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For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity and argument of periapsis parameters for which eccentricity zero ...
The eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: = | | where: e is the eccentricity vector ("Hamilton's vector"). [2]: 25, 62–63
Orbital eccentricity, in astrodynamics, a measure of the non-circularity of an orbit; Eccentric anomaly, the angle between the direction of periapsis and the current position of an object on its orbit; Eccentricity vector, in celestial mechanics, a dimensionless vector with direction pointing from apoapsis to periapsis
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
e is the eccentricity vector (a vector pointing towards the periapsis). In the case of equatorial orbits (which have no ascending node), the argument is strictly undefined. However, if the convention of setting the longitude of the ascending node Ω to 0 is followed, then the value of ω follows from the two-dimensional case: ω = a t a n 2 ( e ...
It is also known as the Laplace vector, [13] [14] the Runge–Lenz vector [15] and the Lenz vector. [8] Ironically, none of those scientists discovered it. [15] The LRL vector has been re-discovered and re-formulated several times; [15] for example, it is equivalent to the dimensionless eccentricity vector of celestial mechanics.
In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly.
Perifocal reference frames are most commonly used with elliptical orbits for the reason that the ^ coordinate must be aligned with the eccentricity vector. Circular orbits, having no eccentricity, give no means by which to orient the coordinate system about the focus. [5]