Talk:Earth radius

message: The heading Neridonal appeared in a 1 April 2007 edit. Surely this should be Meridional. I don't think neridional is even a real word. Certainly it's not in any online dictionary. Also a Google search for it only gives 149 hits, and almost all of those hits are either this article or people who have copied this article verbatim (like answers.com). I'm going to edit this. If someone feels there is some really burning reason why it should be 'neridional' and wants to revert, please add a note here why such an obscure word that doesn't appear in dictionaries should be used. I'm looking at you, User:Kaimbridge, since you made that 1st April edit ... surely you wouldn't be playing an April Fool's joke on Wikipedia ;).
Dr algorythm 03:19, 18 June 2007 (UTC)
replies: text: LOL!!!  Sorry about that——I'm blind in one eye and the other eye's no bargain, with an acutely advancing cataract further complicating things.  So, needless to say, a few typos may escape me!  P=)  ...Hmmm, how come it took someone two and a half months to catch?!? P=/ ~Kaimbridge~14:27, 18 June 2007 (UTC)
thread_title: "Neridional" radius of curvature???

message: On this page the polar radius is derived as being larger than the equatorial radius. Please check this derivation. —The preceding unsigned comment was added by 216.59.226.224 (talk) 04:48, 25 April 2007 (UTC)
replies: text: What do you mean, a (equatorial radius) = 6378.135 and b (polar) = 6356.75? ~Kaimbridge~10:49, 25 April 2007 (UTC)
thread_title: ERROR?

message: Why are we not using SI units here (radii in meters)? MeddlerOnTheRoof (talk) 02:21, 9 May 2008 (UTC)
replies: text: Kilometres are SI. JIMp talk·cont 18:11, 29 December 2009 (UTC)
thread_title:  SI Units 

message: I removed this text:
:This number is derived by square rooting the average (latitudinally cosine corrected) geometric mean of the meridional and transverse equatorial, or "normal" (i.e., perpendicular), arcradii of all surface points on the spheroid
It may be that the number approximates the root of the average. I don't find evidence that this average is used to derive the exact expression. One derivation is here.
I also modified this text
:the radius of a hypothetical perfect sphere which has the same, geometric mean oriented surface area as the spheroid.
The "mean oriented surface area" of a perfect sphere is zero, as each elemental vector area has an equal antipodal counterpart. The vector sum of the oriented area is zero. -Ac44ck (talk) 02:43, 1 November 2008 (UTC)
thread_title:  Changes to section on authalic radius 

message: The original Meridional definition of a meter was one ten-millionth the distance from the North Pole to the Equator, the circumference of the earth is then (about) 40 million meters. Treating the earth as a perfect sphere then gives a nice, and easy to remember approximation for the average radius of the earth: (2/pi)*10^7 meters. This works out to 6366.2km, which is within 0.1% of all of the various figures for the average radius. Pulu (talk) 06:14, 12 November 2008 (UTC)
thread_title: Approximation

message: The current value in the article for polar radius is b = 6,356.7523 km, which would seem to more than accurate enough for an average visitor.
But I have a consistency problem:
The value is attributed to "WGRS 80/84" in the "Fixed radii" section. It is attributed to WGS (E2008) in the "Mean radii" section.
In following links to here, it appears that WGS (E2008) is using the values of a and f from WGS 84.
The table here says those values make b ≈ 6,356,752.314,245 m. It uses the " ≈ " symbol, but reports the value to the nearest micron (1e-6 m)!
NOTE: Take 6,371,008.8 X 3 = 19,113,026.4 minus 6,356,752.314 245 = 12,756,274.09.  Dividing by 2 gives 6,378,137.043 m.  I do not think the
43 mm is all that important when compared to the 6,378,137 meter radius at the equator. 98.245.216.62 (talk) 23:24, 18 April 2022 (UTC)
thread_title:  Polar radius 

