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The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node (Ω). By definition, the reference plane for the Solar System is usually considered to be Earth's orbital plane, which defines the ecliptic, the circular path on the celestial sphere that the Sun appears to follow ...
The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. [ 1 ] [ 2 ] [ a ] From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars . [ 3 ]
The reference plane is assumed to be the xy-plane, and the origin of longitude is taken to be the positive x-axis. k is the unit vector (0, 0, 1), which is the normal vector to the xy reference plane. For non-inclined orbits (with inclination equal to zero), ☊ is undefined.
The image shows the relations between Earth's axial tilt (or obliquity), rotation axis, and orbital plane. The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system.
In celestial mechanics, the orbital plane of reference (or orbital reference plane) is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node .
K̂ is perpendicular to the reference plane. Orbital elements of bodies (planets, comets, asteroids, ...) in the Solar System usually the ecliptic as that plane. x̂, ŷ are in the orbital plane and with x̂ in the direction to the pericenter . ẑ is perpendicular to the plane of the orbit. ŷ is mutually perpendicular to x̂ and ẑ.
The rate of precession depends on the inclination of the orbital plane to the equatorial plane, as well as the orbital eccentricity. For a satellite in a prograde orbit around Earth, the precession is westward (nodal regression), that is, the node and satellite move in opposite directions. [1] A good approximation of the precession rate is
The inclination of a celestial object is the angle between its orbital plane and another reference frame such as the equatorial plane of the object's primary. In the Solar System, inclination of the planets is measured from the ecliptic plane, which is the plane of Earth's orbit around the Sun. [5]