**Introduction.
(From the software manual)**

**EXORB6** is an *easy
to use, high precision and versatile* orbit determination program
working
under Win9x-2000-XP.

EXORB can be used
both to determine an heliocentric orbit (asteroids or comets) and a
geocentric
orbit (satellites), when a set of observed positions is available. It
is based
on a full numerical integration of the Solar System, including the nine
major
planets, the moon and the three asteroids Ceres, Pallas and Vesta [1].
Optionally, the three asteroids and the planet Pluto can be excluded
from the
computation, resulting in about 80% increased speed. In the case of
satellites,
also Mercury, Uranus and Neptune are excluded from the computation. The
program
reads the observational data from an ASCII file that must be created by
the
user with a text editor, using conventions which will be described
later, or
from *(****new***) a MPC formatted file. Then the program gets
from a
library file (PL406F.BIN, PL406SHF.BIN or PLXSH.BIN according to the
case) the
starting conditions which are closer in time to the epoch of the first
observation and numerically integrates the Solar System up to this
epoch
[2]. At this point the program adds a
new body to the system, giving to it either trial starting position and
velocity, or reading them from a file (STARTING.DAT). Then EXORB starts
an
iterative fitting procedure, using a Newton-Gauss least-squares
algorithm. The
time interval covered by the observed data is first integrated using
the trial
starting conditions, then integrated six more times giving each time a
small
increment to the corresponding positional or velocity coordinate. For
each of
the N data point, the differences (residuals) between the observed and
calculated positions are recorded and stored in a 7*N matrix. After the
filling
of this matrix is complete, use of some matrix algebra [3] produces the
vector
of the increments to be given to the six starting positional and
velocity
elements to get an improved set of starting conditions for the body.
The
procedure is iterated until convergence is reached or the iteration is
stopped
by the user. The method is suitable both for finding an exact solution
from
three observations and for finding the least-squares solution from a
larger
number of observations. The output gives both positionals and velocity
elements
at the epoch of the first observation (or integrated up to any other
epoch) and
classical osculating elements, together with their estimated errors
(standard
dev.).