对火星轨道变化问题的最后解释

it is not clear at the oent hy the ven–earth pair exhibits a negative rretion energy exchan and a positive rretion angur oe e ay possibly exp this through observg the neral fact that there are no secur ters pary seiajor axes up to send-order perturbation theories cf

ouer apap cleence 1961 boaletti apap pucao 1998 this eans that the pary orbital energy hich is directly reted to the seiajor axis a ht be uch less affected by perturbg ps than is the angur oe hich retes to e hence， the eentricities of ven and earth can be disturbed easily by jupiter and saturn， hich results a positive rretion the angur oe on the other hand， the seiajor axes of ven and earth are less likely to be disturbed by the jovian ps th the energy exchan ay be liited only ith the ven–earth pair， hich results a negative rretion the exchan of orbital energy the pair

as for the outer jovian pary subsyste， jupiter–saturn and uran–neptune see to ake dynaical pairs hoever， the strength of their uplg is not as strong pared ith that of the ven–earth pair

5 ± 5 x 1010-yr tegrations of outer pary orbits

sce the jovian pary asses are er than the terrestrial pary asses， e treat the jovian pary syste as an dependent pary syste ters of the study of its dynaical stability hence， e added a uple of trial tegrations that span ± 5 x 1010 yr， cdg only the outer five ps the four jovian ps ps pto the results exhibit the rigoro stability of the outer pary syste over this long tie-span orbital nfigurations fig 12， and variation of eentricities and ctions fig 13 sho this very long-ter stability of the outer five ps both the tie and the freency doh e do not sho a here， the typical freency of the orbital osciltion of pto and the other outer ps is alost nstant durg these very long-terration periods， hich is deonstrated the tie–freency a on our ebpa

these o tegrations， the retive nuerical error the total energy as ～10?6 and that of the total angur oentu as ～10?10

51 renances the neptune–pto syste

koshita apap nakai 1996 tegrated the outer five pary orbits over ± 55 x 109 yr they found that four ajor renances beeen neptune and pto are ataed durg the hole tegration period， and that the renances ay be the a caes of the stability of the orbit of pto the ajor four renances found previo research are as follos the follog description，λ denotes the itude，Ω is the longitude of the ascendg node and ? is the longitude of perihelion subscripts p and n denote pto and neptune

ean otion renance beeen neptune and pto 3:2 the critical arguent θ1 3 λp? 2 λn??p li

ates around 180° ith an aplitude of about 80° and a li

ation period of about 2 x 104 yr

the arguent of perihelion of pto pθ2?p?Ωp li

ates around 90° ith a period of about 38 x 106 yr the doant periodic variations of the eentricity and ction of pto are synchronized ith the li

ation of its arguent of perihelion this is anticipated the secur perturbation theory nstructed by kozai 1962

the longitude of the node of pto referred to the longitude of the node of neptune，θ3Ωp?Ωn， circutes and the period of this circution is eal to the period of θ2 li

ation hen θ3 bees zero， ie the longitudes of ascendg nodes of neptune and pto overp， the ction of pto bees axiu， the eentricity bees iu and the arguent of perihelion bees 90° hen θ3 bees 180°， the ction of pto bees iu， the eentricity bees axiu and the arguent of perihelion bea illias apap benn 1971 anticipated this type of renance， ter nfired by i， nobili apap carpo 1989

an arguent θ4?p??n+ 3 Ωp?Ωn li

ates around 180° ith a long period，～ 57 x 108 yr

our nurations， the renances i–iii are ell ataed， and variation of the critical arguents θ1，θ2，θ3 rea si the hole tegration period figs 14–16 hoever， the fourth renance iv appears to be different: the critical arguent θ4 alternates li

ation and circution over a 1010-yr ti 17 this is an terestg fact that koshita apap nakai's 1995， 1996 shorter tegrations ere not able to disclose

6 discsion

hat kd of dynaical echanis atas this long-ter stability of the pary syste? e can iediately thk of o ajor features that ay be responsible for the long-ter stability first， there see to be no significant loer-order renances ean otion and secur beeen any pair a the ne ps jupiter and saturn are close to a 5:2 ean otion renance the fareat eality’， but not jt the renance zone higher-order renances ay cae the chaotic nature of the pary dynaical otion， but they are not strong as to destroy the stable pary otion ith the lifetie of the real r syste the send feature， hich e thk is ore iportant for the long-ter stability of our pary syste， is the difference dynaical distance beeen terrestrial and jovian pary subsystes ito apap tanikaa 1999， 2001 hen e easure pary separations by the utual hill radii r， separations a terrestrial ps are greater than 26rh， hereas those a jovian ps are less than 14rh this difference is directly reted to the difference beeen dynaical features of terrestrial and jovian ps terrestrial ps have saller asses， shorter orbital periods and ider dynaical separation they are strongly perturbed by jovian ps that have rr er orbital periods and narroer dynaical separation jovian ps are not perturbed by any other assive bodies

the present terrestrial pary syste is still beg disturbed by the assive jovian ps hoever， the ide separation and utual teraction a the terrestrial ps renders the disturbance effective the degree of disturbance by jovian ps is oejorder of nitude of the eentricity of jupiter， sce the disturbance caed by jovian ps is a forced osciltion havg an aplitude of oej heighteng of eentricity， for exaple oej～005， is far fro sufficient to provoke stability the terrestrial ps havg such a ide separation as 26rh th e assue that the present ide dynaical separation a terrestrial ps 26rh is probably one of the nificant nditions for the stability of the pary syste over a 109-yr tie-span our detailed analysis of the retionship beeen dynaical distance beeen ps and the stability tie-scale of r syste pary otion is no on-gog

although our nurations span the lifetie of the r syste， the nuber of tegrations is far fro sufficient to fill the itial phase space it is necessary to perfor ore and ore nurations to nfir and exae detail the long-ter stability of our pary dynaics

——以上文段引自 ito， tap tanikaa， k long-terrations and stability of pary orbits our r 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。最新网址：hx

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