% Words:   199
\chapter{Summary of Part~\ref{sch}}
When we look at the number of $r$-turning points we can see that
orbits can be divided in three categories: orbits which, coming
from infinity, go again to infinity, these are call \emph{flyby
orbits} and they can be of either type (null, time-like or
space-like), they have one turning point; \emph{bound orbits}
which have their radial coordinate bound by two finite values
(only time-like geodesics), they have two turning points; and
\emph{crash-escape orbits}, which come from infinity into the
singularity (null, time-like or space-like geodesics), they have
no turning point.

Flyby and bound orbits are familiar in Newtonian gravitation as
Keplerian hyperbolas and Keplerian ellipses. With them are
associated orbits of the second kind, which have no Newtonian
analogues and which, starting from a certain distance (above
horizon), plunge into the singularity (these are \emph{not} radial geodesics in Newtonian gravitation). Crash-escape orbits are
either orbits characterized by imaginary eccentricities, or, in  the 
case of time-like and null orbits, radial geodesics. Geodesics of above types are said to be \emph{ordinary}.

\emph{Exceptional} orbits happen when
the two kinds of orbits coalesce as they asymptotically approach
a~common circle from opposite sides by infinitely spiralling round
it.


In Chapter \ref{n} (null geodesics) we gave explicit solutions for proper and Schwarzschild times, in addition to already known solutions for the radial coordinate.

In Chapter \ref{s} (space-like geodesics) the explicit solutions for radial and time coordinates are evaluated.  As a~consequence of conditions which must be imposed on parameters we showed that there can be no repulsive orbits thus disproving result of \cite{hlr}.

In Chapter \ref{schtl} (time-like geodesics) a minor  error in \cite[equation 113, page 102]{chandrasekhar} was corrected.
%We have evaluated these geodesics explicitly and showed that repulsive %space-like orbits are not allowed disproving . 
