Three Body Orbits

Families / Li–Liao classes

I.A orbits

Class I.A orbits found with Liao’s clean numerical simulation method, for a third body of varying mass.

I.A orbits are periodic solutions of the planar three-body problem. The atlas holds 513 of them, with periods from 4.176 to 199.5, for several mass ratios; 277 of them are linearly stable. They come from Li, Jing & Liao (2018), Over a thousand new periodic orbits of a planar three-body system with unequal masses. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Li, Jing & Liao (2018). Over a thousand new periodic orbits of a planar three-body system with unequal masses. Publications of the Astronomical Society of Japan 70, 64 (doi)

All 513 orbits

I.A.1, a periodic three-body orbitI.A.1 m₃ = 0.5T 4.176I.A.1, a periodic three-body orbitI.A.1 m₃ = 0.75T 5.986I.A.1, a periodic three-body orbitI.A.1 m₃ = 2T 12.65 stableI.A.1, a periodic three-body orbitI.A.1 m₃ = 4T 16.32I.A.1, a periodic three-body orbitI.A.1 m₃ = 5T 53.94 stableI.A.1, a periodic three-body orbitI.A.1 m₃ = 8T 64.95 stableI.A.1, a periodic three-body orbitI.A.1 m₃ = 10T 24.17I.A.2, a periodic three-body orbitI.A.2 m₃ = 0.5T 13.92I.A.2, a periodic three-body orbitI.A.2 m₃ = 0.75T 25.05I.A.2, a periodic three-body orbitI.A.2 m₃ = 2T 11.78 stableI.A.2, a periodic three-body orbitI.A.2 m₃ = 4T 17.65 stableI.A.2, a periodic three-body orbitI.A.2 m₃ = 5T 87.30 stableI.A.2, a periodic three-body orbitI.A.2 m₃ = 8T 110.1I.A.2, a periodic three-body orbitI.A.2 m₃ = 10T 71.27I.A.3, a periodic three-body orbitI.A.3 m₃ = 0.5T 25.94I.A.3, a periodic three-body orbitI.A.3 m₃ = 0.75T 17.36 stableI.A.3, a periodic three-body orbitI.A.3T 37.32I.A.3, a periodic three-body orbitI.A.3 m₃ = 2T 36.68I.A.3, a periodic three-body orbitI.A.3 m₃ = 4T 54.74 stableI.A.3, a periodic three-body orbitI.A.3 m₃ = 5T 128.3I.A.3, a periodic three-body orbitI.A.3 m₃ = 8T 153.4I.A.3, a periodic three-body orbitI.A.3 m₃ = 10T 119.5I.A.4, a periodic three-body orbitI.A.4 m₃ = 0.5T 19.01I.A.4, a periodic three-body orbitI.A.4 m₃ = 0.75T 30.22I.A.4, a periodic three-body orbitI.A.4 m₃ = 2T 36.56 stableI.A.4, a periodic three-body orbitI.A.4 m₃ = 4T 53.99 stableI.A.4, a periodic three-body orbitI.A.4 m₃ = 5T 160.3 stableI.A.4, a periodic three-body orbitI.A.4 m₃ = 8T 196.2I.A.5, a periodic three-body orbitI.A.5 m₃ = 0.5T 28.44I.A.5, a periodic three-body orbitI.A.5 m₃ = 0.75T 20.41I.A.5, a periodic three-body orbitI.A.5 m₃ = 2T 28.11 stableI.A.5, a periodic three-body orbitI.A.5 m₃ = 4T 51.97 stableI.A.5, a periodic three-body orbitI.A.5 m₃ = 5T 160.8 stableI.A.6, a periodic three-body orbitI.A.6 m₃ = 0.5T 15.97I.A.6, a periodic three-body orbitI.A.6 m₃ = 0.75T 10.53I.A.6, a periodic three-body orbitI.A.6 m₃ = 2T 63.11 stableI.A.6, a periodic three-body orbitI.A.6 m₃ = 4T 48.34 stableI.A.6, a periodic three-body orbitI.A.6 m₃ = 5T 199.1I.A.7, a periodic three-body orbitI.A.7 m₃ = 0.5T 14.58I.A.7, a periodic three-body orbitI.A.7 m₃ = 0.75T 36.52I.A.7, a periodic three-body orbitI.A.7T 15.74I.A.7, a periodic three-body orbitI.A.7 m₃ = 2T 61.65I.A.7, a periodic three-body orbitI.A.7 m₃ = 4T 79.69 stableI.A.7, a periodic three-body orbitI.A.7 m₃ = 5T 198.3I.A.8, a periodic three-body orbitI.A.8 m₃ = 0.5T 15.61I.A.8, a periodic three-body orbitI.A.8 m₃ = 0.75T 30.37I.A.8, a periodic three-body orbitI.A.8 m₃ = 2T 60.39 stableI.A.8, a periodic three-body orbitI.A.8 m₃ = 4T 80.64 stableI.A.9, a periodic three-body orbitI.A.9 m₃ = 0.5T 35.28I.A.9, a periodic three-body orbitI.A.9 m₃ = 0.75T 32.19I.A.9, a periodic three-body orbitI.A.9T 43.87I.A.9, a periodic three-body orbitI.A.9 m₃ = 2T 68.53I.A.9, a periodic three-body orbitI.A.9 m₃ = 4T 89.26 stableI.A.10, a periodic three-body orbitI.A.10 m₃ = 0.5T 22.88I.A.10, a periodic three-body orbitI.A.10 m₃ = 0.75T 20.49 