作者君在作品相關中其實已經解釋過這個問題。
不過仍然有人質疑——“你得太含糊了”,“火星軌道的變化比你想象要大得多!”
那好吧,既然作者君的簡單解釋不夠有力,那咱們就看看嚴肅的東西,反正這本書寫到現在,嚷嚷著本書BUG一大堆,用初高中物理在書中挑刺的人也不少。
以下是文章內容:
Lng-er inegrains and sabiliy f planeary rbis in ur Slar syse
Absra
e presen he resuls f very lng-er nuerial inegrains f planeary rbial ins ver 109 -yr ie-spans inluding all nine planes. A quik inspein f ur nuerial daa shs ha he planeary in, a leas in ur siple dynaial del, sees be quie sable even ver his very lng ie-span. A lser lk a he les-frequeny sillains using a l-pass filer shs us he penially diffusive haraer f erresrial planeary in, espeially ha f erury. he behaviur f he eenriiy f erury in ur inegrains is qualiaively siilar he resuls fr Jaques Laskar's seular perurbain hery (e.g. ea~ yr). Hever, here are n apparen seular inreases f eenriiy r inlinain in any rbial eleens f he planes, hih ay be revealed by sill lnger-er nuerial inegrains. e have als perfred a uple f rial inegrains inluding ins f he uer five planes ver he durain f ± 5 × 1010 yr. he resul indiaes ha he hree ajr resnanes in he Nepune–Plu syse have been ainained ver he 1011-yr ie-span.
1 Inrduin
1.1Definiin f he prble
he quesin f he sabiliy f ur Slar syse has been debaed ver several hundred years, sine he era f Nen. he prble has araed any faus aheaiians ver he years and has played a enral rle in he develpen f nn-linear dynais and has hery. Hever, e d n ye have a definie anser he quesin f heher ur Slar syse is sable r n. his is parly a resul f he fa ha he definiin f he er ‘sabiliy’ is vague hen i is used in relain he prble f planeary in in he Slar syse. Aually i is n easy give a lear, rigrus and physially eaningful definiin f he sabiliy f ur Slar syse.
Ang any definiins f sabiliy, here e adp he Hill definiin (Gladan 199): aually his is n a definiin f sabiliy, bu f insabiliy. e define a syse as being unsable hen a lse enuner urs sehere in he syse, saring fr a erain iniial nfigurain (habers, eherill ≈ap;ap; Bss 1996; I ≈ap;ap; anikaa 1999). A syse is defined as eperiening a lse enuner hen bdies apprah ne anher ihin an area f he larger Hill radius. herise he syse is defined as being sable. Henefrard e sae ha ur planeary syse is dynaially sable if n lse enuner happens during he age f ur Slar syse, abu ±5 Gyr. Inidenally, his definiin ay be replaed by ne in hih an urrene f any rbial rssing beeen eiher f a pair f planes akes plae. his is beause e kn fr eperiene ha an rbial rssing is very likely lead a lse enuner in planeary and prplaneary syses (Yshinaga, Kkub ≈ap;ap; akin 1999). f urse his saeen ann be siply applied syses ih sable rbial resnanes suh as he Nepune–Plu syse.
1.Previus sudies and ais f his researh
In addiin he vagueness f he nep f sabiliy, he planes in ur Slar syse sh a haraer ypial f dynaial has (Sussan ≈ap;ap; isd 1988, 199). he ause f his hai behaviur is n parly undersd as being a resul f resnane verlapping (urray ≈ap;ap; Hlan 1999; Lear, Franklin ≈ap;ap; Hlan 001). Hever, i uld require inegraing ver an enseble f planeary syses inluding all nine planes fr a perid vering several 1hly undersand he lng-er evluin f planeary rbis, sine hai dynaial syses are haraerized by heir srng dependene n iniial ndiins.
Fr ha pin f vie, any f he previus lng-er nuerial inegrains inluded nly he uer five planes (Sussan ≈ap;ap; isd 1988; Kinshia ≈ap;ap; Nakai 1996). his is beause he rbial perids f he uer planes are s uh lnger han hse f he inner fur planes ha i is uh easier fll he syse fr a given inegrain perid. A presen, he lnges nuerial inegrains published in jurnals are hse f Dunan ≈ap;ap; Lissauer (1998). Alhugh heir ain arge as he effe f ps-ain-sequene slar ass lss n he sabiliy f planeary rbis, hey perfred any inegrains vering up ~1011 yr f he rbial ins f he fur jvian planes. he iniial rbial eleens and asses f planes are he sae as hse f ur Slar syse in Dunan ≈ap;ap; Lissauer's paper, bu hey derease he ass f he Sun gradually in heir nuerial eperiens. his is beause hey nsider he effe f ps-ain-sequene slar ass lss in he paper. nsequenly, hey fund ha he rssing ie-sale f planeary rbis, hih an be a ypial indiar f he insabiliy ie-sale, is quie sensiive he rae f ass derease f he Sun. hen he ass f he Sun is lse is presen value, he jvian planes reain sable ver 1010 yr, r perhaps lnger. Dunan ≈ap;ap; Lissauer als perfred fur siilar eperiens n he rbial in f seven planes (Venus Nepune), hih ver a span f ~109 yr. heir eperiens n he seven planes are n ye prehensive, bu i sees ha he erresrial planes als reain sable during he inegrain perid, ainaining als regular sillains.
