Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a....95..334k&link_type=abstract
Astronomy and Astrophysics, vol. 95, no. 2, Mar. 1981, p. 334-348.
Astronomy and Astrophysics
Astrophysics
30
Celestial Mechanics, Orbital Mechanics, Star Clusters, Stellar Motions, Stellar Orbits, Three Body Problem, Tides, Circular Orbits, Globular Clusters, Gravitational Fields, Isotropy, Mathematical Models, Orbit Perturbation, Radii, Velocity Distribution
Scientific paper
The circular and elliptic restricted three body systems were used to investigate the stability of stellar orbits in open and globular clusters respectively as a function of the Jacobi constant C (for the circular restricted problem - CRP) or the analogous Jacobi parameter K (for the elliptic restricted problem - ERP). Large numbers (see Table 2) of zero mass particles ("stars") were numerically integrated through 32 and 10 primary (galactic) orbits for the CRP and ERP models respectively and statistics compiled of the fractions which remained bound to the cluster as a function of C or K. Distributions of initially circular and radial stellar orbits were integrated as well as ones with an isotropic velocity distribution. The distribution of initial positions and orbital inclinations corresponded to the case of a spherical cluster. The great stability of retrograde low eccentricity stellar orbits as discussed by Jefferys (1974, 1976) was confirmed and extended to a more realistic distribution of inclinations. Also a star does not necessarily escape from a cluster over a large fraction of the age of the system even if the zero velocity surfaces are wide open. As expected the probability of escape in a given time interval decreases as C or K increases. The Jacobi parameter K in the ERP is a useful quantity to measure the stability of stellar orbits because it varies for a bound orbit in an approximately periodic manner with the true anomaly of the cluster's galactic orbit.
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