  We present an improved analytic calculation for the tidal radius of
satellites and test our results against N-body simulations.
  The tidal radius in general depends upon four factors: the potential of the
host galaxy, the potential of the satellite, the orbit of the satellite and
{\it the orbit of the star within the satellite}. We demonstrate that this last
point is critical and suggest using {\it three tidal radii} to cover the range
of orbits of stars within the satellite. In this way we show explicitly that
prograde star orbits will be more easily stripped than radial orbits; while
radial orbits are more easily stripped than retrograde ones. This result has
previously been established by several authors numerically, but can now be
understood analytically. For point mass, power-law (which includes the
isothermal sphere), and a restricted class of split power law potentials our
solution is fully analytic. For more general potentials, we provide an equation
which may be rapidly solved numerically. Over short times ($\simlt 1-2$ Gyrs
$\sim 1$ satellite orbit), we find excellent agreement between our analytic and
numerical models. Over longer times, star orbits within the satellite are
transformed by the tidal field of the host galaxy. In a Hubble time, this
causes a convergence of the three limiting tidal radii towards the prograde
stripping radius. Beyond the prograde stripping radius, the velocity dispersion
will be tangentially anisotropic.
