Movies of the Periodic Planar Collisionless Three-Body Orbits in Real Space or on Shape Sphere

Xiaoming LI and Shijun LIAO

Shanghai Jiaotong University, China

Parameters:

Body mass: m₁ = m₂ = m₃ = 1

Newton's gravitational constant: G = 1

Initial positions: (-1, 0), (1, 0), (0, 0)

Initial velocities: (v₁, v₂), (v₁, v₂), (-2v₁, -2v₂)

T is the period, T^* = T|E|^3/2 is the scale-invariant period and L_f is the length of the free group element, where E denotes the sum of the kinetic and potential energy of the three-body system.

Periodic orbits

Class and number	v₁	v₂	T	T^*	L_f	Real Space	Shape Sphere
I.A^i.c._₁	0.3471168881	0.5327249454	6.3259139829	9.238	4	movie	movie
I.A^i.c._₂	0.3068934205	0.1255065670	6.2346748391	19.932	8	movie	movie
I.A^i.c._₃	0.6150407229	0.5226158545	37.3205235945	15.048	8	movie	movie
I.A^i.c._₄	0.5379557207	0.3414578545	26.9186696160	39.075	16	movie	movie
I.A^i.c._₅	0.4112926910	0.2607551013	20.7490650080	49.630	20	movie	movie
I.A^i.c._₆	0.4425908552	0.4235138348	35.8334644158	57.728	24	movie	movie
I.A^i.c._₇	0.1214534165	0.1012023800	15.7440944954	59.455	24	movie	movie
I.A^i.c._₈	0.4094945913	0.3628231655	33.8677507235	68.673	28	movie	movie
I.A^i.c._₉	0.5255769251	0.2501253528	43.8698538026	79.277	32	movie	movie
I.A^i.c._₁₀	0.4121028725	0.2833837497	34.2470499687	79.255	32	movie	movie
I.A^i.c._₁₁	0.4364192674	0.4457095477	49.5954033190	76.298	32	movie	movie
I.A^i.c._₁₂	0.1182009612	0.5847367662	48.2723717545	82.749	36	movie	movie
I.A^i.c._₁₃	0.4763527642	0.3789434497	53.4714914343	87.484	36	movie	movie
I.A^i.c._₁₄	0.4027121690	0.2100155085	34.7120153702	89.560	36	movie	movie
I.A^i.c._₁₅	0.3960494651	0.3529413931	46.1340735475	98.289	40	movie	movie
I.A^i.c._₁₆	0.4340543928	0.4606927255	64.1162217970	94.824	40	movie	movie
I.A^i.c._₁₇	0.1842784887	0.5871881740	63.5343529785	101.184	44	movie	movie
I.A^i.c._₁₈	0.4580378828	0.4093753024	66.3519736810	106.147	44	movie	movie
I.A^i.c._₁₉	0.4152505707	0.2913461808	47.9254977196	108.869	44	movie	movie
I.A^i.c._₂₀	0.0969422653	0.5615968396	53.6899444096	101.174	44	movie	movie
I.A^i.c._₂₁	0.4082108156	0.2436851904	48.4868513719	119.241	48	movie	movie
I.A^i.c._₂₂	0.4289870678	0.4723797648	78.3984979261	113.331	48	movie	movie
I.A^i.c._₂₃	0.4138807521	0.3477955684	61.8447789156	127.900	52	movie	movie
I.A^i.c._₂₄	0.4905050535	0.4044215155	85.3859524958	124.747	52	movie	movie
I.A^i.c._₂₅	0.1982770999	0.5760625510	73.2768117405	119.634	52	movie	movie
I.A^i.c._₂₆	0.3991287659	0.1847081193	48.6673769352	129.450	52	movie	movie
I.A^i.c._₂₇	0.4151691260	0.2953409098	61.3228288140	138.477	56	movie	movie
I.A^i.c._₂₈	0.0490506729	0.5901941115	79.1518362736	137.886	60	movie	movie
