Periodic orbits of the non-hierarchical unequal-mass triple system

Xiaoming LI, Xiaochen LI and Shijun LIAO

Parameters:

Body mass: m3=1, m1, m2;

Newton's gravitational constant: G = 1;

Initial positions: (x1, 0), (1, 0), (0, 0);

Initial velocities: (0, v1), (0, v2), (0, -(m1v1 + m2v2)/m3 );

T is the period, The stability of periodic orbits can be linear stable (S) or linear unstable (U).

Periodic orbits
m1 m2 x1 v1 v2 T Stability
0.800 0.750 -0.13235278422595 2.54313073609853 0.30661326433073 5.03845020137260 U
0.800 0.751 -0.13294845165048 2.53688488688741 0.30933747256986 5.06995465995552 U
0.800 0.752 -0.13343702441301 2.53174826780246 0.31129044883893 5.09353879451239 U
0.800 0.753 -0.13387349108903 2.52715606035674 0.31286250459505 5.11321176224960 U
0.800 0.754 -0.13427769025117 2.52290417614399 0.31419528502870 5.13042775043863 U
0.800 0.755 -0.13465945958951 2.51889126149057 0.31535943224219 5.14591164574436 U
0.800 0.756 -0.13502451977561 2.51505829297841 0.31639626159308 5.16008719949432 S
0.800 0.757 -0.13537654053465 2.51136735274534 0.31733243167883 5.17322770806750 S
0.800 0.758 -0.13571803940700 2.50779238961127 0.31818634095757 5.18552170084142 S
0.800 0.759 -0.13605083020365 2.50431460626098 0.31897132686466 5.19710578557066 S
0.800 0.760 -0.13637626948096 2.50091992243202 0.31969742810754 5.20808273812712 S
0.800 0.761 -0.13669540215420 2.49759747528749 0.32037242817688 5.21853221178114 U
0.800 0.762 -0.13700905250053 2.49433868163381 0.32100250898509 5.22851744392088 U
0.800 0.763 -0.13731788365757 2.49113662441954 0.32159267919006 5.23808964998454 U
0.800 0.764 -0.13762243799245 2.48798563623067 0.32214706546626 5.24729101081571 U
0.800 0.765 -0.13792316535422 2.48488100762378 0.32266911681276 5.25615676765385 U
0.800 0.766 -0.13822044337393 2.48181877742969 0.32316175168593 5.26471673052076 U
0.800 0.767 -0.13851459238503 2.47879557853511 0.32362746638596 5.27299638914341 U
0.800 0.768 -0.13880588660816 2.47580852220726 0.32406841648963 5.28101774742745 U
0.800 0.769 -0.13909456268192 2.47285510981361 0.32448647910072 5.28879996121838 U
0.800 0.770 -0.13938082626975 2.46993316440874 0.32488330117086 5.29635983324171 U
0.800 0.771 -0.13966485724742 2.46704077698793 0.32526033752394 5.30371220248945 U
0.800 0.772 -0.13994681382600 2.46417626374238 0.32561888114688 5.31087025433745 U
0.800 0.773 -0.14022683586544 2.46133813168575 0.32596008758808 5.31784577027907 U
0.800 0.774 -0.14050504756439 2.45852505073388 0.32628499480785 5.32464933105629 U
0.800 0.775 -0.14078155966380 2.45573583081756 0.32659453947685 5.33129048340330 U
0.800 0.776 -0.14105647126726 2.45296940296359 0.32688957047057 5.33777787806784 U
0.800 0.777 -0.14132987135648 2.45022480353507 0.32717086012825 5.34411938493849 U
0.800 0.778 -0.14160184006183 2.44750116101019 0.32743911371353 5.35032218975802 U
0.800 0.779 -0.14187244973457 2.44479768481739 0.32769497741611 5.35639287589992 U
0.800 0.780 -0.14214176585726 2.44211365584965 0.32793904516062 5.36233749393616 U
0.800 0.781 -0.14240984782117 2.43944841835948 0.32817186443350 5.36816162115434 U
0.800 0.782 -0.14267674959351 2.43680137299699 0.32839394129565 5.37387041274357 U
