Orbital elements: Difference between revisions
attempt at summarizing the wikipedia articles
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When neglecting the influence of other objects, two celestial bodies orbit one another along a [[wp:conic section|conic]] trajectory. In the orbital plane, the radial equation is thus:
<tt>r = l/(1 + e cos(angle))</tt>
<tt>l</tt>, <tt>e</tt> and <tt>angle</tt> are respectively called the ''semi-latus rectum'', the ''eccentricity'' and the ''true anomaly''. The eccentricity and the true anomaly are two of the six so-called [[wp:orbital elements|orbital elements]] often used to specify an orbit and the position of a point on this orbit.
The four other parameters are the ''semi-major axis'', the ''longitude of the ascending node'', the ''inclination'' and the ''argument of periapsis''.
The semi-major axis is half the distance between [[wp:perihelion and aphelion|perihelion and aphelion]]. It is often noted <tt>a</tt>, and it's not too hard to see how it's related to the semi-latus-rectum : <tt>a = l/(1 - e²)</tt>
The longitude of the ascending node, the inclination and the argument of the periapsis specify the orientation of the orbiting plane with respect to a reference plane defined with three arbitrarily chosen reference distant stars.
Those six parameters, along with dynamical considerations implying notably the [[wp:vis-viva equation|vis-viva equation]], allow for the determination of both the position and the speed of the orbiting object in [[wp:cartesian coordinates|cartesian coordinates]], those two vectors constituting the so-called [[wp:orbital state vectors|orbital state vectors]].
The determination of the speed also requires the knowledge of the so-called ''gravitational parameter'' which we shall consider equal to one here:
<big> µ = GM = 1. </big>
The purpose of this task is to show how to perform this conversion from orbital elements to orbital state vectors in your programming language.
TODO: pick an example from a reputable source, and bring the algorithm description onto this site. (Restating those pages in concise a fashion comprehensible to the coders and readers of this site will be a good exercise.)
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