osculating orbit

It is defined as the distance between the closest points of the osculating orbits of the two bodies in question.

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

See for example osculating circle and osculating orbit.

Since the osculating orbit is easily calculated by two-body methods, and are accounted for and can be solved.

Osculating orbit is the temporary Keplerian orbit about a central body that an object would continue on, if other perturbations were not present.

Its disadvantage is complexity; it cannot be used indefinitely without occasionally updating the osculating orbit and continuing from there, a process known as rectification.

Osculating orbits in a restricted 3-Body problem (video, YouTube)

Encke's method begins with the osculating orbit as a reference and integrates numerically to solve for the variation from the reference as a function of time.

In an orbit that is undergoing perturbations, an osculating orbit together with its (elliptical) osculating elements can still be defined for any point in time along the actual orbit.

The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the solar system.

This illustrates the significant impact that the engine burns have on the orbit and marks the meaning of the osculating orbit, which is the orbit that would be travelled by the spacecraft if at that instant all perturbations, including thrust, would cease.

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.

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.

If all perturbations were to cease at any particular instant, the body would continue in this (now unchanging) conic section indefinitely; this conic is known as the osculating orbit and its orbital elements at any particular time are what are sought by the methods of general perturbations.

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.