0.800 0.783 -0.14294252029318 2.43417197080021 0.32860574471596 5.37946864603307 U
0.800 0.784 -0.14320720468959 2.43155970798331 0.32880771033509 5.38496075890216 U
0.800 0.785 -0.14347084363695 2.42896412139700 0.32900024374856 5.39035088327488 U
0.800 0.786 -0.14373347445379 2.42638478455828 0.32918372338215 5.39564287444616 U
0.800 0.787 -0.14399513125597 2.42382130416465 0.32935850302005 5.40084033685746 U
0.800 0.788 -0.14425584524991 2.42127331702240 0.32952491403563 5.40594664683362 U
0.800 0.789 -0.14451564499170 2.41874048733056 0.32968326736665 5.41096497270782 U
0.800 0.790 -0.14477455661685 2.41622250427128 0.32983385526982 5.41589829269200 U
0.800 0.791 -0.14503260404450 2.41371907986551 0.32997695288419 5.42074941079519 U
0.800 0.792 -0.14528980915971 2.41122994705912 0.33011281962825 5.42552097104301 U
0.800 0.793 -0.14554619197638 2.40875485800982 0.33024170045193 5.43021547021579 U
0.800 0.794 -0.14580177078346 2.40629358254968 0.33036382696149 5.43483526928953 U
0.800 0.795 -0.14605656227638 2.40384590680176 0.33047941843286 5.43938260373773 U
0.800 0.796 -0.14631058167548 2.40141163193231 0.33058868272656 5.44385959282989 U
0.800 0.797 -0.14656384283314 2.39899057302264 0.33069181711578 5.44826824804325 U
0.800 0.798 -0.14681635833064 2.39658255804674 0.33078900903746 5.45261048069022 U
0.800 0.799 -0.14706813956621 2.39418742694303 0.33088043677497 5.45688810884769 U
0.800 0.800 -0.14731919683497 2.39180503076948 0.33096627007994 5.46110286366636 U
0.800 0.801 -0.14756953940192 2.38943523093334 0.33104667073957 5.46525639512489 U
0.800 0.802 -0.14781917556851 2.38707789848739 0.33112179309554 5.46935027729020 U
0.800 0.803 -0.14806811273349 2.38473291348587 0.33119178451906 5.47338601313201 U
0.800 0.804 -0.14831635744880 2.38240016439393 0.33125678584686 5.47736503893897 U
0.800 0.805 -0.14856391547082 2.38007954754520 0.33131693178183 5.48128872837543 U
0.800 0.806 -0.14881079180744 2.37777096664280 0.33137235126180 5.48515839621416 U
0.800 0.807 -0.14905699076157 2.37547433229957 0.33142316779955 5.48897530177602 U
0.800 0.808 -0.14930251597111 2.37318956161365 0.33146949979678 5.49274065210510 U
0.800 0.809 -0.14954737044608 2.37091657777632 0.33151146083435 5.49645560490290 U
0.800 0.810 -0.14979155660280 2.36865530970895 0.33154915994105 5.50012127124424 U
0.800 0.811 -0.15003507629569 2.36640569172649 0.33158270184287 5.50373871809477 U
0.800 0.812 -0.15027793084678 2.36416766322514 0.33161218719437 5.50730897064740 U
0.800 0.813 -0.15052012107307 2.36194116839210 0.33163771279373 5.51083301449270 U
0.800 0.814 -0.15076164731212 2.35972615593542 0.33165937178300 5.51431179763940 U
0.800 0.815 -0.15100250944578 2.35752257883233 0.33167725383466 5.51774623239591 U
0.800 0.816 -0.15124270692239 2.35533039409445 0.33169144532564 5.52113719712506 U
0.800 0.817 -0.15148223877760 2.35314956254850 0.33170202949996 5.52448553788315 U
0.800 0.818 -0.15172110365374 2.35098004863132 0.33170908662068 5.52779206995150 U
0.800 0.819 -0.15195929981801 2.34882182019791 0.33171269411227 5.53105757926996 U
0.800 0.820 -0.15219682517958 2.34667484834164 0.33171292669388 5.53428282377977 U
0.800 0.821 -0.15243367730566 2.34453910722557 0.33170985650449 5.53746853468292 U
