ～10?11 have reaed nearly nstant throughout the tegration eriod fig 1 the secial startu rocedure， ar start， ould have reduced the averad retive errorntal energy f agnitude or ore
retive nurical error of the total angur ontu δaa0 and the total energy δee0nur nurical tegrationsn± 1，2，3， here δe and δa are the atal energy and total angur ontu， resectively， ande0anda0are their itial vaes the horizontal unit is gyr
nte that different oeratg systes， different atheatical li
aries， and different hardare architectures result different nurical errors， through the variationsnff error handlg and nurical alrithsn 1， e can regnize this situation the secur nurical errorntal angur ontu， hich should ly reserved u to achee recision
nitudes
sce the sylectic as reserve total energy and total angur ontu of ndy dynaical systes herently ell， the degree of their reservation ay not f the auracy of nurical tegrations， esecially as a asure of the ositional error of s， ie the errornngitudes to estiate the nurical errornngitudes， e erford the follog rocedures e ared the result of our a loner tegrations ith nns， hich san uch shorter eriods her auracy than the a tegrations for this urose， e erford a uch ore aurate tegration ith a stesize of 0125 d 164 of the a tegrations sanng 3 x 105 yr， startg ith the sa itial nditions as nn e nsider that this test tegration rovides ntrue’ tion of ary orn next， e are the test tegration ith the a tegration， n?1 for the eriod of 3 x 105 yr， e see a differencenalies of the earth ns of ～052° the case of the n?1 tegration this difference can the vae ～8700°， af earth after 5 gyr， sce the error of longitudes creases learly ith ti the sylectic a siirly， the longitude error of to can be estiated as ～12° this vae for to is uch better than the resultna aaaaaa nakai 1996 here the difference is estiated as ～60°
3 nurical results – i gnce at the ra data
nts of ra nurical data the orf s dicates loner starations: no orse enunters f s tk ce
nn of the starbits
first， e eneral character of the loner starur terest here foces articurly on the ner four terrestrial s for hich the orbital tiscales are uch shorter than those of the outer five s as e can see clearly fro the nar orn nrf the terrestrial s differ little beeen the itial and fal art of each nurical tegration， hich sans several gyr the lid les denotg the resent orst ith the sar of dots evennrations b and d this dicates that throughout the entire tegration eriod the alost regur variations of ary orn rea nearly the sa as they are at resent
nur ner ary or the z axis direction at the itial and fal arts of the tegrationsn±1 the axes units are au the xy ne is set to the variant ne of r syste total angur ontua the itial art ofn+1 n 00547 x 10 9 yrfn+1 t n 49886 x 10 9 yrc the itial art of n?1 t 0 to ?00547 x 109 yrd the fal art ofn?1 n ?39727 x 10 9 yr ntal of 23 684 ots are lotted ith an terval of aver 547 x 107 yrnlid les nte the resent orur terrestrial s taken fro de245
nf eentricities and orr the ner four s the itial and fal art of the tegration n+1 is shonn 4 as exected， the character of the variation of ary ort differ significantly beeen the itial and fal art of each tegration， at least for ven， earth and ars the elents of rcury， esecially its eentricity， see to chan to a significant extent this is artly rf thenrtest of all the s， hich leads to a ore raid orther s the nerost ay stability this result aears tonreent ith skar039s 1994， 1996 exectations that r and irregur variations aear the eentricities and ctions of rcury on a tiscale of several 109 yr hoever， the effect of the ossirt fatally affect the glof the hole ary syste og to the sall ass of rcury e ill ntion rf rcury ternn 4 g loass filtered orbital elents
nruter five s sees riroly staver this tisan see al section 5
32 ti–frequency as
nter stanexistence of close enunter events， the chaotic nature of ary dynaics can chan the osciltory eriod and alitude of ary orn graduallynng tisans even such slight fctuations of orn na， articurlynf earth， can otentially have a significant effect on its surface cliate syste through r tion variation cf er 1988
nter channdicitynrrd any fast fourier transforations ffts along the ti axis， and suerosed the resultg eriodgras to dra odsional ti–frequency as the secific aroach to drag these ti–frequency as this aer is very sile – uch siler than the avelet analysis or skar039s 1990， 1993 frequency analysis
