The formation of periodic three-body orbits for Newtonian systems

Open Access

Table 1.

The four braids used in this study.

m	x	y	v_x	v_y

Figure-8 problem (top panel in Fig. 1)
1	0.9700436	−0.24308753	0.466203685	0.43236573
1	−0.9700436	0.24308753	0.466203685	0.43236573
1	0	0	0.93240737	0.86473146

Non-equal-mass problem (= model A, second panel in Fig. 1)

0.87	−0.1855174644	0	0	2.0221546880
0.80	1	0	0	0.3968976468
1.0	0	0	−2.25026390304	0

AI4(0.5) (third panel in Fig. 1)

1	−1	0	0.2009656237	0.2431076328
1	1	0	0.2009656237	0.2431076328
0.5	0	0	−0.8038624948	−0.9724305312

AI68(0.5) (bottom panel in Fig. 1)

1	−1	0	0.2138410831	0.0542938396
1	1	0	0.2138410831	0.0542938396
0.5	0	0	−0.8553643324	−0.2171753584

Notes. The Figure-8, model A, I.A.₄^i.c.(0.5), and $I . A ._{68}^{i . c .} (0.5)$ $Mathematical equation: $ I.A.^{i.c.}_{68}(0.5) $$ . Presented for these braids are the mass of the three components m, the Cartesian positions x, and y, and the corresponding velocities v_x, and v_y. For all particles the Cartesian coordinate z = 0, and velocity v_z = 0.

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