0.800 0.822 -0.15266985343650 2.34241457392405 0.33170355322027 5.54061541762412 U
0.800 0.823 -0.15290535049968 2.34030122827387 0.33169408416501 5.54372415380192 U
0.800 0.824 -0.15314016512345 2.33819905273422 0.33168151441394 5.54679540101341 U
0.800 0.825 -0.15337429364937 2.33610803225482 0.33166590689147 5.54982979463796 U
0.800 0.826 -0.15360773214427 2.33402815415163 0.33164732246337 5.55282794856427 U
0.800 0.827 -0.15384047641154 2.33195940798959 0.33162582002369 5.55579045606480 U
0.800 0.828 -0.15407252200180 2.32990178547195 0.33160145657678 5.55871789062130 U
0.800 0.829 -0.15430386422308 2.32785528033567 0.33157428731487 5.56161080670488 U
0.800 0.830 -0.15453449815038 2.32581988825249 0.33154436569139 5.56446974051380 U
0.800 0.831 -0.15476441863490 2.32379560673533 0.33151174349037 5.56729521067172 U
0.800 0.832 -0.15499362031263 2.32178243504965 0.33147647089218 5.57008771888938 U
0.800 0.833 -0.15522209761271 2.31978037412938 0.33143859653584 5.57284775059173 U
0.800 0.834 -0.15544984476528 2.31778942649724 0.33139816757816 5.57557577551322 U
0.800 0.835 -0.15567685580899 2.31580959618908 0.33135522974986 5.57827224826299 U
0.800 0.836 -0.15590312459821 2.31384088868201 0.33130982740887 5.58093760886211 U
0.800 0.837 -0.15612864480989 2.31188331082613 0.33126200359109 5.58357228325451 U
0.800 0.838 -0.15635340995012 2.30993687077961 0.33121180005854 5.58617668379335 U
0.800 0.839 -0.15657741336043 2.30800157794682 0.33115925734537 5.58875120970435 U
0.800 0.840 -0.15680064822384 2.30607744291955 0.33110441480157 5.59129624752742 U
0.800 0.841 -0.15702310757061 2.30416447742094 0.33104731063471 5.59381217153798 U
0.800 0.842 -0.15724478428381 2.30226269425201 0.33098798194972 5.59629934414922 U
0.800 0.843 -0.15746567110470 2.30037210724075 0.33092646478688 5.59875811629636 U
0.800 0.844 -0.15768576063781 2.29849273119344 0.33086279415813 5.60118882780398 U
0.800 0.845 -0.15790504535596 2.29662458184826 0.33079700408175 5.60359180773746 U
0.800 0.846 -0.15812351760496 2.29476767583095 0.33072912761553 5.60596737473944 U
0.800 0.847 -0.15834116960827 2.29292203061240 0.33065919688853 5.60831583735206 U
0.800 0.848 -0.15855799347142 2.29108766446817 0.33058724313147 5.61063749432588 U
0.800 0.849 -0.15877398118631 2.28926459643976 0.33051329670585 5.61293263491627 U
0.800 0.850 -0.15898912463538 2.28745284629750 0.33043738713190 5.61520153916771 U
0.800 0.851 -0.15920341559557 2.28565243450510 0.33035954311534 5.61744447818703 U
0.800 0.852 -0.15941684574232 2.28386338218567 0.33027979257308 5.61966171440587 U
0.800 0.853 -0.15962940665323 2.28208571108917 0.33019816265794 5.62185350183308 U
0.800 0.854 -0.15984108981181 2.28031944356124 0.33011467978231 5.62402008629759 U
0.800 0.855 -0.16005188661100 2.27856460251330 0.33002936964099 5.62616170568222 U
0.800 0.856 -0.16026178835661 2.27682121139388 0.32994225723308 5.62827859014893 U
0.800 0.857 -0.16047078627072 2.27508929416117 0.32985336688310 5.63037096235587 U
0.800 0.858 -0.16067887149491 2.27336887525664 0.32976272226128 5.63243903766676 U
0.800 0.859 -0.16088603509348 2.27165997957972 0.32967034640314 5.63448302435289 U
