Talk:Minute and second of arc

Number of square arcminutes in a sphere
There isn’t 148,510,800 square minutes in a sphere, if it isn’t a misquotation that is perhaps something that’s only valid for the Earth’s sky. Earth is not a perfect sphere. 2πr = 60·360 = 21,600 arcminutes, r = 21,600/2π, A = 4πr^2 = 4π·(466,560,000/4π^2) = 466,560,000/π ≈ 148,510,660.498 square arcminutes. I'm fixing it, but just if anyone disagrees for some reason (since there's a source and everything for the false info). User:DeclinedShadow 02:50, 17 July 2009 (UTC)

Rewrote this again since someone changed it back, and added some calculations. Anyone of you can just look at the Square degree page, there's the same formula being used. User:DeclinedShadow 03:52, 2 August 2009 (UTC)

from original article, "Arc of Minute"
What the heck is this feature for?? Well, I'll be darned. Shouldn't this be "Minute of Arc"?


 * Yes, it should be "minute of arc" or "arcminute". But I would prefer an article on angular measure, where all such terms can be discussed in one place. Where did you find the link to "arc of minute"? --Zundark, 2001 Nov 2


 * Nautical_mile is one link to here, Minute is another. What's an idea on cleaning this one up?  Doesn't look like the angular measures are made, and I'm new and reluctant to attempt tying loose ends and botching it, or to start a new article that may not be warrented.  I'm expecting this should fit with other standardized units of measure (linear distance, area, volume) in how it looks and behaves.  Once created, perhaps this page ought to redirect to the 'cleaned up' version under Zundark's preferred title.  Would an arc 'Orders of magnitude' be appropriate?  Two ways to look at that one: 1) Arc minute of Earth (as standardized by the Nautical mile vs. the same on the Sun, and 2) Degree vs. Arc minute vs. Radian.  If an old-hand at this doesn't mind steering me in an appropriate direction, I'll tack this on my 'Wiki-to-do' and fuss over it over time. --Romaq 2002 Jan 21

I'll see what I can do on anglar measurements. -- April 09:04 Aug 7, 2002 (PDT)

It seems sensible that one of Minute of arc and Arcsecond should be renamed to fit in with the other. Both belong to Category: Units of angle Icairns 21:39, 25 Jun 2004 (UTC)

First we have to decide which is the "most correct". Arcsecond (or arc second) is far less awkward, anyway. --Elektron 10:28, 2004 Jul 4 (UTC)
 * I find in practice (as an astronomer) that arcminute and arcsecond are most used. Certainly 'second of arc' is never used in my experience. Of course these things crop up in several fields. EddEdmondson 10:32, 4 Jul 2004 (UTC)

merge arcminute and arcsecond articles
I see above that there has been some discussion in the past about merging the articles on arcminute and arcsecond. This may be a good idea to pick up. Most info on one page could be (or already is) on the other. MHD 11:04, 3 February 2006 (UTC)


 * For a comparison, centimetre redirects to metre, but millimetre redirects to 1 E-3 m. Is there a reason to keep both arcminute and arcsecond separate from degree (angle) as well?  It might make sense to merge all three.  Otherwise, merging a minimum of arcsec into arcmin makes sense to me.  Should someone put up a "merge suggested" tag?  --zandperl 04:49, 8 February 2006 (UTC)

I agree: merging all three may be a sensible thing to do, but maybe also a little more time consuming to do, as opposed to just merging the arcminute and arcsecond articles and leaving the degree article as it is.

As to the millimetre/centimetre/metre issue, I have no idea why millimetre links to 1 E-3 m, and not to metre, which it should, in my opinion.

MHD 09:56, 8 February 2006 (UTC)


 * Nobody else seems to care, so I decided to finally start the merging process of arcsecond into this article. There are some information elements in the arcsecond article that I still have to merge into this one, after that is done (hopefully tomorrow), I will make arcsecond redirect to minute of arc. I will also merge the information from milliarcsecond into here. Cheers, MHD 21:09, 26 March 2006 (UTC)


 * (anonymous user): this is an encyclopedia, not a dictionary. We don't need a new article for each prefix of a standard unit.  Merge at will :)