I.A^i.c._₂₉	0.3447503346	0.3930446386	67.3877746400	146.737	60	movie	movie
I.A^i.c._₃₀	0.2203123981	0.5718227262	85.7935924161	138.093	60	movie	movie
I.A^i.c._₃₁	0.4441311511	0.3823106072	82.3618800834	146.756	60	movie	movie
I.A^i.c._₃₂	0.4041322114	0.2191641945	62.4468134238	159.167	64	movie	movie
I.A^i.c._₃₃	0.4089912496	0.3457125084	75.0210999574	157.507	64	movie	movie
I.A^i.c._₃₄	0.4572423635	0.4074171858	95.8806923191	154.561	64	movie	movie
I.A^i.c._₃₅	0.3972193787	0.1691985386	62.6275833821	169.327	68	movie	movie
I.A^i.c._₃₆	0.4160674674	0.2971499303	74.7892110946	168.084	68	movie	movie
I.A^i.c._₃₇	0.1038901209	0.5907210858	92.2887207815	156.291	68	movie	movie
I.A^i.c._₃₈	0.4135366646	0.2710056059	76.0285224477	178.523	72	movie	movie
I.A^i.c._₃₉	0.3967429300	0.3708809839	85.9343829011	176.391	72	movie	movie
I.A^i.c._₄₀	0.4073762182	0.2388431491	76.2219729678	188.847	76	movie	movie
I.A^i.c._₄₁	0.1334658448	0.5838277552	102.8155095976	174.712	76	movie	movie
I.A^i.c._₄₂	0.4015585101	0.2022664462	76.4010838847	199.069	80	movie	movie
I.A^i.c._₄₃	0.4157753114	0.2981866614	88.0489003051	197.691	80	movie	movie
I.A^i.c._₄₄	0.4188475683	0.2770588072	90.4212103693	208.148	84	movie	movie
I.A^i.c._₄₅	0.3960577146	0.1586009694	76.5926988984	209.198	84	movie	movie
I.A^i.c._₄₆	0.4096220179	0.2516961122	89.9866883856	218.506	88	movie	movie
I.A^i.c._₄₇	0.4046803380	0.2225972157	90.1813477230	228.773	92	movie	movie
I.A^i.c._₄₈	0.2744365569	0.3448729405	37.0281899697	98.299	40	movie	movie
I.A^i.c._₄₉	0.5196830772	0.2059463323	61.0651489089	119.273	48	movie	movie
I.A^i.c._₅₀	0.0481112024	0.5584284134	61.5066511920	119.557	52	movie	movie
I.A^i.c._₅₁	0.3240593189	0.3665712251	61.6980804867	146.748	60	movie	movie
I.A^i.c._₅₂	0.4392326535	0.4490130778	107.1704322355	161.864	68	movie	movie
I.A^i.c._₅₃	0.4157392818	0.3443683086	90.2692922120	187.114	76	movie	movie
I.A^i.c._₅₄	0.2591633491	0.5655538324	112.9677142326	175.025	76	movie	movie
I.A^i.c._₅₅	0.4372549674	0.4568896400	121.6765447969	180.390	76	movie	movie
I.A^i.c._₅₆	0.4713347232	0.3856148608	112.7807985048	184.312	76	movie	movie
I.A^i.c._₅₇	0.1538860573	0.5805527776	114.4056830978	193.146	84	movie	movie
I.A^i.c._₅₈	0.4162411626	0.4666456940	130.1232036082	198.902	84	movie	movie
I.A^i.c._₅₉	0.4602603277	0.4047836526	126.1735921874	202.975	84	movie	movie
I.A^i.c._₆₀	0.4260682804	0.4689275280	134.8572983004	198.903	84	movie	movie
I.A^i.c._₆₁	0.4115604103	0.3439515057	103.4777852547	216.720	88	movie	movie
I.A^i.c._₆₂	0.4538585041	0.4151335211	138.9526711783	221.605	92	movie	movie
I.A^i.c._₆₃	0.1807391308	0.5804273075	128.9311229083	211.590	92	movie	movie
I.A^i.c._₆₄	0.0616295799	0.5887684684	121.2588070481	211.428	92	movie	movie
