At any given instance in time, a perturbed planetary orbit is completely determined by six osculating orbital elements. (See Section 10.2.)
Let us choose these elements to be the major radius, ; the mean anomaly at epoch,
; the eccentricity, ; the argument of the perihelion, ;
the inclination to the ecliptic, ; and the longitude of the ascending node,
. In the absence of a disturbing force, ,
, , and
are all constants of the motion.
As is clear from the analysis of the preceding two sections, in the presence of a disturbing force of the form (I.15), the osculating elements evolve in time as follows:
These equations are known collectively as the Gauss planetary equations.