 * I support the merging of the arcminute and milliarcsecond articles, as long as no information from either article is lost/discarded. The content of the two articles is substantially different and the milliarcsecond article contains some interesting facts and trivia. User: Jaganath 16:12 07 June 2006 UTC

other uses of arcminutes and arcseconds
Arcminutes and arcseconds are indeed used when measuring the declination of an object on the sky. When measuring the right ascension (RA), these units are not used (as is correctly stated by User:Zandperl in the article). Instead, RA is measured in:
 * hours, (24 h = 360 degrees -> 1 h = 15 degrees)
 * minutes, (1 minute = 15/60 degrees = 1/4 of a degree = 15 arcminutes) and
 * seconds, (1 second = 15/3600 degrees = 1/240 of a degree = 15 arcseconds)

This a fair thing to put in an article on arcminutes (or arcseconds for that matter).

However, there are numerous other coordinate systems that use the degree (and its subdivisions arcminute and arcsecond), such as Galactic coordinates, though it is also common to express galactic longitude and latitude in ordinary decimal fractions of degrees, the coordinates of an object may be expressed as "l = 48.85 and b = -1.96", meaning that it has a galactic longitude of 48 and 85/100 of a degree and a galactic latitude of minus 1 minus 96/100 of a degree.

Oops, forgot to sign this message yesterday. It was written by me: MHD 11:35, 4 February 2006 (UTC)


 * I also threw the below into the article before, and some cleaned-up version might be appropriate in the article.
 * Astronomers typically measure Right Ascension in hours, minutes, and seconds. RA minutes and seconds are not to be confused with Declination arcminutes and arcseconds, as they are of a different size.
 * In right ascension and longitude, the size of the degree (and therefore arcmin and arcsec) changes with how far you are from the equator.
 * As opposed to a degree of latitude, which always corresponds to about 111 km (69 mi), a degree of longitude corresponds to a distance from 0 to 111 km: it is 111 km times the cosine of the latitude, when the distance is laid out on a circle of constant latitude; if the shortest distance, on a great circle were used, the distance would be even a little less. (Longitude page)
 * Whatever we decide upon should also have a modified version in the arcsecond page.
 * --zandperl 15:12, 4 February 2006 (UTC)

I agree to the fact that information in the arcminute page should also be on arcsecond, that is exactly the reason why I proposed to merge these two articles (see topic above this one). 17:23, 4 February 2006 (UTC)

Visual Acuity Under Cartography?
Visual acuity should be under a different section as best as I can tell. Unfortuntately, I only know about visual acuity what I've read on Wikipedia. Should the section be called "Ophthalmology"? Thanks! Don 20:13, 19 February 2006 (UTC)

Right ascension in cartography
I am only familiar with the term 'Right Ascension' when it is used in astronomy. I am a bit confused as to what it really means in cartography: does it refer to a different concept than geographical longitude, or is is just a different name for the same thing? I understand that the distance over the surface of the earth corresponding to 1 degree of right ascension would vary depending on the geographical latitude (how far from the equator you are). Talking about such variations makes much less sense in astronomy, which is why I removed the reference to astronomy in the Cartography section. In addition: the page about Right ascension does not handle the subject of its use in cartography at all, so I don't think it is wise to have a link pointing from the cartography section of Minute of arc directly to Right ascension. Can somebody help me out on the meaning of 'right ascension' in cartography? And maybe (help me) come up with a clearer description in this section and/or write a section about the use of right ascension in the Right ascension article? Thanks, MHD 12:18, 18 April 2006 (UTC)

Incorrect formula?
Although I am not a firearm afficionado, i think the correct formula is 2*tan(MOA ∙ π/21600)*distance, since you are trying to find the opposite side of an angle, given the adjacent side. It may be that for accurate estimates, the tan is not needed since the results are very close, for example in the example given, the answer computed using tan is approximately 1.04719756 which differs by only 7∙10^-9 inches from the previous value.

