  The motion of Mercury using numerical methods in the framework of a model
including only the non-relativistic Newtonian gravitational interactions of the
solar system, 9 planets in translation (including Pluto) around the sun has
been studied. Since the true trajectory of Mercury is an open, non-planar
curve, we have paid special attention to the exact definition of the advance of
Mercury's perihelion. For this purpose, we have introduced the notions of an
extended and a geometrical perihelion. In addition, for each orbital period, a
mean ellipse was fitted to the trajectory of Mercury. I have shown that the
perihelion advance of Mercury deduced from the behavior of the
Laplace-Runge-Lenz vector, as well as the extended and geometrical perihelion
advance depend on the fitting time interval and for intervals of the order of
1000 years converge to a value of 532.1 arcseconds per century. The behavior of
the perihelia, either extended or geometrical, is strongly impacted by the
influence of Jupiter. The advance of the extended perihelion depends strongly
on the time step used in the calculations, while the advance of the geometrical
perihelion and that deduced by the rotation of the Laplace-Runge-Lenz vector
depends only slightly on it.