stableI.A.10, a periodic three-body orbitI.A.10 m₃ = 2T 68.49I.A.10, a periodic three-body orbitI.A.10 m₃ = 4T 87.27 stableI.A.11, a periodic three-body orbitI.A.11 m₃ = 0.5T 37.84 stableI.A.11, a periodic three-body orbitI.A.11 m₃ = 0.75T 42.80I.A.11, a periodic three-body orbitI.A.11T 49.60I.A.11, a periodic three-body orbitI.A.11 m₃ = 2T 78.69I.A.11, a periodic three-body orbitI.A.11 m₃ = 4T 86.30 stableI.A.12, a periodic three-body orbitI.A.12 m₃ = 0.5T 54.58I.A.12, a periodic three-body orbitI.A.12 m₃ = 0.75T 29.45 stableI.A.12, a periodic three-body orbitI.A.12T 48.27I.A.12, a periodic three-body orbitI.A.12 m₃ = 2T 58.51 stableI.A.12, a periodic three-body orbitI.A.12 m₃ = 4T 80.02 stableI.A.13, a periodic three-body orbitI.A.13 m₃ = 0.5T 39.28I.A.13, a periodic three-body orbitI.A.13 m₃ = 0.75T 39.19 stableI.A.13, a periodic three-body orbitI.A.13 m₃ = 2T 50.55 stableI.A.13, a periodic three-body orbitI.A.13 m₃ = 4T 127.0 stableI.A.14, a periodic three-body orbitI.A.14 m₃ = 0.5T 46.11 stableI.A.14, a periodic three-body orbitI.A.14 m₃ = 0.75T 40.81 stableI.A.14, a periodic three-body orbitI.A.14 m₃ = 2T 81.03I.A.14, a periodic three-body orbitI.A.14 m₃ = 4T 114.2 stableI.A.15, a periodic three-body orbitI.A.15 m₃ = 0.5T 29.02I.A.15, a periodic three-body orbitI.A.15 m₃ = 0.75T 54.26I.A.15, a periodic three-body orbitI.A.15 m₃ = 2T 84.63 stableI.A.15, a periodic three-body orbitI.A.15 m₃ = 4T 113.1I.A.16, a periodic three-body orbitI.A.16 m₃ = 0.5T 37.87 stableI.A.16, a periodic three-body orbitI.A.16 m₃ = 0.75T 82.14I.A.16, a periodic three-body orbitI.A.16 m₃ = 2T 105.2 stableI.A.16, a periodic three-body orbitI.A.16 m₃ = 4T 122.6 stableI.A.17, a periodic three-body orbitI.A.17 m₃ = 0.5T 30.51I.A.17, a periodic three-body orbitI.A.17 m₃ = 0.75T 55.11I.A.17, a periodic three-body orbitI.A.17 m₃ = 2T 111.7I.A.17, a periodic three-body orbitI.A.17 m₃ = 4T 121.6 stableI.A.18, a periodic three-body orbitI.A.18 m₃ = 0.5T 59.77 stableI.A.18, a periodic three-body orbitI.A.18 m₃ = 0.75T 41.14 stableI.A.18, a periodic three-body orbitI.A.18 m₃ = 2T 67.36I.A.18, a periodic three-body orbitI.A.18 m₃ = 4T 119.7 stableI.A.19, a periodic three-body orbitI.A.19 m₃ = 0.5T 54.54 stableI.A.19, a periodic three-body orbitI.A.19 m₃ = 0.75T 62.50I.A.19, a periodic three-body orbitI.A.19 m₃ = 2T 80.20 stableI.A.19, a periodic three-body orbitI.A.19 m₃ = 4T 118.7 stableI.A.20, a periodic three-body orbitI.A.20 m₃ = 0.5T 46.21 stableI.A.20, a periodic three-body orbitI.A.20 m₃ = 0.75T 34.88I.A.20, a periodic three-body orbitI.A.20T 53.69I.A.20, a periodic three-body orbitI.A.20 m₃ = 2T 131.1I.A.20, a periodic three-body orbitI.A.20 m₃ = 4T 163.1 stableI.A.21, a periodic three-body orbitI.A.21 m₃ = 0.5T 62.71 stableI.A.21, a periodic three-body orbitI.A.21 m₃ = 0.75T 67.66I.A.21, a periodic three-body orbitI.A.21 m₃ = 2T 104.9 stableI.A.21, a periodic three-body orbitI.A.21 m₃ = 4T 165.7 stableI.A.22, a periodic three-body orbitI.A.22 m₃ = 0.5T 54.57 stableI.A.22, a periodic three-body orbitI.A.22 m₃ = 0.75T 66.77I.A.22, a periodic three-body orbitI.A.22T 78.40I.A.22, a periodic three-body orbitI.A.22 m₃ = 2T 103.0 stableI.A.22, a periodic three-body orbitI.A.22 m₃ = 4T 160.9 stableI.A.23, a periodic three-body orbitI.A.23 m₃ = 0.5T 57.06I.A.23, a periodic three-body orbitI.A.23 m₃ = 0.75T 52.52 stableI.A.23, a periodic three-body orbitI.A.23 m₃ = 2T 104.5 stableI.A.23, a periodic three-body orbitI.A.23 m₃ = 4T 159.9 stableI.A.24, a periodic three-body orbitI.A.24 m₃ = 0.5T 45.17 stableI.A.24, a periodic three-body orbitI.A.24 m₃ = 0.75T 55.67 stableI.A.24, a periodic three-body orbitI.A.24 m₃ = 2T 90.80 stableI.A.24, a periodic three-body orbitI.A.24 m₃ = 4T 149.0I.A.25, a periodic three-body orbitI.A.25 m₃ = 0.5T 71.48 stableI.A.25, a periodic three-body orbitI.A.25 m₃ = 