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： longternbsp;tegrations and stabilitypry orbitur r systebr≈ abstract we present the resultsvery longternbsp;nurical tegrationspry orbital tions over 109tispans cercurr tegrationsalitatively sirthe results fronbsp;jaces skar≈ap;ap;039;s secur perturbation theory eg035 over， there areapparent secur creasesentricityclationany orbital elentsthe pls， which yrevealedstill lonrternbsp;nurica have al perforoupletrial tegrations cls over the duration of5to systenbsp;have been taed over the an 1 troduction 11defitionthe problebr≈ the estionthe stabilitr r systenbsp;has been debated over several hundred years， sce the erroblenbsp;has attractedfa theticians over the years and has pyeentral rolethe developntnonlear dynacs and chao，do not yet havefite answerthe estionwhether our r systenbsp;is stable opartlesultthe fact that the defitionthe ternbsp;stabilityvague whenis edretionthe problenbsp;of pry tionthe r syste actuallyis not easygivlear， rigoro and physically angful defitionthe stabilitr r syste angdefitionsstability， hereadopt the hill defition gdn 1993: actually thisnoefitionstability， buefystenbsp;as bg unstable whelose enunter urs wherethe syste startg fronbsp;a certa itial nfiguration chaers， wetherill ≈ap;ap; boss 1996; ito ≈ap;ap; tanikaw;is defedexperienclose enunter when o bop;ap;ap; ak urse this statent cannotsily appliedsyste with stable orbital renances suchthe neptune–pto syste 12previo stuhis research adp;ap;ap; wisdonbsp;1988，caethis chaotic behaviournow partly understoodbeesultrenance overppg urray ≈ap;ap; holn 1edtheir strong dependenceitial nditions fronbsp;that revio longternbsp;nurical tegrations cded only the outer five pls ssn ≈ap;ap; wisdonbsp;1988; koshita ≈ap;ap; nakabecae the orbital periodsthe outer pls arech lonr than thosethe ner four pls thatiseasierfollow the systenbsp;foiven tegratio present， the lonst nurical tegrations publishedjournals are thoseduncan ≈ap;ap; lissaue theirtart was the effectry orbits， they perforp;ap;ap; lissauer≈ap;ap;039;s paper， but they decrease theof the sun graduallytheir nuricabecae they nsider the effectry orbits， which cana typical p;ap;ap; lissauer al perford four sir expertsthe orbital tionseven pls venneptune， which vepan109 yr their expertsthe seven pls are not yet≈ap;ap;nbspprehensive， butsee that the terrestrial pls al re stable durg the tegration period， tag alst regur osciltions on the other hand，his urate seanalytical secur perturbation theory skar 1988， skar fds that r and irregur variations can appearthe entricities and clationsthe terrestrial pls， especiallyrcury and arsa tiscaleseveral 109ska resultsskar≈ap;ap;039;s secur perturbation theory shouldnfird and vestigatedfully nurical tegrations this paperpresent prelary resultssix longternbsp;nurical tegrationsall ne pry orbits， verpanseveral 109 yr， ando other tegrations verpan of5sedfor all tegrationsre than 5 yr， g several decf the fundantal ncsionur longternbsp;tegrationsthat r systenbsp;pry tion seebe stableterthe hill stability ntioned above，least oveispan of，our nurical tegrations the systenbsp;was farstable than whatdefedthe hill stability criterion: not only pen durg the tegration period， but al all the pry orbital elents have been nfeda narrow region bothti and freency do， though pry tionsthe puraperto exhibit and overview the resultur longternbsp;nurical tegrations，show typical exale figuresevidencethe very longternbsp;stabilityr systenbsp;pr readers who havespecific and deeper terestur nurical results，have prepareebpa ess ， whereshow raw orbital elents， their lowpass filtered results， variationdeunay elents and angur ntunbsp;deficit， and resultur sile ti–freency analysisallour tegrations section 2briefly exp our dynacal del， nurical thod and itial ntionthe ick resultsthe nurica longternbsp;stabilityr systenbsp;pry tionapparent bothpry ;variationpry orbits owpass filter and cdeiscsionangur ntunbsp; section 5，presenurical tegrations for the outer five pls that spans5ry tion and its possible cae 2 descriptionthe 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。 