I also think it's incorrect. Tangent is a right triangle function, in the main article formula, tan(MOA ∕ 60)*distance, tangent is being applied to an isosceles triangle. Because the two equal angles at the base approach 90 degrees (in these cases) the error is not so great. However, the correct approach is to split the isosceles triangle into two identical right triangles, as the person who posted the above paragraph did, calculate the value for the halves then multiply it by two. So the formula for would be 2*tan(MOA/120)*distance. (JohnMc 7-31-08) —Preceding unsigned comment added by JohnMc (talk • contribs) 00:10, 1 August 2008 (UTC)

Different interpretations of 1&prime; at 100 yards yield differences too tiny to be worth consideration
The calculation by Dexadine, now cited in the article, considers the length along an arc all points of which are 100 yards from the observer. JohnMc, above, treats the distance between the endpoints of that arc. In an edit I reverted, CoastalShooter considers the length of a line perpendicular to the line of sight with one end 100 yards from the observer. The results differ by a few ten-thousands of an inch, not enough to be worth arguing about. It's enough to say that the length is approximately 1.047 inches, which everyone agrees on. Peter Brown (talk) 16:28, 23 December 2019 (UTC)

This is incorrect?
The is no "minute of arc" it is MINUTE OF ANGLE. —The preceding unsigned comment was added by 62.248.159.240 (talk) 17:05, 28 April 2007 (UTC).

How about adding a simple paragraph that discusses the "minute of arc" vs "minute of angle". While it looks to me like astronomer types use arc, the firearms people most definitely do not. So a firearms person coming to this page may be confused, even if arc is technically the correct term (which I am not sure of). So maybe a "common confusion" paragraph/section that explains common usages, etc. Arthurrh 19:57, 9 July 2007 (UTC)

There definitely is a "minute of arc". It is used by vision scientists (too). —Preceding unsigned comment added by 188.142.56.253 (talk) 20:10, 12 February 2011 (UTC) one "arc" is a 1/6 of a revolution. so 1/60 arc, is a degree (6*60 = 360). then 1/60*1/60 = 1/3600, etc (just like time fractioning). its so weird that some people still insisting to use this kind of decimalization Tabascofernandez (talk) 21:51, 14 July 2017 (UTC)

"one "arc" is a 1/6 of a revolution." Huh? An arc is simply a piece of a circle and can be any length or subtend any angle. Cross Reference (talk) 21:29, 1 January 2020 (UTC)

Minute of arc is standard terminology in astronomy; arcseconds not really well-merged...
Re: the previous post -- "Minute of angle" may be the correct terminology in firearms work -- from the article, I gathered that -- but it is never used in astronomy. In astronomy, the correct terminology is "minute of arc". I don't have a reference for this, but I have long experience as a professional optical astronomer. So the moral is, don't be too hasty in categorically saying a term is not used, the world is very big!

Regarding the merging of arcsecond into arcminute, I think it could be improved. Also, there's no noting that the abbreviation "mas" means "milliarcsecond" in some contexts; if you look at e.g. the article on "Teegarden's star" the quoted values for parallax and proper motion make use of the "mas" notation, which directs you to "minute of arc", where there is no longer an explanation of the "mas". 67.142.130.45 = Jthorstensen ; 04:39, 29 April 2007 (UTC)

(A little later) -- I went ahead and touched up the arcsecond discussion a bit, in particular adding an explicit reference to the milliarcsecond; I know it's a standard SI prefix, but it seems to confuse people so it's worth a sentence or two. I can't seem to get my four-tilde signature to work from home, but I am JThorstensen. after milli/ micro sec[ond] in time, the milli/ micro deg[ree] in angle is the best path to proceed, while lacking in temperature (98 Fa[hren], 53 Ce[lsie], 520 Ke[lvin] ). Tabascofernandez (talk) 22:16, 14 July 2017 (UTC)

Minute of Arc, The band
minute of arc the band can be found at www.mypace.com/moa

This appears at the head of this article as of 11:42PM EST. That belongs on a disambiguation page! Whomever posted that needs to take it down and do it right. Thanks. —Preceding unsigned comment added by 69.140.192.220 (talk) 03:44, 9 April 2009 (UTC)

Race Elapsed Time
In terms of racing, I've seen the elapsed time displayed as, say 33'21" (33 minutes, 21 seconds). However, this article is not very clear on what happens in races that last over an hour. Does the minutes continue to count up (93'=60'+33'), does it use the degree symbol °, or is it displayed in some other format?

I request a new section on the use of the arcminute in racing.