0.75T 81.56I.A.25, a periodic three-body orbitI.A.25T 73.28I.A.25, a periodic three-body orbitI.A.25 m₃ = 2T 112.3I.A.25, a periodic three-body orbitI.A.25 m₃ = 4T 157.9 stableI.A.26, a periodic three-body orbitI.A.26 m₃ = 0.5T 70.98 stableI.A.26, a periodic three-body orbitI.A.26 m₃ = 0.75T 52.84 stableI.A.26, a periodic three-body orbitI.A.26 m₃ = 2T 86.30I.A.26, a periodic three-body orbitI.A.26 m₃ = 4T 199.2I.A.27, a periodic three-body orbitI.A.27 m₃ = 0.5T 56.68I.A.27, a periodic three-body orbitI.A.27 m₃ = 0.75T 79.27I.A.27, a periodic three-body orbitI.A.27 m₃ = 2T 143.0I.A.27, a periodic three-body orbitI.A.27 m₃ = 4T 184.6I.A.28, a periodic three-body orbitI.A.28 m₃ = 0.5T 46.21I.A.28, a periodic three-body orbitI.A.28 m₃ = 0.75T 63.89 stableI.A.28, a periodic three-body orbitI.A.28 m₃ = 2T 109.9I.A.28, a periodic three-body orbitI.A.28 m₃ = 4T 198.4I.A.29, a periodic three-body orbitI.A.29 m₃ = 0.5T 62.94 stableI.A.29, a periodic three-body orbitI.A.29 m₃ = 0.75T 93.40I.A.29, a periodic three-body orbitI.A.29 m₃ = 2T 186.6 stableI.A.29, a periodic three-body orbitI.A.29 m₃ = 4T 180.3I.A.30, a periodic three-body orbitI.A.30 m₃ = 0.5T 49.72 stableI.A.30, a periodic three-body orbitI.A.30 m₃ = 0.75T 81.34I.A.30, a periodic three-body orbitI.A.30T 85.79I.A.30, a periodic three-body orbitI.A.30 m₃ = 2T 172.7 stableI.A.30, a periodic three-body orbitI.A.30 m₃ = 4T 178.3I.A.31, a periodic three-body orbitI.A.31 m₃ = 0.5T 77.77I.A.31, a periodic three-body orbitI.A.31 m₃ = 0.75T 64.22 stableI.A.31, a periodic three-body orbitI.A.31T 82.36I.A.31, a periodic three-body orbitI.A.31 m₃ = 2T 130.4 stableI.A.31, a periodic three-body orbitI.A.31 m₃ = 4T 193.2 stableI.A.32, a periodic three-body orbitI.A.32 m₃ = 0.5T 49.17I.A.32, a periodic three-body orbitI.A.32 m₃ = 0.75T 80.18I.A.32, a periodic three-body orbitI.A.32 m₃ = 2T 107.6I.A.32, a periodic three-body orbitI.A.32 m₃ = 4T 192.2 stableI.A.33, a periodic three-body orbitI.A.33 m₃ = 0.5T 84.01 stableI.A.33, a periodic three-body orbitI.A.33 m₃ = 0.75T 46.15 stableI.A.33, a periodic three-body orbitI.A.33 m₃ = 2T 127.5 stableI.A.33, a periodic three-body orbitI.A.33 m₃ = 4T 191.2 stableI.A.34, a periodic three-body orbitI.A.34 m₃ = 0.5T 63.24 stableI.A.34, a periodic three-body orbitI.A.34 m₃ = 0.75T 91.57I.A.34, a periodic three-body orbitI.A.34T 95.88I.A.34, a periodic three-body orbitI.A.34 m₃ = 2T 108.9 stableI.A.35, a periodic three-body orbitI.A.35 m₃ = 0.5T 87.68I.A.35, a periodic three-body orbitI.A.35 m₃ = 0.75T 74.65 stableI.A.35, a periodic three-body orbitI.A.35 m₃ = 2T 105.3I.A.36, a periodic three-body orbitI.A.36 m₃ = 0.5T 79.24 stableI.A.36, a periodic three-body orbitI.A.36 m₃ = 0.75T 64.54 stableI.A.36, a periodic three-body orbitI.A.36 m₃ = 2T 138.4I.A.37, a periodic three-body orbitI.A.37 m₃ = 0.5T 71.32 stableI.A.37, a periodic three-body orbitI.A.37 m₃ = 0.75T 75.62 stableI.A.37, a periodic three-body orbitI.A.37T 92.29I.A.37, a periodic three-body orbitI.A.37 m₃ = 2T 148.4 stableI.A.38, a periodic three-body orbitI.A.38 m₃ = 0.5T 108.5I.A.38, a periodic three-body orbitI.A.38 m₃ = 0.75T 75.92 stableI.A.38, a periodic three-body orbitI.A.38 m₃ = 2T 163.4 stableI.A.39, a periodic three-body orbitI.A.39 m₃ = 0.5T 88.09 stableI.A.39, a periodic three-body orbitI.A.39 m₃ = 0.75T 76.24 stableI.A.39, a periodic three-body orbitI.A.39 m₃ = 2T 177.3 stableI.A.40, a periodic three-body orbitI.A.40 m₃ = 0.5T 71.57 stableI.A.40, a periodic three-body orbitI.A.40 m₃ = 0.75T 105.1I.A.40, a periodic three-body orbitI.A.40 m₃ = 2T 131.3 stableI.A.41, a periodic three-body orbitI.A.41 m₃ = 0.5T 51.57 stableI.A.41, a periodic three-body orbitI.A.41 m₃ = 0.75T 89.48I.A.41, a periodic three-body orbitI.A.41T 102.8 stableI.A.41, a periodic three-body orbitI.A.41 m₃ = 2T 152.8 stableI.A.42, a periodic