O

Obliquity

In general, the angle between the equatorial and orbital planes of a body or, equivalently, between the rotational and orbital poles. For the Earth the obliquity of the ecliptic is the angle between the planes of the equator and the ecliptic; its value is approximately 23°.44.

 

Occultation

The obscuration of one celestial body by another of greater apparent diameter; especially the passage of the Moon in front of a star or planet, or the disappearance of a satellite behind the disk of its primary. If the primary source of illumination of a reflecting body is cut off by the occultation, the phenomenon is also called an eclipse. The occultation of the Sun by the Moon is a solar eclipse. (See eclipse, solar.)

 

Opposition

The phenomenon whereby two bodies have apparent ecliptic longitudes or right ascensions that differ by 180° as viewed by a third body. Oppositions are usually tabulated as geocentric phenomena.

 

Orbit

The path in space followed by a celestial body as a function of time. (See orbital elements.)

 

Orbit, elliptical

A closed orbit with an eccentricity less than 1.

 

Orbit, hyperbolic

An open orbit with an eccentricity greater than 1.

 

Orbit, instantaneous

The unperturbed two-body orbit that a body would follow if perturbations were to cease instantaneously. Each orbit in the solar system (and, more generally, in the many-body setting) can be represented as a sequence of instantaneous ellipses or hyperbolae whose parameters are called orbital elements. If these elements are chosen to be osculating, each instantaneous orbit is tangential to the physical orbit. (See orbital elements; osculating elements.)

 

Orbit, parabolic

An open orbit with an eccentricity of 1.

 

Orbital elements

A set of six independent parameters that specifies an instantaneous orbit. Every real orbit can be represented as a sequence of instantaneous ellipses or hyperbolae sharing one of their foci. At each instant of time, the position and velocity of the body is characterised by its place on one such instantaneous curve. The evolution of this representation is mathematically described by evolution of the values of orbital elements. Different sets of geometric parameters may be chosen to play the role of orbital elements. The set of Keplerian elements is one of many such sets. When the Lagrange constraint (the requirement that the instantaneous orbit is tangential to the actual orbit) is imposed upon the orbital elements, they are called osculating elements.

 

Osculating elements

A set of parameters that specifies the instantaneous position and velocity of a celestial body in its perturbed orbit. Osculating elements describe the unperturbed (two-body) orbit that the body would follow if perturbations were to cease instantaneously. (See orbit, instantaneous; orbital elements.)