I.A^i.c._₆₅	0.4164511851	0.2985460701	101.4417348354	227.296	92	movie	movie
I.A^i.c._₆₆	0.4755802612	0.3834289883	143.4920831622	232.725	96	movie	movie
I.A^i.c._₆₇	0.4189618506	0.3575723235	117.5497551541	235.641	96	movie	movie
I.A^i.c._₆₈	0.3998065241	0.1898070007	90.3562840799	238.958	96	movie	movie
I.A^i.c._₆₉	0.1938115742	0.5776286093	140.9274473884	230.040	100	movie	movie
I.A^i.c._₇₀	0.4311833725	0.4733759409	164.8353415245	235.912	100	movie	movie
I.A^i.c._₇₁	0.0960540551	0.5889671026	134.1667723286	229.832	100	movie	movie
I.A^i.c._₇₂	0.3952890968	0.1508523182	90.5619718006	249.067	100	movie	movie
I.A^i.c._₇₃	0.4395870869	0.4502293684	164.6132228870	247.429	104	movie	movie
I.A^i.c._₇₄	0.3674149486	0.3838228297	119.7236640531	254.456	104	movie	movie
I.A^i.c._₇₅	0.3939961214	0.3865732823	127.4002458975	254.459	104	movie	movie
I.A^i.c._₇₆	0.3430511121	0.3718832371	111.6289843304	254.460	104	movie	movie
I.A^i.c._₇₇	0.4159559963	0.2988672319	114.5882843578	256.902	104	movie	movie
I.A^i.c._₇₈	0.4069867693	0.2365548555	103.9566166835	258.453	104	movie	movie
I.A^i.c._₇₉	0.4589974678	0.4050034288	155.7660607190	251.388	104	movie	movie
I.A^i.c._₈₀	0.4139140441	0.2867091579	116.5535148563	267.382	108	movie	movie
I.A^i.c._₈₁	0.4379684294	0.4556963530	179.1036444528	265.955	112	movie	movie
I.A^i.c._₈₂	0.4126145620	0.3435200139	131.9570363471	275.931	112	movie	movie
I.A^i.c._₈₃	0.4561844518	0.4117892184	168.9508799790	270.024	112	movie	movie
I.A^i.c._₈₄	0.3985475384	0.1801838327	104.3138748764	278.839	112	movie	movie
I.A^i.c._₈₅	0.4126594494	0.2674571676	117.5120633437	277.786	112	movie	movie
I.A^i.c._₈₆	0.3921967782	0.3732670713	137.7155574878	284.106	116	movie	movie
I.A^i.c._₈₇	0.4180525186	0.2985930530	128.3273660780	286.508	116	movie	movie
I.A^i.c._₈₈	0.1382080826	0.5834341742	157.3466528910	266.675	116	movie	movie
I.A^i.c._₈₉	0.3974576989	0.2491169363	115.4448017793	288.116	116	movie	movie
I.A^i.c._₉₀	0.0188646524	0.5900765061	151.9903843649	266.578	116	movie	movie
I.A^i.c._₉₁	0.3947500473	0.1449169673	104.5346721644	288.934	116	movie	movie
I.A^i.c._₉₂	0.4146876683	0.2893277049	130.1851727452	296.995	120	movie	movie
I.A^i.c._₉₃	0.4049707755	0.2243966352	117.9157508493	298.378	120	movie	movie
I.A^i.c._₉₄	0.4948547469	0.3816681253	195.8237684806	299.800	124	movie	movie
I.A^i.c._₉₅	0.4098282065	0.4859736518	199.4325323563	291.389	124	movie	movie
I.A^i.c._₉₆	0.3557656112	0.2101434426	110.1033827881	308.577	124	movie	movie
I.A^i.c._₉₇	0.1458080611	0.5760627737	164.8777227366	285.109	124	movie	movie
I.A^i.c._₉₈	0.4373040972	0.1890148898	125.7688001626	308.577	124	movie	movie
I.A^i.c._₉₉	0.3693848766	0.2787954099	121.4331832032	307.415	124	movie	movie
