Osculating orbit

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.

An osculating orbit and the object's position upon it can be fully described by the six standard Keplerian orbital elements (osculating elements), which are easy to calculate as long as one knows the object's position and velocity relative to the central body. The osculating elements would remain constant in the absence of perturbations. However, real astronomical orbits experience perturbations that cause the osculating elements to evolve, sometimes very quickly. In cases where general celestial mechanical analyses of the motion have been carried out (as they have been for the major planets, the Moon, and other planetary satellites), the orbit can be described by a set of mean elements with secular and periodic terms. In the case of minor planets, a system of proper orbital elements has been devised to enable representation of the most important aspects of their orbits.

Perturbations that cause an object's osculating orbit to change can arise from:

An object's orbital parameters will be different if they are expressed with respect to a non-inertial reference frame (for example, a frame co-precessing with the primary's equator), than if it is expressed with respect to a (non-rotating) inertial reference frame.

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