23 nurical thod we utilizendorder wisdoholn sylectic ;≈ap;ap; holn 1991; koshita， yoshida ≈ap;ap; nakai 1991 witpecial startup procedurereduce the truncation errorangle variables，warnbsp;startsaha ≈ap;ap; tree 1992， 1994 the stepsize for the nurical tegrations8 d throughout all tegrationsthe ne pls n1，2，3， whichabout e，partly follow the previo nurical tegrationall ne plsssn ≈ap;ap; wisdonbsp;1988， 72 d and saha ≈ap;ap; tree 1994， 22532 drounded the decil partthe their stepsizes8ke the stepsiztiple2orderreduce the utionroundoff errorthe≈ap;ap;nbspputatio retionthis， wisdonbsp;≈ap;ap; holn 1991 perford nurical tegrationsthe outer five pry orbits g the sylectiittepsize400 d， 11083the orbital perioesult seebe urate enough， which partly jtifies our thoddeterng th， sce the entricityjupiter 005ch sller than thatrcury 02，needcare when we≈ap;ap;nbsppare these tegrations silyterstepsizes the tegrationthe outer five pls f，fixed the stepsize400 d we adopt gas≈ap;ap;039; f anunctionsthe sylectiother with the thirdorder halley thod danby 1992a lver for keple nuerxbsp;iterationssethalley≈ap;ap;039;s thod15， but they never reached the xbsp; anr tegrations the tervalthe data output200 000 d 547for the calcutionsall ne pls n1，2，3， and about 8000 000 d903for the tegrationthe outer five pls f althoughoutput filterg was done when the nurical tegrations wereprocess，applieowpass filterthe raw orbital data afterhad≈ap;ap;nbsppleted allsection 41 fordetail 24 error estition 241 retive errorstotal energy and angur ntubr≈ orropertiessylectic tegrators， which nserve the physically nservative antities well total orbital energy and angur ntu our longternbsp;nurical tegrations seenbsp;to have been perford with veryaverad retive errorstotal energy 109 andtotal angur ntunbsp;erio special startup procedure， warnbsp;start， would have reduced the averad retive errortotal energyabout one ordergnitudere retive nurical errorthe total angur ntunbsp;δaa0 and the total energy δee0our nurical tegrationsn 1，2，3， whereandare the abte chanthe total energy and total angur ntu respectively， ande0anda0are their itia horizontal unitgyr note that eratg syste， per panel o，can regnize this situationthe secur nurical errorthe total angur ntu which shouldrigoroly preservedto chee precision ry longitudes sce the sylecticpreserve total energy and total angur ntunbsp;of nbody dynacal syste herently well， the degreetheir preservatioota good asurethe uracynurical tegrations， especiallya asurethe ls， ie the errorpr estite the nurical errorthe pry longitudes，perford the follo≈ap;ap;nbsppared the resultourlongternbsp;tegrations withtest tegrations， which spanshorter periods but withhigher uracy than thhis purerford are urate tegration with ad 164thetegrations spanng 3105 yr， startg with theitial np;ap;ap;nbsppare the test tegration with thetegration， n1 for the period3105 yr，seifferencean anoliesthe earth beeen the othe casethifference canextra sirly， the longitude errorpto canestited12 this vae for ptoch better than the resultkoshita ≈ap;ap; nakai 1996 where the ited60 3 nurical results – i gncethe raw data this sectionbriefly review the longternbsp;stabilitypry orbital tion throughsnapshotsraw nurica orbital tionpls ;stabilityallour nurical tegrations:orbital crossgs nor close enunters beeen any pairpls took pce 31 neral descriptionthe stabilitypry orbits first，briefly lookthe neral characterthe longternbsp;stabilitypr terest here foces particurlythe ner four terrestrial pls for which the orbital tiscales areshorter than thosethe outer fivcan see clearly fronbsp;the pnar orbital nfigurations shownfigs 2 and 3， orbital ls arteach nurical tegration， which spans severa lid les denotg the present orbitsthe pls lie alst with the swarnbsp;of dots eventhe fal parttegrationnd d this eriod the alst regur variationspry orbital tion re nearly theas they arepresent vertical viewthe four ner pry orbits fronbsp;thxis artsth axes units are au thepnesetthe variant pner systenbsp;total