I.A^i.c._₁₀₀	0.0670760777	0.5889627892	163.9101889958	284.971	124	movie	movie
I.A^i.c._₁₀₁	0.4024084539	0.3670928188	153.5887772816	313.740	128	movie	movie
I.A^i.c._₁₀₂	0.4101448519	0.2545904027	131.4852184733	317.767	128	movie	movie
I.A^i.c._₁₀₃	0.3976053675	0.1724965035	118.2740940483	318.716	128	movie	movie
I.A^i.c._₁₀₄	0.4070387234	0.3507052842	155.3531711573	324.480	132	movie	movie
I.A^i.c._₁₀₅	0.3654211421	0.1497581124	113.5033068728	328.800	132	movie	movie
I.A^i.c._₁₀₆	0.3288064734	0.2480300294	116.7651488382	328.060	132	movie	movie
I.A^i.c._₁₀₇	0.0921822548	0.5888237645	176.5993385200	303.375	132	movie	movie
I.A^i.c._₁₀₈	0.3943552252	0.1402131694	118.5101674005	328.800	132	movie	movie
I.A^i.c._₁₀₉	0.4164334853	0.2763211125	145.5011286545	337.039	136	movie	movie
I.A^i.c._₁₁₀	0.4033838433	0.2143907433	131.8709942386	338.289	136	movie	movie
I.A^i.c._₁₁₁	0.1818464802	0.5795638348	195.8266870843	321.997	140	movie	movie
I.A^i.c._₁₁₂	0.4109222799	0.3490743143	170.4845107382	354.091	144	movie	movie
I.A^i.c._₁₁₃	0.4159829843	0.2928634271	157.4236701613	356.215	144	movie	movie
I.A^i.c._₁₁₄	0.3968779003	0.1661961334	132.2368607224	358.590	144	movie	movie
I.A^i.c._₁₁₅	0.3369172422	0.2901238678	139.2379425543	366.661	148	movie	movie
I.A^i.c._₁₁₆	0.4786094582	0.2027583452	167.5764021354	367.991	148	movie	movie
I.A^i.c._₁₁₇	0.1262212709	0.5844212753	199.4597414280	340.210	148	movie	movie
I.A^i.c._₁₁₈	0.3596345346	0.3768544947	165.4459242130	362.173	148	movie	movie
I.A^i.c._₁₁₉	0.3735693647	0.3814544097	171.6871768580	362.171	148	movie	movie
I.A^i.c._₁₂₀	0.3940559464	0.1363870337	132.4879124177	368.666	148	movie	movie
I.A^i.c._₁₂₁	0.0398375597	0.5900216545	194.6214443391	340.118	148	movie	movie
I.A^i.c._₁₂₂	0.3366050958	0.1545246545	122.1507473925	368.667	148	movie	movie
I.A^i.c._₁₂₃	0.4148912516	0.3594943116	185.0089900186	372.989	152	movie	movie
I.A^i.c._₁₂₄	0.4021066869	0.2059880758	145.8250755871	378.190	152	movie	movie
I.A^i.c._₁₂₅	0.2984912721	0.2642719294	134.6157747992	387.392	156	movie	movie
I.A^i.c._₁₂₆	0.3151887676	0.2026092096	129.5701866405	388.355	156	movie	movie
I.A^i.c._₁₂₇	0.3682819786	0.0540125357	129.1627539603	388.682	156	movie	movie
I.A^i.c._₁₂₈	0.4094064944	0.2504917575	159.2238172130	387.380	156	movie	movie
I.A^i.c._₁₂₉	0.3963021063	0.1609272065	146.2019999818	398.462	160	movie	movie
I.A^i.c._₁₃₀	0.4858230168	0.1897852046	186.6816128151	407.911	164	movie	movie
I.A^i.c._₁₃₁	0.3938225013	0.1332100629	146.4674258412	408.531	164	movie	movie
I.A^i.c._₁₃₂	0.2844202818	0.2576751665	144.7361096869	427.351	172	movie	movie
I.A^i.c._₁₃₃	0.3613650149	0.0662137880	141.3166709722	428.547	172	movie	movie
I.A^i.c._₁₃₄	0.4052729644	0.2262551267	173.3843818847	437.587	176	movie	movie
