Application of three-body stability to globular clusters: I. The
  stability radius
  The tidal radius is commonly determined analytically by equating the tidal
field of the galaxy to the gravitational potential of the cluster. Stars
crossing this radius can move from orbiting the cluster centre to independently
orbiting the galaxy. In this paper, the stability radius of a globular cluster
is estimated using a novel approach from the theoretical standpoint of the
general three-body problem. This is achieved by an analytical formula for the
transition radius between stable and unstable orbits in a globular cluster. A
stability analysis, outlined by Mardling, is used here to predict the
occurrence of unstable stellar orbits in the outermost region of a globular
cluster in a distant orbit around a galaxy. It is found that the eccentricity
of the cluster-galaxy orbit has a far more significant effect on the stability
radius of globular clusters than previous theoretical results of the tidal
radius have found. A simple analytical formula is given for determining the
transition between stable and unstable orbits, which is analogous to the tidal
radius for a globular cluster. The stability radius estimate is interior to
tidal radius estimates and gives the innermost region from which stars can
random walk to their eventual escape from the cluster. The time-scale for this
random walk process is also estimated using numerical three-body scattering
experiments.
