Osculating orbit

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In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space is the gravitational Keplerian orbit about a central body that it would have if other perturbations were not present.

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, a 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)
A third (or more) body whose gravity perturbs the object's orbit
An acceleration on the body (such as a rocket engine or ion engine if it is a spacecraft).

Diagram of a sequence of osculating orbits for the escape from Earth orbit by the ion-driven SMART-1 spacecraft: http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=35722
A sequence of osculating orbits for the approach to the Moon by the SMART-1 spacecraft: http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=36359

v • d • e Orbits
Orbit types	Box orbit • Circular orbit • Ecliptic orbit • Elliptic orbit • Highly Elliptical Orbit • Graveyard orbit • Hyperbolic trajectory • Inclined orbit • Osculating orbit • Parabolic trajectory • Capture orbit • Escape orbit • Semi-synchronous orbit • Subsynchronous orbit • Synchronous orbit
Earth-centered orbits	Geosynchronous orbit • Geostationary orbit • Sun-synchronous orbit • Low Earth orbit • Medium Earth Orbit • Molniya orbit • Near equatorial orbit • Orbit of the Moon • Polar orbit • Polar sun synchronous orbit • Tundra orbit
Other orbits	Areosynchronous orbit • Areostationary orbit • Lissajous orbit • Lunar orbit • Heliocentric orbit • Heliosynchronous orbit
Orbital elements	Inclination ( $i\,\!$ ) • Longitude of the ascending node ( $\Omega\,\!$ ) • Eccentricity ( $e\,\!$ ) • Argument of periapsis ( $\omega\,\!$ ) • Semi-major axis ( $a\,\!$ ) • Mean anomaly at epoch ( $M_o\,\!$ )
Other orbital parameters	True anomaly ( $v\,$ ) • Semi-minor axis ( $b\,$ ) • Linear eccentricity ( $\epsilon\,$ ) • Eccentric anomaly ( $E\,$ ) • Mean longitude ( $L\,$ ) • True longitude ( $l\,$ ) • Orbital period ( $T\,$ )
Orbital maneuvers	Bi-elliptic transfer • Geostationary transfer orbit • Gravitational slingshot • Hohmann transfer orbit • Orbital inclination change • Orbit phasing • Space rendezvous
Other orbital mechanics topics	Apsis • Celestial coordinate system • Delta-v budget • Epoch • Ephemeris • Equatorial coordinate system • Ground track • Interplanetary Transport Network • Kepler's laws of planetary motion • Lagrangian point • List of orbits • n-body problem • Orbit equation • Orbital state vectors • Retrograde and direct motion • Specific orbital energy • Specific relative angular momentum