  The main effects of the Earth's oblateness on the motion of artificial
satellites are usually derived from the variation of parameters equations of an
average representation of the oblateness disturbing function. Rather, we
approach their solution under the strict mathematical assumptions of Picard's
iterative method. Our approach recovers the known linear trends of the right
ascension of the ascending node and the argument of the perigee, but differs
from the accepted solution in the value of the mean motion. This amended rate
radically improves the in-track errors of typical orbit propagations. In
addition, our truncation of the Picard iterations solution to its secular terms
includes the corrections that must be applied to the osculating initial
conditions in the right propagation of the mean dynamics.
