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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.
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.
It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular ...
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
This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector at the orbital nodes (i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes).