Alessandra Celletti, Gabriella Pinzari
Four classical methods for determining planetary elliptic elements: a
comparison
(1106K, Postcript)

ABSTRACT.  The discovery of the asteroid Ceres by G. Piazzi in 1801 motivated
the development of a mathematical technique proposed by C.F. Gauss,
which allows to recover the orbit of a celestial body starting from a
minimum of three observations. Here we compare the method proposed
by Gauss with the techniques (based on three observations) developed
by P.S. Laplace and by O.F. Mossotti. We also consider another method
developed
by Mossotti, based on four observations. We provide a theoretical and
numerical
comparison among the different procedures. As an application, we consider
the computation of the orbit of the asteroid Juno.