three-body orbitI.A.42 m₃ = 0.5T 55.48I.A.42, a periodic three-body orbitI.A.42 m₃ = 0.75T 115.8I.A.42, a periodic three-body orbitI.A.42 m₃ = 2T 126.1I.A.43, a periodic three-body orbitI.A.43 m₃ = 0.5T 96.66 stableI.A.43, a periodic three-body orbitI.A.43 m₃ = 0.75T 96.60 stableI.A.43, a periodic three-body orbitI.A.43 m₃ = 2T 169.5 stableI.A.44, a periodic three-body orbitI.A.44 m₃ = 0.5T 87.54 stableI.A.44, a periodic three-body orbitI.A.44 m₃ = 0.75T 87.63 stableI.A.44, a periodic three-body orbitI.A.44T 90.42 stableI.A.44, a periodic three-body orbitI.A.44 m₃ = 2T 134.0 stableI.A.45, a periodic three-body orbitI.A.45 m₃ = 0.5T 78.66I.A.45, a periodic three-body orbitI.A.45 m₃ = 0.75T 98.64 stableI.A.45, a periodic three-body orbitI.A.45 m₃ = 2T 123.2 stableI.A.46, a periodic three-body orbitI.A.46 m₃ = 0.5T 64.59 stableI.A.46, a periodic three-body orbitI.A.46 m₃ = 0.75T 115.7I.A.46, a periodic three-body orbitI.A.46 m₃ = 2T 149.4I.A.47, a periodic three-body orbitI.A.47 m₃ = 0.5T 87.02I.A.47, a periodic three-body orbitI.A.47 m₃ = 0.75T 109.4I.A.47, a periodic three-body orbitI.A.47 m₃ = 2T 127.6I.A.48, a periodic three-body orbitI.A.48 m₃ = 0.5T 103.6I.A.48, a periodic three-body orbitI.A.48 m₃ = 0.75T 87.94 stableI.A.48, a periodic three-body orbitI.A.48T 37.03I.A.48, a periodic three-body orbitI.A.48 m₃ = 2T 174.3 stableI.A.49, a periodic three-body orbitI.A.49 m₃ = 0.5T 79.91 stableI.A.49, a periodic three-body orbitI.A.49 m₃ = 0.75T 143.2I.A.49, a periodic three-body orbitI.A.49T 61.07I.A.49, a periodic three-body orbitI.A.49 m₃ = 2T 166.5 stableI.A.50, a periodic three-body orbitI.A.50 m₃ = 0.5T 131.7I.A.50, a periodic three-body orbitI.A.50 m₃ = 0.75T 99.33 stableI.A.50, a periodic three-body orbitI.A.50T 61.51I.A.50, a periodic three-body orbitI.A.50 m₃ = 2T 169.6I.A.51, a periodic three-body orbitI.A.51 m₃ = 0.5T 80.42I.A.51, a periodic three-body orbitI.A.51 m₃ = 0.75T 109.5 stableI.A.51, a periodic three-body orbitI.A.51T 61.70I.A.51, a periodic three-body orbitI.A.51 m₃ = 2T 174.5I.A.52, a periodic three-body orbitI.A.52 m₃ = 0.5T 110.3I.A.52, a periodic three-body orbitI.A.52 m₃ = 0.75T 139.2I.A.52, a periodic three-body orbitI.A.52T 107.2I.A.52, a periodic three-body orbitI.A.52 m₃ = 2T 148.9I.A.53, a periodic three-body orbitI.A.53 m₃ = 0.5T 98.77I.A.53, a periodic three-body orbitI.A.53 m₃ = 0.75T 129.6I.A.53, a periodic three-body orbitI.A.53T 90.27I.A.53, a periodic three-body orbitI.A.53 m₃ = 2T 173.6 stableI.A.54, a periodic three-body orbitI.A.54 m₃ = 0.5T 95.81 stableI.A.54, a periodic three-body orbitI.A.54 m₃ = 0.75T 76.28 stableI.A.54, a periodic three-body orbitI.A.54T 113.0I.A.54, a periodic three-body orbitI.A.54 m₃ = 2T 145.0 stableI.A.55, a periodic three-body orbitI.A.55 m₃ = 0.5T 68.40 stableI.A.55, a periodic three-body orbitI.A.55 m₃ = 0.75T 110.4 stableI.A.55, a periodic three-body orbitI.A.55T 121.7I.A.55, a periodic three-body orbitI.A.55 m₃ = 2T 176.9I.A.56, a periodic three-body orbitI.A.56 m₃ = 0.5T 70.75I.A.56, a periodic three-body orbitI.A.56 m₃ = 0.75T 99.64 stableI.A.56, a periodic three-body orbitI.A.56T 112.8I.A.56, a periodic three-body orbitI.A.56 m₃ = 2T 191.3 stableI.A.57, a periodic three-body orbitI.A.57 m₃ = 0.5T 104.1 stableI.A.57, a periodic three-body orbitI.A.57 m₃ = 0.75T 113.7I.A.57, a periodic three-body orbitI.A.57T 114.4I.A.57, a periodic three-body orbitI.A.57 m₃ = 2T 196.6 stableI.A.58, a periodic three-body orbitI.A.58 m₃ = 0.5T 104.1 stableI.A.58, a periodic three-body orbitI.A.58 m₃ = 0.75T 139.7I.A.58, a periodic three-body orbitI.A.58T 130.1I.A.58, a periodic three-body orbitI.A.58 m₃ = 2T 177.8 stableI.A.59, a periodic three-body orbitI.A.59 m₃ = 0.5T 125.3I.A.59, a periodic three-body orbitI.A.59 m₃ = 0.75T 110.7 stableI.A.59, a periodic three-body orbitI.A.59T 126.2I.A.59, a