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![]() | The contents of the Reference ellipsoid page were merged into Earth ellipsoid#Reference ellipsoid on 26 November 2022. For the contribution history and old versions of the merged article please see its history. |
Coordinates: "These formulae have a closed-form inverse, though the algebra is rather involved. It can be shown that"
Yes there is a closed-form inverse, but this is not it! This is just the initial guess in Bowring's iterative method. While quite accurate at near terrestial points, it is not good for large h (e.g.: satellite positions).
Should (for example) sin(ae/2)^2 be (sin(ae/2))^2 -- the notation used here is not clear... —The preceding unsigned comment was added by 65.95.168.33 ( talk) 01:22, 22 January 2007 (UTC).
In the formulas:
Alpha appears to be undefined. It may be defined by mathematical or geographical convention, but without the appropriate background, I have no idea what values to plug in for a given ellipsoid. 70.89.118.42 ( talk) 00:18, 11 January 2012 (UTC)
Referring to the formula
is the radius of curvature in the prime vertical.
What is the behaviour at the equator and the poles? Clearly, at the equator the latitude is zero so sin(phi) is zero and the result is then N = a, which is clear: a circle of radius a would be tangent to the ellipse at the equator. Notionally interchanging x and y suggests that at the pole the radius of curvature should be b, but the formula does not yield that so far as I can see. The latitude at the poles is 90 degrees so sin(phi) is 1, and the formula becomes
and given that
and
or
Which is not b. So I'm puzzled. Rewriting the formula in terms of eccentricity,
has the same problem if but not if the second eccentricity is used instead,
So, how should I adjust my ideas? NickyMcLean 04:33, 11 May 2007 (UTC)
I have restored the conventional form of the equations for the direct transformation from geodetic to Cartesian coordinates. This was how they appeared on this page until one editor tried to convert every Wiki appearance of eccentricity (e) into angular eccentricity (alpha). I have given references and links to other wiki pages for the inverse transformation.
This whole area of Wiki is a mess, with much duplication of topics. For example this page Reference ellipsoids overlaps with geodetic system, geographic coordinate system , Latitude, Figure of the Earth, Earth Ellipsoid and probably many others. There could be some short term rationalising but perhaps a more thorough appraisal is need. Comments? Peter Mercator ( talk) 21:07, 11 January 2012 (UTC)
The statement in the article
In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid of revolution which he termed an oblate spheroid.
is not true, because in the quoted section of the Principia, Newton simply proves that the shape is oblate, but does not prove that it is a spheroid or ellipsoid. -- 98.234.249.218 ( talk) 12:49, 18 February 2012 (UTC)
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![]() | This redirect does not require a rating on Wikipedia's
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![]() | The contents of the Reference ellipsoid page were merged into Earth ellipsoid#Reference ellipsoid on 26 November 2022. For the contribution history and old versions of the merged article please see its history. |
Coordinates: "These formulae have a closed-form inverse, though the algebra is rather involved. It can be shown that"
Yes there is a closed-form inverse, but this is not it! This is just the initial guess in Bowring's iterative method. While quite accurate at near terrestial points, it is not good for large h (e.g.: satellite positions).
Should (for example) sin(ae/2)^2 be (sin(ae/2))^2 -- the notation used here is not clear... —The preceding unsigned comment was added by 65.95.168.33 ( talk) 01:22, 22 January 2007 (UTC).
In the formulas:
Alpha appears to be undefined. It may be defined by mathematical or geographical convention, but without the appropriate background, I have no idea what values to plug in for a given ellipsoid. 70.89.118.42 ( talk) 00:18, 11 January 2012 (UTC)
Referring to the formula
is the radius of curvature in the prime vertical.
What is the behaviour at the equator and the poles? Clearly, at the equator the latitude is zero so sin(phi) is zero and the result is then N = a, which is clear: a circle of radius a would be tangent to the ellipse at the equator. Notionally interchanging x and y suggests that at the pole the radius of curvature should be b, but the formula does not yield that so far as I can see. The latitude at the poles is 90 degrees so sin(phi) is 1, and the formula becomes
and given that
and
or
Which is not b. So I'm puzzled. Rewriting the formula in terms of eccentricity,
has the same problem if but not if the second eccentricity is used instead,
So, how should I adjust my ideas? NickyMcLean 04:33, 11 May 2007 (UTC)
I have restored the conventional form of the equations for the direct transformation from geodetic to Cartesian coordinates. This was how they appeared on this page until one editor tried to convert every Wiki appearance of eccentricity (e) into angular eccentricity (alpha). I have given references and links to other wiki pages for the inverse transformation.
This whole area of Wiki is a mess, with much duplication of topics. For example this page Reference ellipsoids overlaps with geodetic system, geographic coordinate system , Latitude, Figure of the Earth, Earth Ellipsoid and probably many others. There could be some short term rationalising but perhaps a more thorough appraisal is need. Comments? Peter Mercator ( talk) 21:07, 11 January 2012 (UTC)
The statement in the article
In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid of revolution which he termed an oblate spheroid.
is not true, because in the quoted section of the Principia, Newton simply proves that the shape is oblate, but does not prove that it is a spheroid or ellipsoid. -- 98.234.249.218 ( talk) 12:49, 18 February 2012 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Reference ellipsoid. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018.
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regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 04:19, 14 December 2017 (UTC)