What is "osculating orbit"

n. The orbit that an astronomical body such as a planet, asteroid, comet or satellite would follow if suddenly all perturbing forces other than the gravitational attraction of the Sun or (for a satellite) its planet were to disappear.

In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. ellipse or other conic) that it would have about its central body if perturbations were not present. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity).

The word "osculate" derives from a Latin word meaning "to kiss". Its use in this context derives from the fact that, at any point in time, an object's osculating orbit is precisely tangent to its actual orbit, with the tangent point being the object's location – and has the same curvature as the orbit would have in the absence of perturbing forces.