作者君在作品相关中其实已经解释过这个问题。「请记住邮箱：ltxsba@gmail.com 无法打开网站可发任意内容找回最新地址」

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;tegrtons nd stbltyry orbtsour sr systebr>

bstrct

we present the resultsvery longternbsp;nurcl tegrtonsry orbtl tons over 109tspns cludg ll n spectonour nurcl dt shows tht the ry ton，lestour sle dyncl del， seebe qute stble even over ths very lon lookthe lowestfrequency osctons usowpss flter showsthe potentlly dffusve chrcterterrestrl ry ton， especlly thehvourthe entrctyrcurr tegrtonsqulttvely srthe results fronbsp;jcquesskr&039;s secr perturbton theory e.g.0.35 over， there repprent secr cresesentrctytonny orbtl elentsthe pls， whch yreveledstll lonrternbsp;nurc hve lso perforoupletrl tegrtons cludg tonsthe outer fve pls over the durton of51010 yr. the result dctes tht the three jor resonncesthe neptune–pluto systenbsp;hve been ted over the 1011yr tspn.

1 troducton

1.1deftonthe problebr>

the questonthe stbltr sr systenbsp;hs been debted over severl hundred yers， sce the erroblenbsp;hs ttrctedfus thetcns over the yers nd hs yeentrl rolethe developntnonler dyncs nd cho，do not yet hvefte nswerthe questonwhether our sr systenbsp;s stble oprtlesultthe fct tht the deftonthe ternbsp;stbltyvgue whens usedrtonthe problenbsp;of ry tonthe sr syste ctullys not esygvler， rgorous nd physclly ngful deftonthe stbltr sr syste

ngdeftonsstblty， heredopt the hll defton dn 1993: ctully thsnoeftonstblty， buefystenbsp;s bg unstble whelose encounter urs sowherethe syste strtg fronbsp; cert tl confgurton chers， wetherll & boss 1996; to & tnkw;s defedexperenclose encounter when two bodes pproch one nother wthretherr hl the systenbsp;s defedbestte tht our ry systenbsp;s dynclly stbleno close encounter hppens durg the our sr syste bout ， ths defton yrecedonewhchurrenceny orbtl crossg between ether prpls tkebecuseknow fronbsp;experence thtorbtl crossgvery lkelyled close encounterry nd pry syste yoshg， kokubo & mk course ths sttent cnnotsly ppledsyste wth stble orbtl resonnces suchthe neptune–pluto syste

1.2prevous studes ndof ths reserch

ddtonthe vguenessthe conceptstblty， the plsour sr systenbsp;shohrcter typcldyncl chos sussn & wsdonbsp;1988， cuseths chotc behvournow prtly understoodbeesultresonnce oveppg murry & holn 1999; lecr， frnkl & hol，would requre tegrtg overenselery syste cludg ll ne pls foerod coverg severlgyrthoroughly understnd the longternbsp;evolutonry orbts， sce chotc dyncl syste re chrcterzedther strong dependencetl condtons.

fronbsp;tht potvew，of the prevous longternbsp;nurcl tegrtons cluded only the outer fve pls sussn & wsdonbsp;1988; kosht & nkbecuse the orbtl perodsthe outer pls rech lonr thn thosethe ner four pls thtseserfollow the systenbsp;foven tegrto present， the lonst nurcl tegrtons publshedjournls re thoseduncn & lssue thertrt ws the effectpostsequence srlossthe stbltyry orbts， they perfordtegrtons covergto 1011of the orbtl tonsthe four jov tl orbtl elents nd ssespls re thes thoseour sr systenbsp; duncn & lssuer&039;s pper， but they decrese theof the sun grdullyther nurcbecuse they consder the effectpostsequence srlossth， they found tht the crossg tsclery orbts， whch cn typcl dctorthe stblty tscle，qute senstvethe rtess decreseth theof the sunclosets present vlue， the jovn pls re stble over 1010 yr，perhp & lssuer lso perford four sr expertsthe orbtl tonseven pls venusneptune， whch covepn109 yr. ther expertsthe seven pls re not yet&nbspprehensve， butsee tht the terrestrl pls lso re stble durg the tegrton perod， tg lst regr osctons.

