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Concept
Osculating orbit
Summary
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. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity).
The word osculate is Latin for "kiss". In mathematics, two curves osculate when they just touch, without (necessarily) crossing, at a point, where both have the same position and slope, i.e. the two curves "kiss".
An osculating orbit and the object's position upon it can be fully described by the six standard Kepler 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. 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.
Orbit#Perturbations and Perturbation (astronomy)
Perturbations that cause an object's osculating orbit to change can arise from:
A non-spherical component to the central body (when the central body can be modeled neither with a point mass nor with a spherically symmetrical mass distribution, e.g. when it is an oblate spheroid).
A third body or multiple other bodies whose gravity perturbs the object's orbit, for example the effect of the Moon's gravity on objects orbiting Earth.
A relativistic correction.
Official source
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