angur ntua the itial part9 yrb the fal part84988610 9 yrc the itial partn1 t 000547109 yrd the fal part ofn1t 3918010 ots are plotted withtervabout 2190over 547107 lid leseach panel denote the present orbitsthe four terrestrial pls taken fronbsp;de245 the variationentricities and orbital clations for the ner four plsthe itial and fal partthe tegrationis showxpected， the characterthe variationpry orbital elents does not ercury， especially its entricity， seenbsp;to chana significanpartly becae the orbital tiscaletheis the shortestall the pls， which leadsarapid orbital evotion than other pls; the nerstynearesesult appearsbe agreent with skar≈ap;ap;039;s 1994， 1996 expectations that r and irregur variations appearthe entricities and clationsrcurya tiscaleseveral 109 yr however， the effectthe ry systenbsp;ogthe sllo will ntion briefly the longternbsp;orbital evotionrcury tersection 4 g lowpass filtered orbital elents the orbital tionthe outer five pls see rigoroly stable and ite regur over this tispan see al section 5 32 ti–freency ps although the pry tion exhibits very longternbsp;stability defedthe nonexistenceclose enunter events， the chaotic naturepry dynacs can chan the osciltory period and alitudepry orbital tion gradually over such lon such slight fctuationrbital variationthe freency do， particurlythe caseearth， can ;through r tion variation cf berr 1988 to giveoverviewthe longternbsp;chanperiop;ap;ap;039;s 1990， 1993 freency analysis ass filtered orbital data tofragntsthengtheach data segnt shoulda ltiple2orderapply the fft each fragntthe data haar overppg part: for exale， when the ith data begs fronbsp;tti and endsttit， the next data segnt rans fronbsp;tiδttiδtt， where δttntue this ilreacerta nuer nwhich tnt reaches the total tegration length we applyffteachthe data fragnts， and obtaireency diagra each freency ;obtaed above， the strengthperioceda greyscalelour chart we perfornbsp;the repcent， and nnect all the greyscalelour charts to one graph for eac horizontal axisthese new graphs shouldthe ti， ie the startg tiseach fragntdata ti， where i 1，…， n the vertical axis represents the periodfreencythe osciltionorbital elents we have adoptedfft becaeits overwhelng speed， sce the auntnurical databe d;ap;ap;nbspsterribly hu several tensgbytes a typical exalethe ti–freencreatedthe above proceduresshowna greyscale ;a， which shows the variationperioerio;thihat the perioeriod veredthearly regur trendalitatively the other tegrations and for other pls， although typical freencies elent 42 longternbsp;exchanorbital energy and angur ntubr≈ we calcute very longperiop;ap;ap;nbsper unit ss lretedthe pry orbital enerr unita the systenbsp;is≈ap;ap;nbsppletely lear， the orbital energy and the angur ntunbsp; each freency bbthe pry systenbsp;can caeexchanenergy and angur ntunbsp; the freenc alitudethe lowestfreency osciltion should creasethe systenbsp;is unstable and breaks dow， sucytonbsp;of stabilitynot pronentour longternbsp;tegrations i， the total orbital energy and angur ntunbsp;of the four ner pls and all ne pls are shown for tegration n2 the upper three panels show the longperiop;ap;ap;nbspls calcuted fronbsp;the lowpass filtered deuna， g0，denote the itial vaeseac abte ;the itial vaesplottedth lower three panelseach figure showee0，gg0 andhh0the totaln fctuation shownthe lower panelsvirtually entirelesultthe ssive jovian pls arg the variationsenergy and angur ntunbsp;of the ner four pls and all ne pls，is apparent that the alitudesthosethe ner pls aresller than thoseall ne pls: the alitudesthe outer five pls arerr than thosethe ne does notthat the ner terrestrial pry subsystenbsp;isstable than the outer one: thissilesultthe retive sllnessthe ssesthe four terrestrial pls≈ap;ap;nbsppared with thosethe outer jovia thgnoticethat the ner pry subsystenbsp;stablerapidly than the outer one becaeits shorter orbita canseenthe panels denoted asner 4 i the lonrperioparent thanthe panels denoted astotal 9 actually， the fctuationsthener 4 panels area r extenta resultthe orbital variationth，cannot