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 . 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 . 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  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.).