n he her hand, in his aurae sei-analyial seular perurbain hery (Laskar 1988), Laskar finds ha large and irregular variains an appear in he eenriiies and inlinains f he erresrial planes, espeially f erury and ars n a ie-sale f several 109 yr (Laskar 1996). he resuls f Laskar's seular perurbain hery shuld be nfired and invesigaed by fully nuerial inegrains.
In his paper e presen preliinary resuls f si lng-er nuerial inegrains n all nine planeary rbis, vering a span f several 109 yr, and f her inegrains vering a span f ± 5 × 1010 yr. he al elapsed ie fr all inegrains is re han 5 yr, using several dediaed Ps and rksains. ne f he fundaenal nlusins f ur lng-er inegrains is ha Slar syse planeary in sees be sable in ers f he Hill sabiliy enined abve, a leas ver a ie-span f ± 4 Gyr. Aually, in ur nuerial inegrains he syse as far re sable han ha is defined by he Hill sabiliy rierin: n nly did n lse enuner happen during he inegrain perid, bu als all he planeary rbial eleens have been nfined in a narr regin bh in ie and frequeny dain, hugh planeary ins are shasi. Sine he purpse f his paper is ehibi and vervie he resuls f ur lng-er nuerial inegrains, e sh ypial eaple figures as evidene f he very lng-er sabiliy f Slar syse planeary in. Fr readers h have re speifi and deeper ineress in ur nuerial resuls, e have prepared a ebpage (aess ), here e sh ra rbial eleens, heir l-pass filered resuls, variain f Delaunay eleens and angular enu defii, and resuls f ur siple ie–frequeny analysis n all f ur inegrains.
In Sein e briefly eplain ur dynaial del, nuerial ehd and iniial ndiins used in ur inegrains. Sein is deved a desripin f he quik resuls f he nuerial inegrains. Very lng-er sabiliy f Slar syse planeary in is apparen bh in planeary psiins and rbial eleens. A rugh esiain f nuerial errrs is als given. Sein 4 ges n a disussin f he lnges-er variain f planeary rbis using a l-pass filer and inludes a disussin f angular enu defii. In Sein 5, e presen a se f nuerial inegrains fr he uer five planes ha spans ± 5 × 1010 yr. In Sein 6 e als disuss he lng-er sabiliy f he planeary in and is pssible ause.
Desripin f he nuerial inegrains
(本部分涉及比較複雜的積分計算,作者君就不貼上來了,貼上來了起點也不一定能成功顯示。)
. Nuerial ehd
e uilize a send-rder isd–Hlan syplei ap as ur ain inegrain ehd (isd ≈ap;ap; Hlan 1991; Kinshia, Yshida ≈ap;ap; Nakai 1991) ih a speial sar-up predure redue he runain errr f angle variables,‘ar sar’(Saha ≈ap;ap; reaine 199, 1994).
he sepsize fr he nuerial inegrains is 8 d hrughu all inegrains f he nine planes (N±1,,), hih is abu 1/11 f he rbial perid f he inners plane (erury). As fr he deerinain f sepsize, e parly fll he previus nuerial inegrain f all nine planes in Sussan ≈ap;ap; isd (1988, 7. d) and Saha ≈ap;ap; reaine (1994, 5/ d). e runded he deial par f he heir sepsizes 8 ake he sepsize a uliple f in rder redue he auulain f rund-ff errr in he puain presses. In relain his, isd ≈ap;ap; Hlan (1991) perfred nuerial inegrains f he uer five planeary rbis using he syplei ap ih a sepsize f 400 d, 1/10.8 f he rbial perid f Jupier. heir resul sees be aurae enugh, hih parly jusifies ur ehd f deerining he sepsize. Hever, sine he eenriiy f Jupier (~0.05) is uh saller han ha f erury (~0.), e need se are hen e pare hese inegrains siply in ers f sepsizes.
In he inegrain f he uer five planes (F±), e fied he sepsize a 400 d.
e adp Gauss' f and g funins in he syplei ap geher ih he hird-rder Halley ehd (Danby 199) as a slver fr Kepler equains. he nuber f aiu ierains e se in Halley's ehd is 15, bu hey never reahed he aiu in any f ur inegrains.
he inerval f he daa upu is 00 000 d (~547 yr) fr he alulains f all nine planes (N±1,,), and abu 8000 000 d (~1 9rain f he uer five planes (F±).
Alhugh n upu filering as dne hen he nuerial inegrains ere in press, e applied a l-pass filer he ra rbial daa afer e had pleed all he alulains. See Sein 4.1 fr re deail.