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.

Formulas

From the true anomaly

The 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 anomaly

The 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 anomaly

The 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
Thu Feb 18 22:25:40 2010

orbit in space (extrasolar planets)
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orbit in space (extrasolar planets)

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) ...

velocity of a planet in orbit
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velocity of a planet in orbit

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 ...

post 149
theeccentricsage.blogspot.com
post 149

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"
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A great book review by our entertainment connoisseur! (Photo: Contributed) - Castanet.net
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A great book review by our entertainment connoisseur! (Photo: Contributed)

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 . ...
Polling and Political Wrap-Up, 1/20/10 - Daily Kos (blog)
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Polling and Political Wrap-Up, 1/20/10

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 ...



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The Pants and Dec show - Mirror.co.uk
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The Pants and Dec show

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. ...



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From Google News Search: "Eccentric anomaly"
Thu Feb 11 22:53:27 2010

chapter60 eccentric mean gif
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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

bhbarbancourtdistillery0002 jpg
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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

plmars walmart jpg
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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"
Mon Jan 25 15:10:58 2010