Talk:Eccentric anomaly

untitled 2005

I think the calculation of $E$ from $M$ is not correct. Could someone point out if there is any error in the following. If noone replies in a while I will replace the expression in the page.

If $M=E-e\,\sin E$, the iteration relation would read $E_{i+1}=M+e\,\sin E_{i}$. Then, by taking $E_{0}=M$ and using expansions of trigonometric functions, we obtain:

• $E_{1}=M+e\,\sin M$
• $E_{2}=M+e\,\sin M+{\frac {1}{2}}e^{2}\sin 2M$
• $E_{3}=M+e\,\sin M+{\frac {1}{2}}e^{2}\sin 2M+{\frac {1}{8}}e^{3}(3\sin 3M-\sin M)$

Also it should be noted that this series expansion fails for $e>0.6627434$ (Murray, C. D. & Dermott, S. F. 1999, Solar System Dynamics, Cambridge University Press, Cambridge; p.35).

I have now added the information above to the page. at0 23:57, 29 Mar 2005 (UTC)

untitled 2007

This sentense in meaningless:

"The eccentric anomaly is the angle between the direction of periapsis and the current position of an object on its orbit"

since an angle is defined from two directions. An angle cannot be defined from one direction and a point. —Preceding unsigned comment added by 62.180.229.222 (talk) 06:21, 5 November 2007 (UTC)

Position has direction, it's a vector from center of a system to orbiting object. So, normalized position vector is a direction vector, but there's no need to normalize it, as angle could be taken from any two vectors, not necessarily unit vectors.

Correct placement of the material

The eccentric/true anomalies logically belongs to the article Ellipse, these are two different ways of assigning a parameter to an ellipse in general, not only to an elliptic Kepler orbit. True anomaly is the then equally applicable to a parabola and a hyperbola. This as opposed to mean anomaly that only is relevant for an elliptic Kepler orbit, this is just a parameter transformation for the analytic solution of the differential equation of the two body problem. It has no geometrical significance for an ellipse as a geometric shape!

I plan to update the Ellipse article such that the proper definitinons of true and eccentric anomalies are included. I think the eccentric/true anomaly articles then should be reduced to pointers to Ellipse.

The picture of this article would be fine if just the word "orbit" is removed!

Stamcose (talk) 15:28, 22 November 2008 (UTC)

I have now updated the Ellipse article and the material of this article (except "mean anomaly") is now in the the Ellipse article. The convertion between "eccentric anomaly" and "mean anomaly" is in Kepler orbit where the mathematical analysis is carried through for which the "mean anomaly" is meaningful as a mathematical transformation of variable!

Correponding transformation

$M=E-e\,\sin {E}.\,\!$

could be OK in a Mean anomaly article but not here! And the computation M => E is nowadays done with the Newton-Raphson algorithm, not as described here!

Stamcose (talk) 15:56, 23 November 2008 (UTC)

Undid restore of content

I undid the last edit by Lasunncty which restored the Oct. 30 version. I agree with Stamcose that the content should be applicable to ellipses in general and not just orbits. However, I also think the current state of the article needs cleanup (for grammar, or just reduce to complete redirect/disambiguation). In any case I do not think a poorer version of the same content on the ellipse page should be in this article.

I myself was about to edit the article because I found it too confusing with only reference to periapsis etc. and not the semimajor axis, and the attempts to dance around using the focus (orbited body) as the frame of reference rather than the ellipse center, then I saw the Talk and history and saw the content was really elsewhere.

If there is any turmoil over this, I just ask the interested parties to work it out on the talk page. --Walt (talk) 17:28, 22 January 2009 (UTC)

The figure is too complicated

I believe that the figure has too many details to be the definitive figure... It may be used to advocate some points later on, but the definitive figure should more like that of True Anomaly (same figure may apply here...) —Preceding unsigned comment added by 132.69.148.150 (talk) 14:31, 7 July 2010 (UTC)

Wrong Variable Name

In the section "From the true anomaly" the true anomaly is designated by the Greek letter theta and a reference is made to the diagram in which the true anomaly is designated by the Latin letter f. Since I do not know how to do it, would someone please make the necessary correction. Thank you. Nfr-Maat (talk) 21:47, 13 November 2014 (UTC)

Figure eccentricity label is wrong

Where in the figure you see e, it should be ae. Can anyone correct that? — Preceding unsigned comment added by 94.168.45.98 (talk) 14:40, 15 November 2018 (UTC)

Confusing reference point

The Graphical Representation section of the page is confusing.
As I understand it in orbital mechanics, point P is normally relative to point F in the diagram.
However, cosE(x/a) would be incorrect for that. (it is correct if P is relative to point C, which is not clearly defined in the article.)

Something like this would make more sense:
E = ACos((ae + x) / a)
Where: ae is linearEccentricity ( semiMajorAxis * eccentricity),
x is the horizontal component of point P,
a is the semiMajorAxis.

Note also that if AoP is not 0 then this will need to be taken into account too.

The diagram used to show ae instead of e as the linearEccentricity but has been changed. I don't know why this was done as e normally represents the eccentricity. — Preceding unsigned comment added by 122.60.125.153 (talk) 19:29, 26 April 2019 (UTC)

counterclockwise?

I feel that

The eccentric anomaly is measured in the same direction as the true anomaly, shown in the figure as ...

would be clearer if (counterclokwise) or something like is added after the word direction. pietro 151.29.43.102 (talk) 14:27, 10 November 2024 (UTC)