Christopher, Salem, OR (talk) 07:50, 1 July 2010 (UTC)
 * This has nothing to do with racing or timing, Arcminutes are a measure of angle not time.  — M3TA  (  info  ) @  09:36, 29 August 2010 (UTC)

Unit conversions valid
I just checked all of the unit conversions using Google as a calculator both with Google's value of pi and with MathWorld's value of pi. The only value I was unable to verify to all digits was minute of arc in radians (which has one more significant figure than Google supports). Given that these conversions involve only integers and pi, I am shocked by this label on this article: "The factual accuracy of this article may be compromised by unit conversions quoted to a greater precision than can be justified from the original data. Please help improve this article by truncating values to a suitable number of significant figures." I haven't edited wikipedia in a while, so I am reluctant to remove this label. rs2 (talk) 20:35, 29 July 2010 (UTC)
 * Agreed, so have removed the label.  — M3TA  (  info  ) @  09:36, 29 August 2010 (UTC)

Merge
I think we should merge Minute of Angle into this article. Note that Minute of angle with lowercase "a" already redirects here. AliveFreeHappy (talk) 20:55, 6 October 2010 (UTC)


 * It probably shouldn't do that. These are two distinct things. Retitling to (say) "Minute of Angle (firearms)" and "Minute of Arc (geometry)" would help, with topnotes to the other on each page. htom (talk) 00:25, 19 October 2010 (UTC)

Error: Reason for "not SI"
Currently the article contains the statement: "However, they [arcsecond and arcminute] are not themselves SI units because they are dimensionless.". This looks false to me -- is there a reference for this? Regardless of whether one considers units of angle to be dimensionless, that does not preclude them from being SI units. They are presumably not SI units for some other reason, perhaps because instead SI chooses radian as the unit for angle. Gwideman (talk) 01:14, 8 June 2011 (UTC)

Someone please fix the recursive self-linking
The article says "This article is about geometry. For firearms terminology, see Minute of Angle." When you click on "Minute of Angle", it brings you right back to this page, because "Minute of Angle" is set to redirect here. Something is obviously wrong...71.109.153.28 (talk) 04:17, 6 February 2012 (UTC)

Shouldn't prad, etc., be defined in this article?
I see prad, etc., used at least in the units-of-angle table to express various angle units in terms of other ones.

But nowhere in Wikipedia could I find "prad" per se. Googling, I learned that prad stands for picoradian, one-trillionth (10-12) of a radian. But even the term "picoradian" occurs only once in Wikipedia, and does not seem to be defined there.

So I would recommend that any unit used here that can't be linked to its definition elsewhere in Wikipedia be defined here.Daqu (talk) 02:09, 25 April 2012 (UTC)

Table in "Symbols and abbreviations" section is wrong
The table is titled "The sexagesimal system of angular measurement", but this is far from a purely sexagesimal system. If it were sexagesimal, each second would be divided into 60 thirds or tierces, not 1000 milliseconds. I think it should just say "common units of angular measurement", or something. —Steve Summit (talk) 18:08, 17 December 2015 (UTC)

Can't link page to other wikipedias
e.g. https://he.wikipedia.org/wiki/%D7%93%D7%A7%D7%AA_%D7%A7%D7%A9%D7%AA --MeUser42 (talk) 11:13, 18 January 2016 (UTC)
 * Generally speaking, you can link anything like this דקת_קשת. The reason why you don't see a link on the side is that the English version describes both minute and second of arc (Q22066400), while other languages describe either minute (Q209426) or second of arc (Q829073) in separate articles. If other languages merge them into one article, it can be linked in Q22066400. I'm not sure how the links can be done otherwise, since only one link per language is permitted. 19:29, 18 January 2016 (UTC)


 * "...only one link per language is permitted..." in Wikidata. Multiple/additional links can still be added manually.  And should be if it is beneficial to the encyclopaedia.  Wikidata rules are of no consequence when compared to what is of benefit to our articles.  If they have a problem with it, they need to fix it there, not distort the navigation of articles to make their coding neater. SpinningSpark 21:03, 18 January 2016 (UTC)
 * Sounds great if you know how it could be done. + m t  23:19, 18 January 2016 (UTC)
 * See Help:Interlanguage links. SpinningSpark 23:37, 18 January 2016 (UTC)

sexagesimal obsoletion
we have sec[ond] as the 1/3600 of an hour. then we use milli-sec, micro-sec etc, good. what if we had deg[ree] as 1/360 of a revolution? then we have milli-deg, micro-deg, etc. {specifying sec as time (not any other) and deg as angle (only, e.g. 34 Ce[lsie] }

Tabascofernandez (talk) 21:41, 14 July 2017 (UTC)

Where does the approximation of a football at 775m come from?
The sidebar illustration says a soccer ball (22 cm diameter) subtends an angle of 1 arcminute at a distance of approximately 775 meters.