message: The lede paragraph begins:
:Because the Earth is not perfectly spherical, no single value serves as its natural radius. Instead, being nearly spherical, a range of values from 6,357 km to 6,378 km (≈3,950 – 3,963 mi) spans all proposed radii according to need,...
I cannot make sense of "spans all proposed radii according to need".  Does this mean that these figures a are the range of numbers used in geologic and astrophysical computations?  If so, it should say so.  The numbers are clearly within the range of the actual maximum and minimus listed later in the article. How about this for the lede:
:"Radius" is normally a characteristic of perfect spheres. Because of the equatorial bulge, the Earth is not perfectly spherical, so no single value serves as its natural radius.  The radius is at its minimum at the floor of the Arctic Ocean at the North Pole.  The average of the two poles is 6,357 km.  The radius is at its maximum at the summit of Mount Chimborazo near the equator.  The average radius along the equator is 6,378 km.  As a result of this variation, Earth radius has come to mean the distance from some "center" of the Earth to a point on some idealized surface that models the Earth.  Mathematical models are used to calculate approximate values for the variation in Earth's radius.  Several different ways of modeling the Earth as a sphere all yield a convenient mean radius of 6371 km (≈3,959 mi).  This article deals primarily with spherical and ellipsoidal models of the Earth. See Figure of the Earth for a more complete discussion of models.
:Note: Earth radius is sometimes used as a unit of distance, especially in astronomy and geology. It is usually denoted by R_\oplus.
::--☑ SamuelWantman 02:47, 19 March 2009 (UTC)
thread_title:  Yet another source of confusion 

message: This gfx http://en.wikipedia.org/wiki/File:Lowresgeoidheight.jpg is kind of wrong, that Longitudes goes from 0 --> 180° (E) and from 0 --> -180° (W)
193.162.192.70 (talk) 08:22, 29 June 2009 (UTC)
replies: text: It's a reasonable representation. Just interpret the x axis as longitudinal difference from the prime meridian. It doesn't claim to represent "absolute" longitude, and longitude isn't absolute in any case. 180°W – 180°E is just a convention, and not the only one in use. Strebe (talk) 03:53, 30 June 2009 (UTC)
thread_title:  http://en.wikipedia.org/wiki/Earth_radius 

message: The second sentence of the article needs an easy improvement:
"Because the Earth is not perfectly spherical, no single value serves as its natural radius. Instead, being nearly spherical, a range of values from 6,357 km to 6,378 km (≈3,950 – 3,963 mi) spans all proposed radii according to need..."
As everyone knows, the earth spheroid's radius of curvature varies between 6335 and 6400 km-- so apparently the author intends "all proposed radii" to not include radius of curvature. Which it does, unless the exclusion is made plain. Tim Zukas (talk) 18:29, 30 August 2010 (UTC)
replies: text: Good point. Strebe (talk) 19:18, 30 August 2010 (UTC)
replies: text: Much better now-- but might as well say "to points on the sea-level surface..." Dunno offhand how far from the center of the earth to the top of the highest equatorial mountain. Tim Zukas (talk) 19:51, 30 August 2010 (UTC)
replies: text: It does not (or need not) refer to mean sea level specifically. The article lists actual minimum and maximum, so I have revised the lede accordingly. Strebe (talk) 20:28, 30 August 2010 (UTC)
thread_title:  The second sentence ("all proposed radii...") 

message: Not sure if the two Moritz refs are the same or different, but the one I'm citing seems to be dated 2000 even though 1980 appears in the title.  It's here:  http://www.springerlink.com/content/0bgccvjj5bedgdfu/about/ and on the "about" page it gives a year 2000 date.  Also it's cited as year 2000 in Method of calculating tsunami travel times in the Andaman Sea region by Monte Kietpawpan et al. ☺Coppertwig (talk) 23:24, 11 December 2010 (UTC)
replies: text: According to this page, Volume 74, Number 1 of the Journal of Geodesy was published in March 2000, so I think you're right.  Also, as corroborating evidence, I was able to export a BibTex-formatted citation, which also includes a date of 2000. Jakew (talk) 21:52, 12 December 2010 (UTC)
thread_title:  Date of Moritz 

message: I don't want a mathematical treatise on how to measure the radius of the earth. This is an encyclopedia, I expect to see a number. The radius of the earth from the centre to the equator is X. The radius of the earth from the centre to the poles is Y. Why can't some of you freakin rocket scientists do something straight forward and simple to answer the average person's question for a change? And no it doesn't have to be this way. And yes, you can provide a simple bloody answer. Everything isn't a shade of flippin grey. This is the problem with Wikipedia, you egg heads make it worthless to look for information. This is not a math course. It is an encyclopedia. Please provide information that is understandable. For God's sake.  — Preceding unsigned comment added by 75.119.254.110 (talk) 08:12, 25 December 2011 (UTC)
replies: text: Fix it if is broken. Or whine. Your choice. I might as well whine about people who think the world should be arranged to suit their own personal, simplistic ways of thinking and, instead of helping, throw abusive tantrums when they don’t get exactly what the want… for free, even. And, Happy Holidays. Strebe (talk) 21:26, 25 December 2011 (UTC)
replies: text: Agreed, however seeing as there as a variety of reasons and ways to measure this, any value listed should be qualified. Perhaps the R1 value should be listed because it's the mean radius?  — Preceding unsigned comment added by Bbbg123 (talk • contribs) 18:38, 4 April 2019 (UTC)
thread_title:  For just an average guy, this article is sheer CRAP 

