Osculating orbit

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In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space (at a given moment of time) is the gravitational Kepler orbit (i.e. ellipse or other conic) that it would have about its central body (corresponding to its actual position and velocity for that given moment of time) if perturbations were not present.^[1]

An osculating orbit and the object's position upon it are fully described by the six standard Keplerian orbital elements, which are easy to calculate as long as one knows the object's position and velocity relative to the central body. However, perturbations can cause the osculating elements to evolve, sometimes very quickly. In such cases, a more complex set of proper orbital elements may better describe the most important aspects of the orbit.

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 ("kissing") its actual orbit, with the tangent point being the object's location.

Possible perturbations that could cause an object's osculating orbit to change include:

A non-spherical component to the central body (i.e., the central body is not a point mass or is an oblate spheroid)
A third (or more) body whose gravity perturbs the object's orbit
A non-gravitational force acting on the body. For example caused by
- Thrust from a rocket or ion engine
- Releasing, leaking, venting or ablation of a material
- Collisions with other objects
- Atmospheric drag
- Radiation pressure
- Solar wind pressure