neglect the ntribution fronbsp;other terrestrial pls，we will seesubseent sections 44 longternbsp;uplgseveral neighbourgpairs letseears showositive rretionthe angur ntunbsp;variationthe ven–earth syste rcury exhibits certa negative rretionsthe angur ntunbsp;vers the ven–earth syste which seebeaction caedthe nservationangur ntunbsp; the terrestrial pry subsyste itnot clearthewhy the ven–earth pair exhibitegative rretionenergy exchan anositive rretionangur ntunbsp; y this through observg the neral fact that there aresecur terpry sejor axesto sendorder perturbation theories cf brouwer ≈ap;ap; clence 1961; baletti ≈ap;ap; puc ans that the pry orbital energy whicherturbg pls thanthe angur ntunbsp;exchan which retese hence， the entricitiesven and earth caniter and saturn， which resultsa ; the other hand， the sejor axesven and earth are less likelybe air， which resultsa negative rretionthe exchanorbital energythe pair as for the outer jovian pry subsyste jupiter–saturn and uran–neptune seenbsp;todynaca， the strengththeir uplgnotstrong≈ap;ap;nbsppared with thatthe ven–earth pair 55ry orbits sce the jovian pry sses arerr than the terrestrial pry sses，treat the jovian pry systenbsp;asdependent pry systenbsp; terthe studyits dynaca，addeoupletrial tegrations that span5ls p results exhibit the rigoro stabilitythe outer pry systenbsp;over this lon nfiguration， and variationentricities and clation show this very longternbsp;stabilitythe outer five plsboth theand the freencdo not showhere， the typical freencythe orbital osciltionpto and the other outer plsalst nstant durg these very longternbsp;tegration periods， whichdenstratedthe ti–freencyon our webpa these o tegrations， the retive nurical errorthe total energy was 106 and thatthe total angur ntunbsp;was 1010 51 renancesthe neptune–pto systebr≈ koshita ≈ap;ap; nakai 1996 tegrated the outer five pry orbitsthey found that four jor renances beeen neptune and pto are taed durg the whole tegration period， and that the renances ythecaesthe stabilitythe orbior four renances foundprevio research arhe follog description，λ denotes thelongitude，the longitudethe ascento and neptune an tion renance beeen neptune and pto 3:2 the critical argunt32 λnp librates around 180 withalitudeaboutanibration periodabout 2104 yr the arguntperihelionpto pθ2pp librates aroundwiteriodabout 38106 yr the donant perioto are synchronized with the librationits argunt oanticipatedthe secur perturbation theory nstructedkozai 1962 the longitudethe nodepto referredthe longitudethe nodeneptune，θ3pn， circutes and the periodthis circutionealthe periodθbes zero， ie the longitudesascenp;ap;ap; benn 1971 anticipated this typerenance， ter nfirdini， nobili ≈ap;ap; carpo 1989 an argunt θ4pn 3librates around 180 witong period， 57108 yr our nurical tegrations， the renances i–iii are well taed， and variationthe critical argunts θ1，θ2，θ3 re sir durg the whole tegration period figs 14–16 however， the fourth renanceappearsbe p;ap;ap; nakai≈ap;ap;039;s 1995， 1996 shorter tegrations were not abledisclose 6 ssion what kddynacal chanisnbsp;tas this longternbsp;stabilitythe pry systenbsp;we can iep;ap;ap; tanikawa 1ry separationsthe tual hill raarations ang terrestrial pls are greater than 26rh， whereas those ang jovian pls are less tha ls have sller sses， shorter orbital periods and wider dynaca are strongly perturbedjovian pls that have rr sses， lonr orbital periods and narrower dynaca pls are not perturbedany other ssive bodies the present terrestrial pry systenbsp;is still beg p; 26rhprobably ohesignificant nry systenbsp;over a 109y detailed analysisthe retionship beeen dynacal ls and the stability tiscaler systenbsp;pry tionnow ongog although our nurical tegrations span the lifetithe r syste the nuertegrationsfar fronbsp;sufficientfill the itial phasnecessaryperfornbsp;re andnurical tegrationsnfirnbsp;and exanedetail the longternbsp;stabilitr pry dynacs 以上文段引自 ito， t≈ap;ap; tanikawa， k longternbsp;tegrations and stabilitypry orbitur r syst， 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。