periodic three-body orbitI.A.59 m₃ = 2T 161.3I.A.60, a periodic three-body orbitI.A.60 m₃ = 0.5T 64.89 stableI.A.60, a periodic three-body orbitI.A.60 m₃ = 0.75T 100.0 stableI.A.60, a periodic three-body orbitI.A.60T 134.9I.A.60, a periodic three-body orbitI.A.60 m₃ = 2T 198.9 stableI.A.61, a periodic three-body orbitI.A.61 m₃ = 0.5T 130.4I.A.61, a periodic three-body orbitI.A.61 m₃ = 0.75T 140.4I.A.61, a periodic three-body orbitI.A.61T 103.5I.A.61, a periodic three-body orbitI.A.61 m₃ = 2T 181.3I.A.62, a periodic three-body orbitI.A.62 m₃ = 0.5T 70.28 stableI.A.62, a periodic three-body orbitI.A.62 m₃ = 0.75T 111.0 stableI.A.62, a periodic three-body orbitI.A.62T 139.0I.A.62, a periodic three-body orbitI.A.62 m₃ = 2T 186.0 stableI.A.63, a periodic three-body orbitI.A.63 m₃ = 0.5T 112.4 stableI.A.63, a periodic three-body orbitI.A.63 m₃ = 0.75T 126.7 stableI.A.63, a periodic three-body orbitI.A.63T 128.9 stableI.A.64, a periodic three-body orbitI.A.64 m₃ = 0.5T 101.3I.A.64, a periodic three-body orbitI.A.64 m₃ = 0.75T 99.88I.A.64, a periodic three-body orbitI.A.64T 121.3 stableI.A.65, a periodic three-body orbitI.A.65 m₃ = 0.5T 129.7I.A.65, a periodic three-body orbitI.A.65 m₃ = 0.75T 111.3 stableI.A.65, a periodic three-body orbitI.A.65T 101.4 stableI.A.66, a periodic three-body orbitI.A.66 m₃ = 0.5T 112.0I.A.66, a periodic three-body orbitI.A.66 m₃ = 0.75T 131.8 stableI.A.66, a periodic three-body orbitI.A.66T 143.5I.A.67, a periodic three-body orbitI.A.67 m₃ = 0.5T 121.8 stableI.A.67, a periodic three-body orbitI.A.67 m₃ = 0.75T 111.7 stableI.A.67, a periodic three-body orbitI.A.67T 117.5I.A.68, a periodic three-body orbitI.A.68 m₃ = 0.5T 83.85 stableI.A.68, a periodic three-body orbitI.A.68 m₃ = 0.75T 87.21 stableI.A.69, a periodic three-body orbitI.A.69 m₃ = 0.5T 96.94 stableI.A.69, a periodic three-body orbitI.A.69 m₃ = 0.75T 125.3 stableI.A.69, a periodic three-body orbitI.A.69T 140.9I.A.70, a periodic three-body orbitI.A.70 m₃ = 0.5T 110.8I.A.70, a periodic three-body orbitI.A.70 m₃ = 0.75T 133.4 stableI.A.70, a periodic three-body orbitI.A.70T 164.8I.A.71, a periodic three-body orbitI.A.71 m₃ = 0.5T 129.0I.A.71, a periodic three-body orbitI.A.71 m₃ = 0.75T 145.7 stableI.A.71, a periodic three-body orbitI.A.71T 134.2 stableI.A.72, a periodic three-body orbitI.A.72 m₃ = 0.5T 115.5I.A.72, a periodic three-body orbitI.A.72 m₃ = 0.75T 100.4 stableI.A.73, a periodic three-body orbitI.A.73 m₃ = 0.5T 82.32I.A.73, a periodic three-body orbitI.A.73 m₃ = 0.75T 133.8 stableI.A.73, a periodic three-body orbitI.A.73T 164.6I.A.74, a periodic three-body orbitI.A.74 m₃ = 0.5T 94.45I.A.74, a periodic three-body orbitI.A.74 m₃ = 0.75T 136.8 stableI.A.74, a periodic three-body orbitI.A.74T 119.7I.A.75, a periodic three-body orbitI.A.75 m₃ = 0.5T 85.76 stableI.A.75, a periodic three-body orbitI.A.75 m₃ = 0.75T 123.0 stableI.A.75, a periodic three-body orbitI.A.75T 127.4I.A.76, a periodic three-body orbitI.A.76 m₃ = 0.5T 130.6I.A.76, a periodic three-body orbitI.A.76 m₃ = 0.75T 134.1 stableI.A.76, a periodic three-body orbitI.A.76T 111.6I.A.77, a periodic three-body orbitI.A.77 m₃ = 0.5T 130.1 stableI.A.77, a periodic three-body orbitI.A.77 m₃ = 0.75T 134.4 stableI.A.77, a periodic three-body orbitI.A.77T 114.6 stableI.A.78, a periodic three-body orbitI.A.78 m₃ = 0.5T 105.3 stableI.A.78, a periodic three-body orbitI.A.78 m₃ = 0.75T 153.8 stableI.A.78, a periodic three-body orbitI.A.78T 104.0 stableI.A.79, a periodic three-body orbitI.A.79 m₃ = 0.5T 138.8 stableI.A.79, a periodic three-body orbitI.A.79 m₃ = 0.75T 134.7 stableI.A.79, a periodic three-body orbitI.A.79T 155.8 stableI.A.80, a periodic three-body orbitI.A.80 m₃ = 0.5T 89.89I.A.80, a periodic three-body orbitI.A.80 m₃ = 0.75T 125.9I.A.80, a periodic three-body orbitI.A.80T 116.6 stableI.A.81, a