Abstract
We report on the different results concerning the stability of the hierarchical triple systems where a close binary is accompanied by a third star. There are different possible approaches to answer the question of the stability limits for such triple stars: the most direct investigations can be undertaken in integrating numerically the respective equations of motion for many different initial conditions. It is then difficult to take into account all the important parameters like eccentricities, inclination, phases and masses. Analytical approaches and qualitative methods are more approriate to deal with this problem; the respective results confirm the numerically found results that:
1. for prograde orbits the ratio semimajor axis of the inner orbits to the periastron position of the outer orbit is approximately 3.2
2. for retrograde orbits this ratio is just some 10 percents smaller
3. the results are not sensitive in what concerns the masses involved
4. There is a tendency that the inclinations and eccentricities change slightly the stability limits mentioned above.
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References
Aarseth, S.J., Anasova, J.P., Orlov, V.V., Szebehely, V.G.: 1994, Close triple approaches and escape in the three-body problem, Cel.Mech. and Dynamic.Astron., 60, 131–137
Abt, Helmut, A.: 1986,: The Ages and Dimensions of Trapezian Systems, AJ 304, p.688–694
Batten, Alan, H.: 1973, Binary and multiple systems of stars, Pergamon Press.
Docobo, J.A.: 1977, Aplicación de la teoría de Perturbaciones al estudio de sistema estelares triples, Tesis Doctoral, Universidad de Zaragoza
Docobo, J.A., Prieto, C.: 1988, The Stellar Three-body Problem. Explicit Formulation for Computing Peturbations, Pub. Obs.Ast R.M. Aller 46
Docobo, J.A., Prieto, C., Ling, J.F.: 1992, Calculation of Perturbations in the Stellar Three-Body Problem in Mc Alister and Hartkopf (eds.) Complementary Approaches to Double and Multiple Star Research, IAU Colloquium 135, ASP Conference Serie, 32, 223–224
Donnison, J.R., Mikulskis, D.F.: 1992, Three-body orbital stability criteria for circular orbits, MNRAS, 254, 21–26
Donnison, J.R., Mikulskis, D.F.: 1994, Three-body orbital stability criteria for circular retrograde orbits, MNRAS, 266, 25–30
Donnison, J.R., Mikulskis, D.F.: 1995, The effect of eccentricity on the three-body orbital stability criteria and its importance for triple star systems. MNRAS, 272, 1–10
Eggleton, P. P., Kiseleva, L. G.: 1995, An empirical condition for Stability of Hierarchical triple systems, ApJ, 455, 640–645
Ferrer, S., Osacar, C.: 1992, Harrington's Hamiltonian in the stellar problem of three bodies: Reductions, relative equilibria and bifurcations, Cel.Mech. and Dynamic.Astron., 58, 245–275
Hadjidemetriou, J., Dvorak, R.: 1996: The hierarchical three body problem as two two-dimensional coupled mappings, in J. Seiradakis (ed), 2nd Hellenic Astronomical meeting, 571–577
Harrington, R.S.: 1968, AJ, 73, 190–194
Harrington, R.S.: 1972, Stability criteria for triple stars, Celest.Mech., 6, 322–327
Harrington, R.S.: 1975a, Production of triple stars by the dynamical decay of small stellar systems, AJ, 80, 1081–1086
Harrington, R.S.: 1975b, Production of triple stars by the dynamical decay of smaller systems, AJ, 80, 1081–1086
Heintz, W.D.: 1969, Journ. Royal. astr. Soc. Canada 63, p.275
Huang, T.Y., Valtonen, M.J.: 1987, An approximate solution to the energy change of a circular binary i a parabolic three body encounter, MNRAS, 267, 333–344
Kiseleva, L. G., Eggleton, P. P., Anasova, J.P.: 1994, A note on the stability of hierarchical triple stars with initially orbits, MNRAS, 267, 161–166
Kiseleva, L. G., Eggleton, P. P., Orlov, V.V.: 1994, Instability of close triple systems with coplanar initial doubly circular motion, MNRAS, 270, 936–946
Marchal, Ch.,: 1990, The three-body problem, Studies in Astronautics Vol 5, Elsevier.
Marchal, Ch., Saari, D.G.: 1975, Hill regions for the general three-body problem, Celest.Mech., 12, 115–129
Marchal, Ch., Bozis, G.: 1982, Hill stability and distance curves for the general three-body problem, Celest.Mech., 26, 311–333
Marchal, C., Yoshida, J., Sun, Y.S.: 1984, A test of escape valid even for very small mutual distance I. The acceleration and the escape velocities of the third body. Celest.Mech., 33, 193–207
Mikkola, S., Valtonen, M.: 1986 MNRAS, 223, 269
Saari, D.G.: 1974, SIAM, J. Appl. Math, 26, 806–815
Söderhjelm, S.: 1982, Studies of the Stellar Three-body Problem. Astron.Astrophys., 107, 54–60
Söderhjelm, S.: 1984, Third — order and tidal effects in the stellar three-body problem, Astron.Astrophys., 141, 232
Szebehely, V., Zare, K.: 1977, Stability of Classical Triplets and their hierarchy, Astron. Astrophys., 58, 145–152
Szebehely, V.: 1970, Theory of Orbits, Academic Press
Szebehely, V.G.: 1971, Mass effects in the problem of three bodies, Celest.Mech., 6, 84–107
Valtonen, M. J.: 1988, The general three-body problem, Vistas in Astronomy 32, 23–48
Worley, C.E.: 1967, On the Evolution of Double Stars (J. Dommanget, ed.), Commun.Obs.roy, Belgique, Ser. B, no. 17
Wallenquist, A.: 1944, On the apparent distribution and properties of triple and multiple stars, Ann. Uppsala Obs. 1, part 5.
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Dvorak, R. Third Body Perturbations of Double Stars. Celestial Mechanics and Dynamical Astronomy 68, 63–73 (1997). https://doi.org/10.1023/A:1008287614810
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DOI: https://doi.org/10.1023/A:1008287614810