peclly 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.