0.800 0.860 -0.16109226805649 2.26996263246352 0.32957626172833 5.63650312378815 U
0.800 0.861 -0.16129756130287 2.26827685965156 0.32948049005878 5.63849953063747 U
0.800 0.862 -0.16150190568328 2.26660268727530 0.32938305263628 5.64047243303883 U
0.800 0.863 -0.16170529198306 2.26494014183271 0.32928397013936 5.64242201277939 U
0.800 0.864 -0.16190771092498 2.26328925016760 0.32918326269960 5.64434844546583 U
0.800 0.865 -0.16210915317205 2.26165003944973 0.32908094991748 5.64625190068920 U
0.800 0.866 -0.16230960933014 2.26002253715580 0.32897705087753 5.64813254218464 U
0.800 0.867 -0.16250906995068 2.25840677105108 0.32887158416314 5.64999052798610 U
0.800 0.868 -0.16270752553318 2.25680276917182 0.32876456787076 5.65182601057630 U
0.800 0.869 -0.16290496652777 2.25521055980830 0.32865601962371 5.65363913703219 U
0.800 0.870 -0.16310138333767 2.25363017148856 0.32854595658549 5.65543004916610 U
0.800 0.871 -0.16329676632161 2.25206163296275 0.32843439547276 5.65719888366267 U
0.800 0.872 -0.16349110579622 2.25050497318807 0.32832135256781 5.65894577221206 U
0.800 0.873 -0.16368439203835 2.24896022131429 0.32820684373068 5.66067084163897 U
0.800 0.874 -0.16387661528734 2.24742740666989 0.32809088441095 5.66237421402840 U
0.800 0.875 -0.16406776574732 2.24590655874860 0.32797348965912 5.66405600684781 U
0.800 0.876 -0.16425783358937 2.24439770719660 0.32785467413766 5.66571633306591 U
0.800 0.877 -0.16444680895373 2.24290088180009 0.32773445213176 5.66735530126831 U
0.800 0.878 -0.16463468195192 2.24141611247344 0.32761283755975 5.66897301577008 U
0.800 0.879 -0.16482144266883 2.23994342924774 0.32748984398321 5.67056957672540 U
0.800 0.880 -0.16500708116484 2.23848286225975 0.32736548461679 5.67214508023437 U
0.800 0.881 -0.16519158747779 2.23703444174141 0.32723977233777 5.67369961844707 U
0.800 0.882 -0.16537495162506 2.23559819800959 0.32711271969537 5.67523327966507 U
0.800 0.883 -0.16555716360547 2.23417416145638 0.32698433891972 5.67674614844043 U
0.800 0.884 -0.16573821340130 2.23276236253967 0.32685464193071 5.67823830567221 U
0.800 0.885 -0.16591809098020 2.23136283177410 0.32672364034648 5.67970982870073 U
0.800 0.886 -0.16609678629704 2.22997559972245 0.32659134549176 5.68116079139961 U
0.800 0.887 -0.16627428929582 2.22860069698722 0.32645776840599 5.68259126426553 U
0.800 0.888 -0.16645058991154 2.22723815420273 0.32632291985117 5.68400131450606 U
0.800 0.889 -0.16662567807194 2.22588800202734 0.32618681031953 5.68539100612536 U
0.800 0.890 -0.16679954369941 2.22455027113613 0.32604945004109 5.68676040000805 U
0.800 0.891 -0.16697217671266 2.22322499221379 0.32591084899087 5.68810955400111 U
0.800 0.892 -0.16714356702855 2.22191219594785 0.32577101689605 5.68943852299403 U
0.800 0.893 -0.16731370456380 2.22061191302213 0.32562996324291 5.69074735899724 U
0.800 0.894 -0.16748257923668 2.21932417411050 0.32548769728359 5.69203611121876 U
0.800 0.895 -0.16765018096877 2.21804900987090 0.32534422804266 5.69330482613931 U
0.800 0.896 -0.16781649968654 2.21678645093957 0.32519956432362 5.69455354758580 U
0.800 0.897 -0.16798152532310 2.21553652792559 0.32505371471517 5.69578231680328 U
0.800 0.898 -0.16814524781978 2.21429927140554 0.32490668759733 5.69699117252544 U
