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龙腾小说吧 -> 玄幻魔法 -> 死在火星上 对火星轨道变化问题的最后解释
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- 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 prehensve， 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 putto 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 pre 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 pleted 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 pred 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 pre 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.
the vrtonentrctes nd orbtl tons for the ner four plsthe tl nd fl prtthe tegrtons showxpected， the chrcterthe vrtonry orbtl elents does not dffer sgnfcntly between the tl nd fl prtech tegrton，lest for venus， erthelentsrcury， especlly ts entrcty， seenbsp;to chn sgnfcnprtly becuse the orbtl tsclethes the shortestll the pls， whch ledsrpd orbtl evoluton thn other pls; the nerstyneresesult ppersbeso greent wthskr&039;s 1994， 1996 expecttons thtr nd rregr vrtons pperthe entrctes nd tonsrcury tscleseverl 109 yr. however， the effectthe possble stbltythe orbtrcurot ftlly ffect the globl stbltythe whole ry systenbsp;owgthe sllo wll nton brefly the longternbsp;orbtl evolutonrcurytersecton 4 usg lowpss fltered orbtl elents.
the orbtl tonthe outer fve pls see rgorously stble nd qute regr over ths tspn see lso secton 5.
3.2 t–frequency ps
lthough the ry ton exhbts very longternbsp;stblty defedthe nonexstenceclose encounter events， the chotc nturery dyncs cn chn the osctory perod nd ltudery orbtl ton grdully over such lon such slght fluctutonsorbtl vrtonthe frequency do， prtcrlythe cseerth， cn potentlly hvgnfcnt effectts surfce clte systenbsp;through sr ston vrton cf. berr 1988.
to gveovervewthe longternbsp;chnperodctyry orbtl ton，perfordfst fourer trnsfortons ffts long thexs， nd superposed the resultg perodgrdrw twodsonl t–frequency ps. the specfc pprochdrwg these t–frequency ths ppervery sle –sler thn the wvelet nlysskr&039;s 1990， 1993 frequency nlyss.
dvde the lowpss fltered orbtl dt tofrgntsthengthech dt segnt should ltple2orderpply the fft.
ech frgntthe dt hr oveppg prt: for exle， when the th dt begs fronbsp;tt nd endsttt， the next dt segnt rns fronbsp;tδttδtt， where δtt.contue ths dvson untlrecert nuer nwhch tnt reches the totl tegrton length.
we pplyfftechthe dt frgnts， nd obtrequency dgr.
ech frequency dgrnbsp;obted bove， the strengthperodcty cnreced greysclecolour chrt.
we perfornbsp;the recent， nd connect ll the greysclecolour chrts to one grph for ec horzontl xsthese new grphs shouldthe t， .e. the strtg tsech frgntdt t， where 1，…， n. the vertcl xs represents the perodfrequencythe osctonorbtl elents.
we hve doptedfft becusets overwhelng speed， sce the untnurcl dtbe dposed to frequency ponentsterrbly hu severl tensgbytes.
typcl exlethe t–frequencretedthe bove proceduresshown greyscle dgrnbsp;， whch shows the vrtonperodctythe entrcty nd tonerthn fg. 5， the drk re shows thtthedctedthe vluethe bscss， the perodcty dctedthe ordtestronr thnthe lghter re round t.cn recognze fronbsp;thht the perodctythe entrcty nd tonerth only chns slghtly over the entre perod coveredtherly regr trendqulttvely the other tegrtons nd for other pls， lthough typcl frequences dfferbynd elentelent.
4.2 longternbsp;exchnorbtl energy nd ngr ntubr>
we clcte very longperodc vrton nd exchnry orbtl energy nd ngr ntunbsp;usg fltered duny elents l， g， h. g nre equvlentthe ry orbtl ngr ntunbsp;nd ts vertcl ponent per unt ss. lrtedthe ry orbtl enerr unt the systenbsp;s pletely ler， the orbtl energy nd the ngr ntunbsp; ech frequency bbthe ry systenbsp;cn cuseexchnenergy nd ngr ntunbsp; the frequenc ltudethe lowestfrequency oscton should cresethe systenbsp;s unstble nd breks dow， sucytonbsp;of stbltynot pronentour longternbsp;tegrtons.
