The accuracy of two procedures for solving the sphere reconstitution problem for the Hipparcos project is evaluated. This problem involves deriving the astrometric parameters (positions, proper motions, and parallax) of about 40,000 primary stars from the abscissae. These procedures involve: (1) solving condition equations where the observed data are arcs between stars, and (2) solving condition
... [Show full abstract] equations where the observed data are the abscissae themselves. Both methods are found to attain an accuracy of about 0.002 arcsec in each astrometric parameter.