0.800 0.899 -0.16830765712776 2.21307471191855 0.32475849114747 5.69818015104363 U
0.800 0.900 -0.16846874320970 2.21186287996141 0.32460913334617 5.69934928627454 U
0.800 0.901 -0.16862849604129 2.21066380598398 0.32445862198293 5.70049860982648 U
0.800 0.902 -0.16878690561284 2.20947752038478 0.32430696466179 5.70162815106439 U
0.800 0.903 -0.16894396193083 2.20830405350680 0.32415416880676 5.70273793717354 U
0.800 0.904 -0.16909965501945 2.20714343563346 0.32400024166724 5.70382799322201 U
0.800 0.905 -0.16925397492210 2.20599569698480 0.32384519032321 5.70489834222206 U
0.800 0.906 -0.16940691170294 2.20486086771384 0.32368902169034 5.70594900519007 U
0.800 0.907 -0.16955845544835 2.20373897790307 0.32353174252503 5.70698000120566 U
0.800 0.908 -0.16970859626839 2.20263005756120 0.32337335942929 5.70799134746951 U
0.800 0.909 -0.16985732429832 2.20153413661998 0.32321387885556 5.70898305936017 U
0.800 0.910 -0.17000462970000 2.20045124493122 0.32305330711138 5.70995515048980 U
0.800 0.911 -0.17015050266333 2.19938141226403 0.32289165036403 5.71090763275889 U
0.800 0.912 -0.17029493340770 2.19832466830206 0.32272891464500 5.71184051641002 U
0.800 0.913 -0.17043791218337 2.19728104264102 0.32256510585440 5.71275381008057 U
0.800 0.914 -0.17057942927285 2.19625056478630 0.32240022976532 5.71364752085460 U
0.800 0.915 -0.17071947499234 2.19523326415071 0.32223429202805 5.71452165431368 U
0.800 0.916 -0.17085803969302 2.19422917005235 0.32206729817423 5.71537621458690 U
0.800 0.917 -0.17099511376246 2.19323831171266 0.32189925362090 5.71621120439995 U
0.800 0.918 -0.17113068762594 2.19226071825454 0.32173016367456 5.71702662512342 U
0.800 0.919 -0.17126475174778 2.19129641870062 0.32156003353499 5.71782247682010 U
0.800 0.920 -0.17139729663266 2.19034544197163 0.32138886829917 5.71859875829164 U
0.800 0.921 -0.17152831282690 2.18940781688495 0.32121667296503 5.71935546712426 U
0.800 0.922 -0.17165779091978 2.18848357215318 0.32104345243508 5.72009259973372 U
0.800 0.923 -0.17178572154480 2.18757273638287 0.32086921152015 5.72081015140955 U
0.800 0.924 -0.17191209538095 2.18667533807339 0.32069395494284 5.72150811635842 U
0.800 0.925 -0.17203690315395 2.18579140561582 0.32051768734107 5.72218648774691 U
0.800 0.926 -0.17216013563750 2.18492096729205 0.32034041327152 5.72284525774340 U
0.800 0.927 -0.17228178365451 2.18406405127387 0.32016213721295 5.72348441755933 U
0.800 0.928 -0.17240183807828 2.18322068562226 0.31998286356955 5.72410395748975 U
0.800 0.929 -0.17252028983375 2.18239089828670 0.31980259667417 5.72470386695311 U
0.800 0.930 -0.17263712989864 2.18157471710462 0.31962134079149 5.72528413453049 U
0.800 0.931 -0.17275234930467 2.18077216980092 0.31943910012120 5.72584474800403 U
0.800 0.932 -0.17286593913866 2.17998328398759 0.31925587880106 5.72638569439478 U
0.800 0.933 -0.17297789054376 2.17920808716342 0.31907168090989 5.72690695999986 U
0.800 0.934 -0.17308819472048 2.17844660671380 0.31888651047060 5.72740853042906 U
0.800 0.935 -0.17319684292791 2.17769886991062 0.31870037145309 5.72789039064067 U
0.800 0.936 -0.17330382648478 2.17696490391218 0.31851326777713 5.72835252497681 U
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