  Various astrophysical processes are known, where the fly-by of a massive
object affects matter initially supported against gravity by rotation. Examples
are perturbations of galaxies, protoplanetary discs or planetary systems. We
approximate such events as subset of the restricted three-body problem by
considering only perturbations of non-interacting low-mass objects initially on
circular Keplerian orbits. In this paper we present a new parametrisation of
the initial conditions of this problem. Under certain conditions the initial
positions of the low-mass objects can be specified largely independent of the
initial position of the perturber. Exploiting additionally the known scalings
of the problem reduces the parameter space of initial conditions for one
specific perturbation to two dimensions. To this two-dimensional initial
condition space we have related the final properties of the perturbed
trajectories of the low-mass objects from our numerical simulations. That way,
maps showing the effect of the perturbation on the low-mass objects have been
created, which provide a new view on the perturbation process. Comparing the
maps for different mass-ratios reveals that the perturbations by low- and
high-mass perturbers are dominated by different physical processes. The
equal-mass case is a complicated mixture of the other two cases. Since the
final properties of trajectories with similar initial conditions are usually
also similar, the results of the limited number of integrated trajectories can
be generalised to the full presented parameter space by interpolation. Since
our results are also unique within the accuracy strived for, they constitute
general numerical solutions for this subset of the restricted three-body
problem. As such, they can be used to predict the evolution of real physical
problems by simple transformations like scaling and without further
simulations. (...)
