Talk:Orbit determination

No references
I added a few books that I have on this subject in the "Further Reading" section, but there are no citations that I can see anywhere in this article. After having some of my edits deleted for lack of citation (edits that amount to something on the order of, say, "The sky is blue."), this is "concerning." Anyway, I hope someone knowledgeable about this topic will fix this article up; it should be referenced by the "Comet" article (and probably a few others), IMHO. Rb88guy (talk) 18:46, 27 August 2009 (UTC)
 * Added the unreferenced template. Rb88guy (talk) 23:48, 27 August 2009 (UTC)

This article is a disgrace to Wikipedia. It gives only a brief history of the subject; it gives no technical information; it mentions nothing about the uses of orbit determination (e.g., GPS, determination of the Earth's gravitational field); it mentions none of the leading texts on the subject (e.g., Fundamentals of Astrodynamics and Applications by Vallado, Methods of Orbit Determination by Escobal). I could write a much better article, but there are many other experts more qualified than I. Gottliebpet (talk) 20:20, 5 May 2010 (UTC)

use in GPS
Don't the satellites themselves or the groundstations use orbit determination? If so, then this is still a very important application that deserves to be mentioned. Martijn Meijering (talk) 18:17, 26 August 2013 (UTC)

Gibbs' method
I've been doing some research on Gibbs lately and found out something that could be relevant to this article. Around the 1880s, Gibbs came up with a method to deduce orbits from three observations, which has been called simpler than Gauss's approach. You can see the method used and discussed in [http://articles.adsabs.harvard.edu/full/1889AJ......9..113B scanned version of Beebe, W. & Phillips, A. W., Astronomical Journal, vol. 9, iss. 207, p. 113-117 (1889)]. I'm not so familiar with orbit determination so I'm not sure if it's worth mentioning, but, there you have it. --Nanite (talk) 17:11, 30 August 2013 (UTC)
 * The Gibbs paper in question is J. W. Gibbs, "On the determination of elliptic orbits from three complete observations.." (1889), reproduced in The Scientific Papers Vol 2 (1906), pp. 118–.
 * Also, here is a 2001 book (Fundamentals of Astrodynamics and Applications by Vallado), which discusses the Gibbs method in context of other orbital determination methods. It looks like the book could be a handy reference for this article in general. Nanite (talk) 14:27, 16 February 2014 (UTC)

-Below comments from another author- — Preceding unsigned comment added by 2600:1700:BAE1:9A0:8879:7D72:D75:E4F (talk) 17:43, 11 December 2020 (UTC) In my view the Gibbs method suffers from a fatal flaw: it requires three co-planar Earth (or Sun) centered vectors, and no time information. But, without knowing the time of measurement, one cannot transform the observed vectors (e.g. radar, by definition measured from a point not at the center of Earth) into an Earth-centered vector. Once you have the time information (Epoch), you only need two vectors and can use the Gauss method, which was developed long before Gibbs. Thus the Gibbs method is but a mathematical oddity, interesting as background, but of no practical value. Later additions (e.g. Herrick-Gibbs) deal with e.g. improving accuracy for small angles, but they suffer from the same fatal flaw. Comments anyone? Did I miss anything? — Preceding unsigned comment added by 2600:1700:BAE1:9A0:8879:7D72:D75:E4F (talk) 17:41, 11 December 2020 (UTC)

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Gauss' Method
Gauss' Method with three observations has a weakness that causes it to fail when the apparent motion of the (say) asteroid across the observer's sky exhibits no curvature—i.e., when the three points on the sky fall on the same line. In such cases, the {a1, b1, c1; a2, b2, c2; a3, b3, c3} matrix has a zero determinant. That determinant forms the denominator of expressions used to calculate the coefficients of the eight-degree polynomial that must be solved to get the asteroid's heliocentric distance at time 2. Geometrically, the determinant of that array is proportional to the volume of a tetrahedron formed in a coordinate system in which the geocenter is fixed at the origin, with the other three vertices being the three positions of the asteroid. When there is no volume, the tetrahedron becomes a "kite," and Gauss' method will fail. The procedure that should have found the heliocentric distance of the asteroid at time 2 loses all connection with reality.

Fortunately, there are variations of the method for producing good preliminary orbits that don't have this weakness. One of them, using four observations instead of three, is found in A.D. Dubyago's book The Determination of Orbits, Chapter Six. You'll find this method presented in work-sheet format at

https://jenab6.livejournal.com/78393.html

A fully worked example case (involving the asteroid 1 Ceres) is presented for the benefit of programmers.

A freeware program, written (by me) for the HP Prime calculator, that implements the four-observation method for determining a preliminary asteroid orbit can be downloaded from

https://my.cloudme.com/jenab6/ORBIT4_1 Jenab6 (talk) 02:16, 8 October 2018 (UTC)