message: This radius definition was added in these edits. “Ellipsoidal quadratic mean radius” doesn’t exist in the literature. It appears to be original research which has a lot of references on the Web, but they all go back to a single, unpublished source who appears to be promoting it. I will delete this edit in a week if there is no published source forthcoming. Strebe (talk) 06:28, 2 January 2012 (UTC)
thread_title: Ellipsoidal quadratic mean radius

message: Newton's law of universal gravitation#Gravitational field
:With a few simplifications:
:: g =
 G {M \over {r^2}}
Gravitational constant
: G = 6.67384 \times 10^{-11} \ \mbox{m}^3 \ \mbox{kg}^{-1} \ \mbox{s}^{-2} = 6.67384 \times 10^{-11} \ {\rm N}\, {\rm (m/kg)^2}
Mass of Earth
:M = 5.9722 × 1024 kg
Earth's gravity
:Standard gravity is, by definition, 9.80665 m/s2 
Putting it all together:
:9.80665 = (6.67384e-11 * 5.9722e24) / r^2
:r = sqrt((6.67384e-11 * 5.9722e24) / 9.80665) =   6,375,213.43562 meters
Standard gravitational radius = 6,375.213 km -Ac44ck (talk) 03:22, 3 July 2012 (UTC)
thread_title:  Standard gravitational radius 

message: The location in radians spherical coordinates: (1,-π/2,1) = (1, 3τ/4,1). The first one is radius of Earth, the -π/2 or 3τ/4 is 90 degrees west, and the last 1 is the angle from N. Pole or (π/2-1)rad north = (τ/4 -1) rad north which is 32.7042204869 degrees N.
I know this location by Google maps is north of Canton, MS, USA just a few hundred feet from US 51. But, problem is the radius. I put one in for the radius as for a place holder, but I would like to know is the exact value of the Earth's radius at N32.7042204869, W90.0000000000 taking into account all of the different elevations (like changes caused by the moon and sun), deformations (like geoid height), and drifts (like continental drift). I am thinking of having something like the annual South Pole remarking ceremony marking this location. How do I find all of this together in a simple way? 
I am also thinking about the fact that the length of the arc with an ellipse is different from an arc with a circle. How does this affect radians?
John W. Nicholson (talk) 12:55, 19 February 2013 (UTC)
replies: text: This is not a trivial problem to solve. Note that the Talk page is for discussing improvements to the article. You should find a geodesy discussion board for this sort of question. Thanks. Strebe (talk) 00:44, 20 February 2013 (UTC)
thread_title:  Earth radius at N32.704220, W90.000000? 

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thread_title:  External links modified 

message: See Talk:Figure_of_the_Earth#Spherical. --Jack Upland (talk) 12:54, 3 March 2016 (UTC)
replies: text: Let's centralize the discussion there. fgnievinski (talk) 15:56, 3 March 2016 (UTC)
thread_title:  Spherical 

message: There was a note (above) on an approximation for the radius of the Earth. It is perhaps better counted as a definitional value based on the definition of units, both SI kilometers and the still widely-used nautical miles. The radius of the Earth (in the sense of the simple mean (a+b)/2) is very nearly given by 20000/pi kilometers or 10800/pi nautical miles. Do the division, and you get approximately 6366 km or 3438 nautical miles. These values match the simple mean radius to 99.98%. In both cases, the numerator is the number of base units from pole to pole, which for both kilometers and nautical miles were originally defined to be an integral number from equator to pole. There are 10,000 km from pole to equator or 20,000 from pole to pole, and there are 90·60=5400 nautical miles from pole to equator or 10800 from pole to pole. Meanwhile pi here is just the angle from pole to pole expressed in radians. Another way to put it: the radius of the Earth in nautical miles is numerically equal to the number of minutes of angle in one radian: approximately 3438. 174.199.34.212 (talk) 16:39, 4 November 2016 (UTC)
replies: text: IMO this value is important enough to be listed in the table: When using nmi, the math is simple using nautical miles: R_E = (360deg * 60nmi/deg)/(2*pi) = 3437.7467708nmi = 6366.7070195 km. This is the spherical earth equatorial radius.  — Preceding unsigned comment added by Bbbg123 (talk • contribs) 18:42, 4 April 2019 (UTC)
replies: text: This edit did not read coherently for several reasons. I have tried to improve it, but the original source's intent is not clear to me. Please provide the original text so that it can be rendered coherently. Or, perhaps we should choose a different account. Strebe (talk) 21:20, 4 April 2019 (UTC)
replies: text: In the end, I deleted it. Earth's radius (circumference, really) factors into the definition of "nautical mile", not the other way around. Therefore, nautical mile is not a definition for earth radius and does not belong listed among them. Strebe (talk) 19:47, 5 April 2019 (UTC)
thread_title:  Definitional value (or approximation) 