， the totl orbtl energy nd ngr ntunbsp;of the four ner pls nd ll ne pls re shown for tegrton n2. the upper three pnels show the longperodc vrtontotl energy denoted se e0， totl ngr ntunbsp; g g0， nd the vertcl ponenthof the ner four pls clcted fronbsp;the lowpss fltered dun， g0，denote the tl vluesec bsolute dfference fronbsp;the tl vluesplottedth lower three pnelsech fgure showee0，gg0 ndhh0the totln fluctuton shownthe lower pnelsvrtully entrelesultthe ssve jovn pls.
corg the vrtonsenergy nd ngr ntunbsp;of the ner four pls nd ll ne pls，s pprent tht the ltudesthosethe ner pls resller thn thosell ne pls: the ltudesthe outer fve pls rrr thn thosethe ne does nottht the ner terrestrl ry subsystenbsp;sstble thn the outer one: thsslesultthe rtve sllnessthe ssesthe four terrestrl pls pred wth thosethe outer jov thgnotcetht the ner ry subsystenbsp;yunstblerpdly thn the outer one becusets shorter orbt cnseenthe pnels denoted sner 4 the lonrperodc nd rregr osctons repprent thnthe pnels denoted stotl 9. ctully， the fluctutonsthener 4 pnels rer extent resultthe orbtl vrtonth，cnnot neglect the contrbuton fronbsp;other terrestrl pls，we wll seesubsequent sectons.
4.4 longternbsp;couplgseverl neghbourgprs
letseedvdul vrtonsry orbtl energy nd ngr ntunbsp;expressedthe lowpss fltered dunndshow longternbsp;evolutonthe orbtl energyechnd the ngr ntunbsp;notce thtpls fornbsp;pprent prsterorbtl energy nd ngr ntunbsp; prtcr， venus nd erth typc the fgures， they show negtve corrtonsexchnenergy nd postve corrtonsexchnngr ntu the negtve corrtonexchnorbtl energy ns tht the two pls fornbsp; closed dyncl systenbsp; terthe orbt postve corrtonexchnngr ntunbsp;ns tht the two pls re sltneously under cert longternbsp; for perturbers re jupter，cn see tht mrs showostve corrtonthe ngr ntunbsp;vrtonthe venus–erth syste rcury exhbts cert negtve corrtonsthe ngr ntunbsp;versus the venus–erth syste whch seebecton cusedthe conservtonngr ntunbsp; the terrestrl ry subsyste
tnot clerthewhy the venus–erth pr exhbtegtve corrtonenergy exchn nostve corrtonngr ntunbsp; y possbly ex ths through observg the nerl fct tht there resecr terry sejor xesto secondorder perturbton theores cf. brouwer & clence 1961; blett & puc ns tht the ry orbtl energy whchdrectly rtedthe sejor xhtch less ffectedperturbg pls thnthe ngr ntunbsp;exchn whch rtese. hence， the entrctesvenus nd erth cndsturbed eslyjupter nd sturn， whch results postve corrtonthe ngr ntunbsp; the other hnd， the sejor xesvenus nd erth re less lkelybe dsturbedthe jov the energy exchn ylted only wth the venus–erth pr， whch results negtve corrtonthe exchnorbtl energythe pr.
s for the outer jovn ry subsyste jupter–sturn nd urnus–neptune seenbsp;todync， the strengthther couplgnotstrong pred wth thtthe venus–erth pr.
551010yr tegrtonsouter ry orbts
sce the jovn ry sses rrr thn the terrestrl ry sses，tret the jovn ry systenbsp;sdependent ry systenbsp; terthe studyts dync，ddeoupletrl tegrtons tht spn51010 yr， cludg only the outer fve pls the four jovn pls plu results exhbt the rgorous stbltythe outer ry systenbsp;over ths lon confgurton， nd vrtonentrctes nd ton show ths very longternbsp;stbltythe outer fve plsboth thend the frequencdo not showhere， the typcl frequencythe orbtl osctonpluto nd the other outer plslst constnt durg these very longternbsp;tegrton perods， whchdenstrtedthe t–frequencyon our webp.
these two tegrtons， the rtve nurcl errorthe totl energy ws 106 nd thtthe totl ngr ntunbsp;ws 1010.
