  Chaos indicators, like the Lyapunov exponent lambda, are widely used in
celestial mechanics to characterize the dynamical behavior of bodies. The
stability of their orbit can be determined by the calculation of the local
exponential divergence of arbitrarily close initial conditions in phase space.
As the equations to calculate lambda are given, a straight prediction of the
orbital stability should be possible. However, one finds in the literature a
lot of discrepancies between different studies dedicated to the same object.
  As a possible explanation for this we investigated in the presented work the
effects of the used computer hardware and integration methods on the outcome of
such stability computations. Therefore we calculated the Lyapunov time of
different asteroids as a measure of chaoticity. Exploring the very fine
structure of the nearby phase space of the initial conditions, we are able to
explain the reason of the differences in the published Lyapunov times for some
objects. Applying methods of robust statistics we introduce the computability
index kappa as a measure of repeatability of the results. This kappa gives an
estimate, how much the obtained Lyapunov time will change, e.g. when repeating
the same calculations with a different integration method.