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thread_title:  External links modified 

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thread_title:  External links modified (January 2018) 

message: There is a move discussion in progress on Talk:Earth's circumference which affects this page. Please participate on that page and not in this talk page section. Thank you.  —RMCD bot 23:03, 6 January 2019 (UTC)
replies: text: Again: Talk:Earth%27s_circumference#Requested_move_27_April_2021. fgnievinski (talk) 01:59, 28 April 2021 (UTC)
thread_title:  Move discussion in progress 

message: There are several problems with the definition of the
Global mean radius of curvature
as defined is this article.  This order of increasing
importance there are:
* The final expression could be simplified by putting it in terms of \tanh^{-1} e.
* There's no authority cited for this definition of R_4.
* The area average incorrectly uses a spherical area elements.  Using ellipsoidal area elements gets you a more complex expression.
* The text talks about a "mean Gaussian curvature" and yet the mean of the radius is computed.
On the last point, it's probably makes more sense to average curvatures
instead of radii of curvature.  The latter is badly behaved if a portion
of the surface is flat.  This isn't the case here of course; but this
illustrates the problem.  In fact the correct area weighted mean of the
Gaussian curvature is
: \langle K \rangle = \frac{4\pi}A 
(this follows from the Gauss-Bonnet theorem)
and the resulting mean radius of curvature is then just the authalic
radius R_2.
Unless some authority can be found that uses the quantity
R_4 as defined here, I recommend removing this
section.  An alternative is to replace is with a section giving the
connection of the mean Gaussian curvature to R_2.
 and , you might want to weigh in here. cffk (talk) 21:56, 14 August 2021 (UTC)
replies: text: For the record, R_4 is within 14 m of R_2; to first order in the flattening, there are both equal to R_1=(2a+b)/3. cffk (talk) 13:19, 15 August 2021 (UTC)
replies: text:  I changed this section to use the area average of K, as discussed above. cffk (talk) 13:14, 20 August 2021 (UTC)
replies: text:   thank you for your edits, it makes sense. I've taken the liberty of merging the two parts about R2 in a single section. Also, a citation would still be valuable, especially considering the previous mistaken formulation. fgnievinski (talk) 06:56, 21 September 2021 (UTC)
replies: text:   Sorry, I don't know of a citation that makes the connection in this way.  The result is a quite straightforward consequence of Gauss-Bonnet; so if any textbook mentions it, it's likely to be as a brief mention. cffk (talk) 18:32, 21 September 2021 (UTC)
thread_title:  Global mean radius of curvature 

message: In the table ("Published values") only 2 look (to me) like actual measurements.
Can you provide a few more?
In particular: distance to the shores in the Arctic and Antarctic. But also some "hot spots" like Everest, Malaysia, South Pole.  (NB:  I couldn’t find it with Google). 
MBG02 (talk) 23:30, 6 April 2022 (UTC)
thread_title:  Actual values 

message: With e.g. the WGS84 ellipsoid the mean Earth radius is 6,371 km.
Per the Mean value theorem is follows that there are points where this radius is exact.
Where are they? (Should be added to the article, e.g. in the form of a lattitude). Lklundin (talk) 18:46, 4 September 2023 (UTC)
replies: text: In relation to the earth's radius, this is not anything that appears in  reliable sources, which suggests it’s not important. Without a citation, a calculation would just be  original research. Strebe (talk) 15:54, 5 September 2023 (UTC)
replies: text: OK, thanks for checking. Lklundin (talk) 16:19, 5 September 2023 (UTC)
thread_title:  Mean Earth Radius exact where ?