on the other hnd，hs urte senlytcl secr perturbton theoryskr 1988，skr fds thtr nd rregr vrtons cn pperthe entrctes nd tonsthe terrestrl pls， especllyrcury nd mrs tscleseverl 10sk resultskr&039;s secr perturbton theory shouldconfrd nd vestgtedfully nurcl tegrtons.

ths pperpresent prry resultssx longternbsp;nurcl tegrtonsll ne ry orbts， coverpnseverl 109 yr， ndtwo other tegrtons coverpn of51010 yr. the totl psedfor ll tegrtonsre thn 5 yr， usg severl dedcted pcsof the fundntl conclusonsour longternbsp;tegrtonstht sr systenbsp;ry ton seebe stbleterthe hll stblty ntoned bove，lest ovespn of，our nurcl tegrtons the systenbsp;ws frstble thn whtdefedthe hll stblty crteron: not only ddclose encounter hppen durg the tegrton perod， but lso ll the ry orbtl elents hve been confed nrrow regon botht nd frequency do， though ry tonsthe purposeths pperto exhbt nd overvew the resultsour longternbsp;nurcl tegrtons，show typcl exle fguresevdencethe very longternbsp;stbltysr systenbsp;r reders who hvespecfc nd deeper terestsour nurcl results，hve prepreebp ess ， whereshow rw orbtl elents， ther lowpss fltered results， vrtonduny elents nd ngr ntunbsp;defct， nd resultsour sle t–frequency nlyssllour tegrtons.

secton 2brefly ex our dyncl del， nurcl thod nd tl condtons usedou 3devoted descrptonthe quck resultsthe nurc longternbsp;stbltysr systenbsp;ry tonpprent bothry postons nd orbt esttonnurcl errorsls 4 goestscussonthe lonstternbsp;vrtonry orbts usowpss flter nd cludescussonngr ntunbsp; secton 5，presenurcl tegrtons for the outer fve pls tht spns51010 yr.secton 6lso dscuss the longternbsp;stbltythe ry ton nd ts possble cuse.

2 descrptonthe nurcl tegrtons

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。

2.3 nurcl thod

we utlzecondorder wsdoholn sylectc pourtegrton thod wsdonbsp;& holn 1991; kosht， yoshd & nk 1991 wtpecl strtup procedurereduce the truncton errorngle vrbles，wrnbsp;strtsh & tree 1992， 1994.

the stepsze for the nurcl tegrtons8 d throughout ll tegrtonsthe ne pls n1，2，3， whchbout 111the orbtl perodthe nersor the deterntonstepsze，prtly follow the prevous nurcl tegrtonll ne plssussn & wsdonbsp;1988， 7.2 d nd sh & tree 1994， 22532 d.rounded the decl prtthe ther stepszes8ke the stepsztple2orderreduce the tonroundoff errorthe&nbspputto rtonths， wsdonbsp;& holn 1991 perford nurcl tegrtonsthe outer fve ry orbts usg the sylectttepsze400 d， 110.83the orbtl peroesult seebe urte enough， whch prtly justfes our thoddeterng th， sce the entrctyjupter 0.05ch sller thn thtrcury 0.2，needcre when we&nbsppre these tegrtons slyterstepszes.

the tegrtonthe outer fve pls f，fxed the stepsze400 d.

we dopt guss&039; f nunctonsthe sylectother wth the thrdorder hlley thod dnby 1992 solver for keple nuerxbsp;tertonssethlley&039;s thod15， but they never reched the xbsp; nr tegrtons.

the tervlthe dt output200 000 d 547for the clctonsll ne pls n1，2，3， nd bout 8000 000 d903for the tegrtonthe outer fve pls f.

lthoughoutput flterg ws done when the nurcl tegrtons wereprocess，ppleowpss flterthe rw orbtl dt fterhd&nbsppleted llsecton 4.1 fordetl.

