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In celestial mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. For the point p=(x,y) on an ellipse with the equation the eccentric anomaly is the angle E such that 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. FormulasFrom the true anomalyThe eccentric anomaly can be computed from the true anomaly by the formulas where e is the eccentricity, hence where is the angular coordinate of point (X,Y) in polar coordinates. The following relation also holds: and hence From the mean anomalyThe eccentric anomaly E is related to the mean anomaly M by the formula This equation does not have a closed-form solution for E given M. It is usually solved by numerical methods, e.g. Newton-Raphson method. Radius and eccentric anomalyThe radius (distance from the focus of attraction to the orbiting body) is related to the eccentric anomaly by the formula From Wikipedia under the
GNU Free Documentation License  physicsforums.com Silly Lung Wed, 13 Aug 2008 07:43:12 GM The planet is defined by 5 orbital elements (period, mass, . eccentricity. , longitude of periastron, and mean . anomaly. ). I wrote a code that will plot the radial velocity of the planet vs. time. I'm using the systemic console (www.oklo.org) ... physicsforums.com ehrenfest Sun, 04 Nov 2007 19:05:58 GM is the radial distance, LaTeX Code: \\theta(t) is the true anomaly, LaTeX Code: a is the semi-major axis, and LaTeX Code: e is the eccentricity. To get the velocity vector you will need to add mean anomaly and . eccentric anomaly. to the ...  theeccentricsage.blogspot.com Schmetterling ue, 12 Aug 2008 00:41:00 GM if i am, in fact, being nice to her, we'll just call it an . anomaly. --me stirring the waters just to make sure we don't get stuck in a rut (er--canal, i guess, if we want to avoid mixing metaphors)--or something like that. ... From Google Blog Search: "Eccentric anomaly"  news.google.com Castanet.net The answers are carefully and temptingly revealed through two converging time lines: Mead as a grade school outcast and Mead as a University anomaly . ... news.google.com Daily Kos (blog) Their result is a bit of anomaly for their polling thus far--the Democrat actually leads. Incumbent Democrat Tim Bishop has a two-point edge over Republican ... and more » news.google.com Mirror.co.uk An eccentric star is born. It's good that embarrassing anomaly Sir Trevor what am I doing here? McDonald has finally thrown in the towel. ... and more » From Google News Search: "Eccentric anomaly"  wlym.com 379px x 201px | 1.30kB [source page] Getting the mean anomaly from the eccentric anomaly Starting with the eccentric anomaly blue angle it is easy to find the mean anomaly total area both red and green First  bunnyhugs.org 400px x 533px | 90.70kB [source page] Rhum Barbancourt Distillery Visit Saturday October 25th 2008 Barbancourt is an interesting distillery Calling the House of Barbanourt eccentric would be a stretch but it is definitely an anomaly in the rum world Standing out as it does from the  plancksconstant.org 322px x 546px | 24.70kB [source page] inclination is much higher than the other planets and as I note below its orbit is highly eccentric At times it is closer to the Sun than Neptune One could call this planet an anomaly Put all these unusual items together with the fact that the probe is powered by 24 pounds of the eponymous plutonium and I would like to coin the word eponomaly to describe this series of From Yahoo Image Search: "Eccentric anomaly" |