I.A^i.c._₁₃₅	0.2792503345	0.2309398618	146.5213559661	447.823	180	movie	movie
I.A^i.c._₁₃₆	0.4088863339	0.2475714173	186.9603460122	456.990	184	movie	movie
I.A^i.c._₁₃₇	0.2755037979	0.2512907499	155.4548586490	467.296	188	movie	movie
I.A^i.c._₁₃₈	0.3000356874	0.1954805934	152.1599660045	468.121	188	movie	movie
I.A^i.c._₁₃₉	0.2759217512	0.2671023857	164.8956499133	486.678	196	movie	movie
I.A^i.c._₁₄₀	0.3060236507	0.1574877923	155.4631165813	488.269	196	movie	movie
I.A^i.c._₁₄₁	0.2738106556	0.2266665399	157.9002511121	487.729	196	movie	movie
I.A^i.c._₁₄₂	0.2716635736	0.2803602873	173.2990630202	505.979	204	movie	movie
I.A^i.c._₁₄₃	0.2690738475	0.2460748830	166.5414191753	507.230	204	movie	movie
I.A^i.c._₁₄₄	0.2813047676	0.2931043691	185.0094674080	525.199	212	movie	movie
I.A^i.c._₁₄₅	0.2844033114	0.2864772055	184.1463025888	525.201	212	movie	movie
I.A^i.c._₁₄₆	0.3406159593	0.0878815592	176.4815564147	548.142	220	movie	movie
I.A^i.c._₁₄₇	0.2745076841	0.2185259293	182.4778598891	567.527	228	movie	movie
I.A^i.c._₁₄₈	0.5236560165	0.2615293843	77.5451687834	138.512	56	movie	movie
I.A^i.c._₁₄₉	0.5252433392	0.2395323622	97.1790201428	178.571	72	movie	movie
I.A^i.c._₁₅₀	0.2485711669	0.2285602706	62.8143378441	199.118	80	movie	movie
I.A^i.c._₁₅₁	0.4717436769	0.4159399383	127.4097749092	191.768	80	movie	movie
I.A^i.c._₁₅₂	0.4244996083	0.4906100936	136.0765222404	187.283	80	movie	movie
I.A^i.c._₁₅₃	0.3303010815	0.4704859697	107.3481952603	198.916	84	movie	movie
I.A^i.c._₁₅₄	0.2538439618	0.5599410925	121.1861154175	193.495	84	movie	movie
I.A^i.c._₁₅₅	0.4824594978	0.3739325421	131.7096541850	214.035	88	movie	movie
I.A^i.c._₁₅₆	0.4299480127	0.4772693278	179.4317919632	254.406	108	movie	movie
I.A^i.c._₁₅₇	0.2242029652	0.5716643145	178.2257295831	285.417	124	movie	movie
I.A^i.c._₁₅₈	0.4721688158	0.3825825184	189.2718322389	310.866	128	movie	movie
I.A^i.c._₁₅₉	0.2338958736	0.5689557210	190.6014315264	303.881	132	movie	movie
I.A^i.c._₁₆₀	0.4067612870	0.2352215102	131.6910976773	328.058	132	movie	movie
I.A^i.c._₁₆₁	0.4664129400	0.2183545493	147.4412391934	328.060	132	movie	movie
I.A^i.c._₁₆₂	0.1082811863	0.5839631505	185.8736775605	321.788	140	movie	movie
I.A^i.c._₁₆₃	0.3733531828	0.0372160210	116.4750673801	348.816	140	movie	movie
I.A^i.c._₁₆₄	0.3289795673	0.2068164036	118.9835822292	348.468	140	movie	movie
I.A^i.c._₁₆₅	0.4000579116	0.1916547891	132.0453999094	348.465	140	movie	movie
I.A^i.c._₁₆₆	0.4122855598	0.2657302751	159.0067612686	377.047	152	movie	movie
I.A^i.c._₁₆₇	0.3897682267	0.3744628158	189.3994398298	391.821	160	movie	movie
I.A^i.c._₁₆₈	0.3218496119	0.1559752782	132.7019091118	408.535	164	movie	movie
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