2.4 error estton

2.4.1 rtve errorstotl energy nd ngr ntubr>

ordgohe bsc propertessylectc tegrtors， whch conserve the physclly conservtve qunttes well totl orbtl energy nd ngr ntu our longternbsp;nurcl tegrtons seenbsp;to hve been perford wth veryverd rtve errorstotl energy 109 ndtotl ngr ntunbsp;1011 hve reed nerly constnt throughout the tegrton pero specl strtup procedure， wrnbsp;strt， would hve reduced the verd rtve errortotl energybout one ordergntudere.

rtve nurcl errorthe totl ngr ntunbsp;δ0 nd the totl energy δee0our nurcl tegrtonsn 1，2，3， wherendre the bsolute chnthe totl energy nd totl ngr ntu respectvely， nde0nd0re ther t horzontl untgyr.

note tht dfferent opertg syste， dfferent thetcl lbrres， nd dfferent hrdwre rchtectures resultdfferent nurcl errors， through the vrtonsroundoff error hndlg nd nurc the upper pnel o，cn recognze ths stutonthe secr nurcl errorthe totl ngr ntu whch shouldrgorously preservedto chee precson.

2.4.2 errorry longtudes

sce the sylectcpreserve totl energy nd totl ngr ntunbsp;of nbody dyncl syste herently well， the degreether preservtoot good surethe urcynurcl tegrtons， especlly surethe postonl errorpls， .e. the errorr estte the nurcl errorthe ry longtudes，perford the follow&nbsppred the resultourlongternbsp;tegrtons wthtest tegrtons， whch spnshorter perods but wthhgher urcy thn thhs purpose，perford re urte tegrton wth d 164thetegrtons spnng 3105 yr， strtg wth thetl condtons thonsder tht ths test tegrton provdeswtseudotrue solutonry orbt， we&nbsppre the test tegrton wth thetegrton， n1. for the perod3105 yr，sefferencen nolesthe erth between the two the csethfference cnextrptedthe vlue 8700， boutrottonserth fter 5 gyr， sce the errorlongtudes creses lerly wth the sylectc p. srly， the longtude errorpluto cnestted12. ths vlue for plutoch better thn the resultkosht & nk 1996 where the dfferenceestted60.

3 nurcl results – . ncethe rw dt

ths sectonbrefly revew the longternbsp;stbltyry orbtl ton throughsnpshotsrw nurc orbtl tonpls dctes longternbsp;stbltyllour nurcl tegrtons:orbtl crossgs nor close encounters between ny prpls took ce.

3.1 nerl descrptonthe stbltyry orbts

frst，brefly lookthe nerl chrcterthe longternbsp;stbltyr terest here focuses prtcrlythe ner four terrestrl pls for whch the orbtl tscles reshorter thn thosethe outer fvcn see clerly fronbsp;the nr orbtl confgurtons shownfgs 2 nd 3， orbtl postonsthe terrestrl pls dffer lttle between the tl nd fl prtech nurcl tegrton， whch spns sever sold les denotg the present orbtsthe pls le lst wth the swrnbsp;of dots eventhe fl prttegrtonnd d. ths dctes tht throughout the entre tegrton perod the lst regr vrtonsry orbtl ton re nerly thes they represent.

vertcl vewthe four ner ry orbts fronbsp;thxs drectonthe tl nd fl prtsth xes unts re u. thenesetthe vrnt nesr systenbsp;totl ngr ntu the tl prt 9 yr.b the fl prt 84.988610 9 yr.c the tl prtn1 t 00.0547109 yr.d the fl prt ofn1t 3.918010 93.972710 9 yr.ech pnel， totl23 684 pots re plotted wthtervbout 2190over 5.47107. sold lesech pnel denote the present orbtsthe four terrestrl pls tken fronbsp;de245.