nnts of the sa lenh the lenh of each data segnt should f 2n aly the fft
nf the data has a r g art: for exale， hen the ith data tti and ends at tti+t， the next data segnt rans fro ti+δt≤ti+δt+t， here δt?t e ntue this division until e reach a certa nuber n by hich tn+t reaches the total tegration lenh
nnts， and oras
each frequency diagra ove， the strenh of eriodicity can be reced ur chart
nr the recent， and nnect all the greyscale or lour charts to one grah for each tegration the horizontal axis of these ne grahs should be the ti， ie the startg tis of each fragnt of data ti， here i 1，…， n the vertical axis reresents the eriod or frequency of the osciltion of orbital elents
nted an fft verhelg seed， sce the aount of nurical data tonnents is terrie several tens of gbytes
nf the ti–frequency a created cedures is shonnreyscale diagra as fig 5， hich shos the variation of eriodicity the eentricity and ction of earthnnn 5， the dark area shos that at the ti dicated n the adicity dicated nr thannhter area around it e can regnize fro this a that the eriodicity of the eentricity and ction of earth only chans slightly nd vered n this nearly regur trend is qualitatively the santher tegrations and for other s， although tyical frequencies differ by and elent by elent
nf orur ontu
ndic variation and exchan of ary orur ontu g filtered deunay elents l， g， h g and h are equivalent to the ary orntu and its vertical onent er unit ass l is reted to the ary ory e er unit ass as e?μ22l2 if the syste is letely lear， the ory and the angur ontu each frequency nlearity the ary syste can cae an exchan of energy and angur ontu na the alitude of the loestfrequency osciltion should crease if the syste is unstan gradually hoever， such a syto of staentnner tegrations
nntu of the four ner s and all ne s are shon for tegration n+2 the uer three anels sho the lonriodic variation of total energy denoted ase e0， total angur ontun0， and the vertical onentnf the ner four s calcuted fro the loass filtered deunay elentse0， g0， h0 denote the itial vaes of each quantity the a the itial vaes is lotted ner three anelsn0 andhh0 of the total of ne s the fctuation shonner anels is virtually entirely a result of the assive jovian s
nntu of the ner four s and all ne s， it is aarent that the alitudes of those of the ner s are uch saller than those of all ne s: the alitudes of the outer five s are uch rr than those of the ner s this does not an that the ner terrestrial ary sure stane: this is sily a result of the retive sallness of the asses of the four terrestrial s ared ith those of the outer jovian s another thg e notice is that the ner ary subsyste ay re raidly than the outer one rbital tiscales this can be seen nted asner 4nereriodic and irregur osciltions are ore aarent than nted astotal 9 actually， the fctuations thener 4 anels are to a r extent as a result of the orf the rcury hoever， e cannot neglect the ntrither terrestrial s， as e ill see nns
nhurg airs
letn dividual variations of ary orur ontu exressed ass filtered deunay elents figs 10 and 11 sho loner evotion of the orf each nntu nrations e notice thatnr aarent airsnrur ontu exchan articur， ven and earth ake a tyical airnures， they sho negative rretionsnf energy and ositive rretionsnf angur ontu the negative rretionnf ory ans that the o s for a closed dynaical systenf the orsitive rretionnf angur ontu ans that the o s are siultaneoly under certa loner erturr erturbers are juiter and saturn aln 11， e can see that ars shos a ositive rretionnntu variation to the ven–earth syste rcury exhiative rretionsnntu vers the ven–earth syste， hich sees to n caed f angur ontu the terrestrial ary subsyste
nnt hy the ven–earth air exhny exchan and a ositive rretionnntu exchan e ay ossieneral fact that there are no secur tersnr axes u to sendorder erturries cf uer aaaaaa clence 1961 aletti aaaaaa ucao 1998 this ans that the ary ory hich is directly reted to the seiajor axis a ight be uch less affected nur ontu exchan hich retes to e hence， the eentricities of ven and earth can be disturbed easily by juiter and saturn， hich resultsnsitive rretionnntu exchan on the other hand， the seiajor axes of ven and earth are less likely to vian s th the energy exchan ay nly ith the ven–earth air， hich results nnny the air
