tonthe 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 ty