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 recen
