  The objetive of this work is to investigate the influence of the corrections
to the spherical symmetrical accretion of an infinity gas cloud characterized
by a polytropic equation into a massive object due to the post-Newtonian
approximation.The post-Newtonian corrections to the critical values of the flow
velocity, sound velocity and radial distance are obtained from the system of
hydrodynamics equations in spherical coordinates. The critical point in the
post-Newtonian approximation accretion does not correspond to the transonic
point like in Newtonian theory. An equation for the Mach number was obtained as
a function of a dimensionless radial coordinate. It was considered that the
ratio of the sound velocity far the massive body and the speed of light was of
order $a_\infty/c=10^{-2}$. The analysis of the solution led to following
results: the Mach number for the Newtonian and post-Newtonian accretion have
practically the same values for radial distances of order of the critical
radial distance; by decreasing the radial distance the Mach number for the
Newtonian accretion is bigger than the one for the post-Newtonian accretion;
the Mach number increases by decreasing the ratio of the specific heats; the
difference between the Newtonian and post-Newtonian Mach numbers when the ratio
$a_\infty/c\ll10^{-2}$ is insignificant. The effect of the correction terms in
post-Newtonian Bernoulli equation is more perceptive for the lowest values of
the radial distance, and the solutions for $a_\infty/c>10^{-2}$ does not lead
to a continuous inflow and outflow velocity at the critical point. A comparison
of the solutions with those that follow from a relativistic Bernoulli equation
shows that the dependence of the Mach number with the radial distance of the
former is bigger than the post-Newtonian ones.