5.1 resonncesthe neptune–pluto systebr>
kosht & nk 1996 tegrted the outer fve ry orbts they found tht four jor resonnces between neptune nd pluto re ted durg the whole tegrton perod， nd tht the resonnces ythecusesthe stbltythe orbor four resonnces foundprevous reserch rhe followg descrpton，λ denotes thelongtude，the longtudethe scendg node nds the longtud nenote pluto nd neptune.
n ton resonnce between neptune nd pluto 3:2. the crtcl rgunt32 λnp lbrtes round 180 wthltudeboutnbrton perodbout 2104 yr.
the rguntperhelonpluto pθ2pp lbrtes roundwterodbout 3.8106 yr. the donnt perodc vrtonsthe entrcty nd tonpluto re synchronzed wth the lbrtonts rgunt ontcptedthe secr perturbton theory constructedkoz 1962.
the longtudethe nodepluto referredthe longtudethe nodeneptune，θ3pn， crctes nd the perodths crctonequlthe perodθbes zero， .e. the longtudesscendg nodesneptune nd pluto ovep， the tonpluto besthe entrcty bes nbsp;nd the rguntperhelon bes 90. whenbes 180， the tonpluto besthe entrcty bes xbsp;nd the rguntperhelon bes 9 & benson 1971 ntcpted ths typeresonnce，ter confrdmn， nobl & crpo 1989.
n rgunt θ4pn 3lbrtes round 180 wtong perod， 5.7108 yr.
our nurcl tegrtons， the resonnces – re well ted， nd vrtonthe crtcl rgunts θ1，θ2，θ3 re sr durg the whole tegrton perod fgs 14–16 . however， the fourth resonnceppersbe dfferent: the crtcl rguntlterntes lbrton nd crcton over 1010yr tscn terestg fct tht kosht & nk&039;s 1995， 1996 shorter tegrtons were not bledsclose.
6 dscusson
wht kddyncl chnsnbsp;ts ths longternbsp;stbltythe ry systenbsp;we cn edtely thktwo jor fetures tht yresponsble for the longternbsp;， there seenbsp;tono sgnfcnt lowerorder resonnceston nd secr between ny pr ng the n nd sturn re close 5:2ton resonnce the fus gret equlty， but not justthe resonnc resonnceuse the chotc nturethe ry dyncl ton， but they re notstrongto destroy the stble ry ton wth the tthe rel sr syste the second feture， whchthkre ortnt for the longternbsp;stbltr ry systethe dfferencedyncl dstnce between terrestrl nd jovn ry subsyste to & tnkw 1999， sure ry seprtonsthe tul hll rd r， seprtons ng terrestrl pls re greter thn 26rh， wheres those ng jovn pls re less th dfferencedrectly rtedthe dfference between dyncl feturesterrestrl nd jov pls hve sller sses， shorter orbtl perods nd wder dync re strongly perturbedjovn pls tht hverr sses， lonr orbtl perods nd nrrower dync pls re not perturbedny other ssve bodes.
the present terrestrl ry systenbsp;s stll beg dsturbedthe ssve jov， the wde seprton nd tul tercton ng the terrestrl pls renders the dsturbnce effectve; the degreedsturbncejovn plsoejordergntudethe entrctyjupter， sce the dsturbnce cusedjovn pls forced oscton hvgltude oentrcty， for exl，fr fronbsp;suffcentprovoke stbltythe terrestrl pls hvg sucde seprton ssu tht the present wde dyncl seprton ng terrestrl pls > 26rhprobbly ohesgnfcnt condtons for tg the stbltythe ry systenbsp;over 109y detled nlyssthe rtonshp between dyncl dstnce between pls nd the stblty tsclesr systenbsp;ry tonnow ongog.
lthough our nurcl tegrtons spn the tthe sr syste the nuertegrtonsfr fronbsp;suffcentfll the tl phsnecessryperfornbsp;re ndnurcl tegrtonsconfrnbsp;nd exnedetl the longternbsp;stbltr ry dyncs.
以上文段引自 to， t.& tnkw， k. longternbsp;tegrtons nd stbltyry orbtsour sr 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nture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。 - 没看完？将本书加入收藏我是会员，将本章节放入书签复制本书地址，推荐给好友获取积分章节错误？点此举报
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