periodic three-body orbitI.A.81 m₃ = 0.5T 117.9I.A.81, a periodic three-body orbitI.A.81 m₃ = 0.75T 157.3 stableI.A.81, a periodic three-body orbitI.A.81T 179.1I.A.82, a periodic three-body orbitI.A.82 m₃ = 0.5T 124.5I.A.82, a periodic three-body orbitI.A.82 m₃ = 0.75T 122.9 stableI.A.82, a periodic three-body orbitI.A.82T 132.0I.A.83, a periodic three-body orbitI.A.83 m₃ = 0.5T 121.7 stableI.A.83, a periodic three-body orbitI.A.83 m₃ = 0.75T 157.9 stableI.A.83, a periodic three-body orbitI.A.83T 169.0 stableI.A.84, a periodic three-body orbitI.A.84 m₃ = 0.5T 135.4 stableI.A.84, a periodic three-body orbitI.A.84 m₃ = 0.75T 166.8I.A.84, a periodic three-body orbitI.A.84T 104.3 stableI.A.85, a periodic three-body orbitI.A.85 m₃ = 0.5T 124.4I.A.85, a periodic three-body orbitI.A.85 m₃ = 0.75T 158.1 stableI.A.85, a periodic three-body orbitI.A.85T 117.5 stableI.A.86, a periodic three-body orbitI.A.86 m₃ = 0.5T 88.99 stableI.A.86, a periodic three-body orbitI.A.86 m₃ = 0.75T 179.9 stableI.A.86, a periodic three-body orbitI.A.86T 137.7I.A.87, a periodic three-body orbitI.A.87 m₃ = 0.5T 100.1 stableI.A.87, a periodic three-body orbitI.A.87 m₃ = 0.75T 123.6 stableI.A.87, a periodic three-body orbitI.A.87T 128.3I.A.88, a periodic three-body orbitI.A.88 m₃ = 0.5T 151.0 stableI.A.88, a periodic three-body orbitI.A.88 m₃ = 0.75T 135.0I.A.88, a periodic three-body orbitI.A.88T 157.3 stableI.A.89, a periodic three-body orbitI.A.89 m₃ = 0.5T 130.2 stableI.A.89, a periodic three-body orbitI.A.89 m₃ = 0.75T 158.9 stableI.A.89, a periodic three-body orbitI.A.89T 115.4I.A.90, a periodic three-body orbitI.A.90 m₃ = 0.5T 107.9 stableI.A.90, a periodic three-body orbitI.A.90 m₃ = 0.75T 128.2 stableI.A.90, a periodic three-body orbitI.A.90T 152.0 stableI.A.91, a periodic three-body orbitI.A.91 m₃ = 0.5T 121.9 stableI.A.91, a periodic three-body orbitI.A.91 m₃ = 0.75T 169.8 stableI.A.91, a periodic three-body orbitI.A.91T 104.5 stableI.A.92, a periodic three-body orbitI.A.92 m₃ = 0.5T 133.9I.A.92, a periodic three-body orbitI.A.92 m₃ = 0.75T 181.0 stableI.A.92, a periodic three-body orbitI.A.92T 130.2 stableI.A.93, a periodic three-body orbitI.A.93 m₃ = 0.5T 154.7I.A.93, a periodic three-body orbitI.A.93 m₃ = 0.75T 170.2 stableI.A.93, a periodic three-body orbitI.A.93T 117.9 stableI.A.94, a periodic three-body orbitI.A.94 m₃ = 0.5T 101.6I.A.94, a periodic three-body orbitI.A.94 m₃ = 0.75T 155.4I.A.94, a periodic three-body orbitI.A.94T 195.8I.A.95, a periodic three-body orbitI.A.95 m₃ = 0.5T 163.9 stableI.A.95, a periodic three-body orbitI.A.95 m₃ = 0.75T 192.1 stableI.A.95, a periodic three-body orbitI.A.95T 199.4I.A.96, a periodic three-body orbitI.A.96 m₃ = 0.5T 130.3 stableI.A.96, a periodic three-body orbitI.A.96 m₃ = 0.75T 180.8 stableI.A.96, a periodic three-body orbitI.A.96T 110.1 stableI.A.97, a periodic three-body orbitI.A.97 m₃ = 0.5T 138.5 stableI.A.97, a periodic three-body orbitI.A.97 m₃ = 0.75T 192.4 stableI.A.97, a periodic three-body orbitI.A.97T 164.9 stableI.A.98, a periodic three-body orbitI.A.98 m₃ = 0.5T 110.5I.A.98, a periodic three-body orbitI.A.98 m₃ = 0.75T 181.9 stableI.A.98, a periodic three-body orbitI.A.98T 125.8I.A.99, a periodic three-body orbitI.A.99 m₃ = 0.5T 147.0 stableI.A.99, a periodic three-body orbitI.A.99 m₃ = 0.75T 175.4 stableI.A.99, a periodic three-body orbitI.A.99T 121.4I.A.100, a periodic three-body orbitI.A.100 m₃ = 0.5T 115.8 stableI.A.100, a periodic three-body orbitI.A.100 m₃ = 0.75T 149.0 stableI.A.100, a periodic three-body orbitI.A.100T 163.9 stableI.A.101, a periodic three-body orbitI.A.101 m₃ = 0.5T 180.2I.A.101, a periodic three-body orbitI.A.101 m₃ = 0.75T 153.9I.A.101, a periodic three-body orbitI.A.101T 153.6 stableI.A.102, a periodic three-body orbitI.A.102 m₃ = 0.5T 139.0 stableI.A.102, a periodic three-body orbitI.A.102 