nuter jovian ary subsyste， juiter–saturn and uran–une see to ake dynaical airs hoever， the strenh of their ulg is not as strong ared ith that of the ven–earth air
nrations of outer ary orbits
nvian ary asses are uch rr than the terrestrial ary asses， e treat the jovian ary syste as an deendent ary systenf the study of its dynaical stability hence， e added a ule of trial tegrations that san ± 5 x 1010 yr， cdg only the outer five s the four jovian s s to the results exhi stauter ary systenng tisan orns fig 12， and variation of eentricities and ctions fig 13 sho this very loner stauter five snth the ti and the frequency doas although e do not sho as here， the tyical frequency of the or and the other outer s is alost nstant durg these very loner tegration eriods， hich is deonstrated the ti–frequency as on our ee
nns， the retive nurical errorntal energy as ～10?6 and that of the total angur ontu as ～10?10
nnances n syste
na aaaaaa nakai 1996 tegrated the outer five ary orver ± 55 x 109 yrnund that four ajor renances n the hole tegration eriod， and that the renances ay f the staf to the ajor four renances foundn research are as follosng descrition，λ denotes the an longitude， is the longitude of the ascendg node and ? is the longitude of erihelion sute to and une
nn renance 3:2 the critical argunt θ1 3 λ? 2 λn?? liund 180° ith an alitude of aut 80° and a liut 2 x 104 yr
nn of to θ2?? liund 90° ith a eriod of aut 38 x 106 yr the doant eriodic variations of the eentricity and ction of to are synchronized ith the lif its argunt of erihelion this is anticiated the secur erturry nstructed zai 1962
nf the node of to referred to the longitude of the node of une，θ3?n， circutes and the eriod of this circution is equal to the eriod of θ2 l hen θ3 ngitudes of ascendg nodes of une and to ， the ction of to bees axiu， the eentricity unt of erihelion bees iu， the eentricity unt of erihelion a illias aaaaaa n 1971 anticiated this tye of renance， ter nfird 1989
nunt θ4???n+ 3 ?n liund 180° ith a long eriod，～ 57 x 108 yr
nns， the renances i–iii are ell ataed， and variation of the critical argunts θ1，θ2，θ3 rea siir durg the hole tegration eriod figs 14–16never， the fourth renance iv aears to be different: the critical argunt θ4 alternates l a 1010yr tiscale fig 17 this is an terestg fact that koa aaaaaa nakai039s 1995， 1996 shorter tegrations ere not ase
nn
nf dynaical chanis atas this loner staf the ary syste? e can idiately thk of o ajor features that ay r the loner stability first， there see to erorder renances an otion and secur ng the ne s juiter and saturn are close to a 5:2 an otion renance the fao ‘great equality’， t jtnnance zone higherorder renances ay cae the chaotic nature of the ary dynaical otion，n destroy the stan ith the lifeti of the real r syste the send feature， hich e thk is ore iortant for the loner staur ary syste， is the difference dynaical distance beeen terrestrial and jovian ary su aaaaaa tanikaa 1999， 2001 hen e asure ary searations by the utual hill radii r， searations aong terrestrial s are greater than 26rh， hereas those aong jovian s are less than 14rh this difference is directly reted to the difference beeen dynaical features of terrestrial and jovian s terrestrial s have saller asses， shorter ords and ider dynaical searation they are strongly erturvian s that have rr asses， lonr ords and narroer dynaical searation jovian s are not erturther assive dies
the resent terrestrial ary syste is still never， the ide searation and utual teraction aong the terrestrial s renders the disturbance effective the degree of disturvian s is oejorder of agnitude of the eentricity of juiter， sce the disturvian s is a forced osciltion havg an alitude of oej heighteng of eentricity， for exale oej～005， is far fro sufficient to rovoke stability the terrestrial s havg such a ide searation as 26rh th e assu that the resent ide dynaical searation aong terrestrial s aaaaa 26rh is rost significant nditions for atag the staf the ary syste nur detailed analysis of the retionshi beeen dynaical distance beeen s and the star syste ary otion is no ong
nrations san the lifeti of the r syste， the nuns is far fro sufficient to fill the itial hase sace it is necessary to erfor ore and ore nurical tegrations to nfir and exaenter staur ary dynaics
n， taaaaa tanikaa， k loner tegrations and starr syste on not r astron c 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。