m₃ = 0.75T 186.0 stableI.A.102, a periodic three-body orbitI.A.102T 131.5 stableI.A.103, a periodic three-body orbitI.A.103 m₃ = 0.5T 146.8 stableI.A.103, a periodic three-body orbitI.A.103T 118.3 stableI.A.104, a periodic three-body orbitI.A.104 m₃ = 0.5T 174.3I.A.104, a periodic three-body orbitI.A.104T 155.4 stableI.A.105, a periodic three-body orbitI.A.105 m₃ = 0.5T 109.5I.A.105, a periodic three-body orbitI.A.105T 113.5I.A.106, a periodic three-body orbitI.A.106 m₃ = 0.5T 105.3I.A.106, a periodic three-body orbitI.A.106T 116.8I.A.107, a periodic three-body orbitI.A.107 m₃ = 0.5T 162.0 stableI.A.107, a periodic three-body orbitI.A.107T 176.6 stableI.A.108, a periodic three-body orbitI.A.108 m₃ = 0.5T 186.9I.A.108, a periodic three-body orbitI.A.108T 118.5 stableI.A.109, a periodic three-body orbitI.A.109 m₃ = 0.5T 147.0 stableI.A.109, a periodic three-body orbitI.A.109T 145.5 stableI.A.110, a periodic three-body orbitI.A.110 m₃ = 0.5T 116.7I.A.110, a periodic three-body orbitI.A.110T 131.9 stableI.A.111, a periodic three-body orbitI.A.111 m₃ = 0.5T 180.3I.A.111, a periodic three-body orbitI.A.111T 195.8 stableI.A.112, a periodic three-body orbitI.A.112 m₃ = 0.5T 110.2I.A.112, a periodic three-body orbitI.A.112T 170.5 stableI.A.113, a periodic three-body orbitI.A.113 m₃ = 0.5T 147.3 stableI.A.113, a periodic three-body orbitI.A.113T 157.4 stableI.A.114, a periodic three-body orbitI.A.114 m₃ = 0.5T 118.5 stableI.A.114, a periodic three-body orbitI.A.114T 132.2 stableI.A.115, a periodic three-body orbitI.A.115 m₃ = 0.5T 179.4I.A.115, a periodic three-body orbitI.A.115T 139.2 stableI.A.116, a periodic three-body orbitI.A.116 m₃ = 0.5T 124.3I.A.116, a periodic three-body orbitI.A.116T 167.6I.A.117, a periodic three-body orbitI.A.117 m₃ = 0.5T 163.6 stableI.A.117, a periodic three-body orbitI.A.117T 199.5 stableI.A.118, a periodic three-body orbitI.A.118 m₃ = 0.5T 189.1 stableI.A.118, a periodic three-body orbitI.A.118T 165.4I.A.119, a periodic three-body orbitI.A.119 m₃ = 0.5T 172.0I.A.119, a periodic three-body orbitI.A.119T 171.7I.A.120, a periodic three-body orbitI.A.120 m₃ = 0.5T 178.5 stableI.A.120, a periodic three-body orbitI.A.120T 132.5 stableI.A.121, a periodic three-body orbitI.A.121 m₃ = 0.5T 164.0 stableI.A.121, a periodic three-body orbitI.A.121T 194.6 stableI.A.122, a periodic three-body orbitI.A.122 m₃ = 0.5T 172.0 stableI.A.122, a periodic three-body orbitI.A.122T 122.2 stableI.A.123, a periodic three-body orbitI.A.123 m₃ = 0.5T 179.7 stableI.A.123, a periodic three-body orbitI.A.123T 185.0 stableI.A.124, a periodic three-body orbitI.A.124 m₃ = 0.5T 133.4I.A.124, a periodic three-body orbitI.A.124T 145.8 stableI.A.125, a periodic three-body orbitI.A.125 m₃ = 0.5T 190.9I.A.125, a periodic three-body orbitI.A.125T 134.6I.A.126, a periodic three-body orbitI.A.126 m₃ = 0.5T 196.4 stableI.A.126, a periodic three-body orbitI.A.126T 129.6I.A.127, a periodic three-body orbitI.A.127 m₃ = 0.5T 172.1 stableI.A.127, a periodic three-body orbitI.A.127T 129.2I.A.128, a periodic three-body orbitI.A.128 m₃ = 0.5T 128.6I.A.128, a periodic three-body orbitI.A.128T 159.2 stableI.A.129, a periodic three-body orbitI.A.129 m₃ = 0.5T 194.7I.A.129, a periodic three-body orbitI.A.129T 146.2 stableI.A.130, a periodic three-body orbitI.A.130 m₃ = 0.5T 128.9I.A.130, a periodic three-body orbitI.A.130T 186.7I.A.131, a periodic three-body orbitI.A.131 m₃ = 0.5T 149.5 stableI.A.131, a periodic three-body orbitI.A.131T 146.5 stableI.A.132, a periodic three-body orbitI.A.132 m₃ = 0.5T 135.9I.A.132, a periodic three-body orbitI.A.132T 144.7I.A.133, a periodic three-body orbitI.A.133 m₃ = 0.5T 189.2 stableI.A.133, a periodic three-body orbitI.A.133T 141.3I.A.134, a periodic three-body orbitI.A.134 m₃ = 0.5T 188.8 stableI.A.134, a periodic three-body orbitI.A.134T 173.4 stableI.A.135, a periodic three-body orbitI.A.135 m₃ = 0.5T 130.9 stableI.A.135, a periodic three-body orbitI.A.135T 146.5I.A.136, a periodic three-body orbitI.A.136 m₃ = 0.5T 197.7 stableI.A.136, a periodic three-body orbitI.A.136T 187.0 stableI.A.137, a periodic three-body orbitI.A.137 m₃ = 0.5T 155.0 stableI.A.137, a periodic three-body orbitI.A.137T 155.5I.A.138, a periodic three-body orbitI.A.138 m₃ = 0.5T 158.1 stableI.A.138, a periodic three-body orbitI.A.138T 152.2I.A.139, a periodic three-body orbitI.A.139 m₃ = 0.5T 185.5I.A.139, a periodic three-body orbitI.A.139T 164.9I.A.140, a periodic three-body orbitI.A.140 m₃ = 0.5T 156.9 stableI.A.140, a periodic three-body orbitI.A.140T 155.5 stableI.A.141, a periodic three-body orbitI.A.141 m₃ = 0.5T 197.4 stableI.A.141, a periodic three-body orbitI.A.141T 157.9I.A.142, a periodic three-body orbitI.A.142 m₃ = 0.5T 170.9 stableI.A.142, a periodic three-body orbitI.A.142T 173.3I.A.143, a periodic three-body orbitI.A.143 m₃ = 0.5T 163.7I.A.143, a periodic three-body orbitI.A.143T 166.5I.A.144, a periodic three-body orbitI.A.144 m₃ = 0.5T 183.7 stableI.A.144, a periodic three-body orbitI.A.144T 185.0I.A.145, a periodic three-body orbitI.A.145 m₃ = 0.5T 183.6 stableI.A.145, a periodic three-body orbitI.A.145T 184.1 stableI.A.146, a periodic three-body orbitI.A.146 m₃ = 0.5T 196.5 stableI.A.146, a periodic three-body orbitI.A.146T 176.5 stableI.A.147, a periodic three-body orbitI.A.147 m₃ = 0.5T 198.9I.A.147, a periodic three-body orbitI.A.147T 182.5I.A.148, a periodic three-body orbitI.A.148T 77.55I.A.149, a periodic three-body orbitI.A.149T 97.18I.A.150, a periodic three-body orbitI.A.150T 62.81I.A.151, a periodic three-body orbitI.A.151T 127.4I.A.152, a periodic three-body orbitI.A.152T 136.1I.A.153, a periodic three-body orbitI.A.153T 107.3I.A.154, a periodic three-body orbitI.A.154T 121.2I.A.155, a periodic three-body orbitI.A.155T 131.7I.A.156, a periodic three-body orbitI.A.156T 179.4I.A.157, a periodic three-body orbitI.A.157T 178.2I.A.158, a periodic three-body orbitI.A.158T 189.3I.A.159, a periodic three-body orbitI.A.159T 190.6I.A.160, a periodic three-body orbitI.A.160T 131.7 stableI.A.161, a periodic three-body orbitI.A.161T 147.4I.A.162, a periodic three-body orbitI.A.162T 185.9I.A.163, a periodic three-body orbitI.A.163T 116.5I.A.164, a periodic three-body orbitI.A.164T 119.0I.A.165, a periodic three-body orbitI.A.165T 132.0 stableI.A.166, a periodic three-body orbitI.A.166T 159.0 stableI.A.167, a periodic three-body orbitI.A.167T 189.4I.A.168, a periodic three-body orbitI.A.168T 132.7 stableI.A.169, a periodic three-body orbitI.A.169T 143.8I.A.170, a periodic three-body orbitI.A.170T 172.8 stableI.A.171, a periodic three-body orbitI.A.171T 159.8 stableI.A.172, a periodic three-body orbitI.A.172T 160.0 stableI.A.173, a periodic three-body orbitI.A.173T 185.1 stableI.A.174, a periodic three-body orbitI.A.174T 190.9 stableI.A.175, a periodic three-body orbitI.A.175T 160.2 stableI.A.176, a periodic three-body orbitI.A.176T 153.9I.A.177, a periodic three-body orbitI.A.177T 197.5 stableI.A.178, a periodic three-body orbitI.A.178T 143.9 stableI.A.179, a periodic three-body orbitI.A.179T 160.4 stableI.A.180, a periodic three-body orbitI.A.180T 173.9 stableI.A.181, a periodic three-body orbitI.A.181T 187.2 stableI.A.182, a periodic three-body orbitI.A.182T 174.4 stableI.A.183, a periodic three-body orbitI.A.183T 192.5 stableI.A.184, a periodic three-body orbitI.A.184T 187.7 stableI.A.185, a periodic three-body orbitI.A.185T 164.8 stableI.A.186, a periodic three-body orbitI.A.186T 188.1 stableI.A.187, a periodic three-body orbitI.A.187T 176.2I.A.188, a periodic three-body orbitI.A.188T 183.6I.A.189, a periodic three-body orbitI.A.189T 169.8I.A.190, a periodic three-body orbitI.A.190T 188.4 stable