When I calculate this I get 756 metres. Wouldn't a better "approximation" be 750 metres (or 3/4 of a kilometre)? — Preceding unsigned comment added by 86.151.138.137 (talk) 14:06, 2 July 2018 (UTC) Agreed. I saw the dubious notation and did the calculation as well and got 756.30 as well. — Preceding unsigned comment added by Pmsteven (talk • contribs) 19:21, 3 August 2020 (UTC)
 * Thanks, 0.22 / tan(radians($1⁄60$)) = 756.30 m or approximately 750 m. Now removing dubious tag. + m t  21:35, 3 August 2020 (UTC)
 * Changed legend from 750 to 756 meters – why be more approximate than necessary? But now the legend disagrees with the diagram! Peter Brown (talk) 14:09, 4 August 2020 (UTC)
 * Updated image to say 756 m. + m t  02:59, 5 August 2020 (UTC)
 * Well done! Good that somebody following this knows how to update an image. Perhaps the diagram File:Race between Achilles and the tortoise.gif, used in Achilles and the tortoise, can be addressed? It supposes that a tortoise runs at 5 m/s, which is an unreasonable speed for a tortoise. The Guinness world record is 0.28 m/s. I have edited the text to suppose that the tortoise runs more slowly, but I have no idea how to alter the diagram.  Perhaps there is a Wikipedia project devoted to fixing images? Peter Brown (talk) 17:51, 5 August 2020 (UTC)
 * For that GIF, I'd suggest commenting on commons:File talk:Race between Achilles and the tortoise.gif to note the error/correction. Otherwise, you could suggest this to commons:Commons:Graphic Lab/Illustration workshop for someone to take a look at. These edits are much easier if the source image is SVG. I.e., this article would be improved if the figure were re-drafted with Inkscape. + m t  01:50, 6 August 2020 (UTC)
 * Thanks, I'll do both. Peter Brown (talk) 03:04, 6 August 2020 (UTC)

Beware flat-earther misinterpretation
Were it not for the growing presence of flat earth conspiracy theorists, I would not be sensitive to the statement, which appears in a list of examples, that


 * A milliarcsecond is about the size of a dime atop the Eiffel Tower, as seen from New York City.

Of course this is misleading because a dime at the top of the Eiffel Tower could not be seen from New York even on a perfectly clear day with infinite visibility because of the curvature of the earth. Putting the dime on top of the tower doesn't help.

It's also ambiguous because it doesn't specify whether the distance between the cities is along the planet's surface as the crow flies, or through the earth as the neutrino flies (which is about 210 km shorter than the air travel distance of 5853 km).

The last problem with this example is that it is not numerically accurate. A milliarcsecond is bigger than the example supposes. The United States Mint says the diameter of a dime is 17.91 mm. At the distance between Paris and New York, a dime would subtend an angle of only about 0.63 or 0.65 milliarcseconds, depending on whether the dime was viewed by Ray Milland or by light somehow bending around the Earth's surface.

A better example might be


 * A milliarcsecond is about the size of a half dollar, seen from a distance equal to that between the Washington Monument and the Eiffel Tower.

Given that the Eiffel_Tower is at 48°51′29.6″N 2°17′40.2″E and the Washington_Monument is at 38°53′22″N 77°2′7″W, the great-circle distance between them is 6162 km computed using the haversine formula for shortest surface distance. As the U.S. Mint describes a half dollar as 30.61 mm in diameter, the angle would be arctangent(30.61 mm / 6162 km) ≈ 1.025 milliarcseconds.

By the way, the article actually does not seem to say anywhere how the angles are computed, but a better formula would be 2×arctangent(d/(2D)), where d is the diameter of the object viewed and D is the distance from the observer to the center of the object, rather than simply arctangent(d/D). For these numerical examples, the discrepancy is negligible, but it would become signficant when d and D become more similar in size.

--Scwarebang (talk) 21:45, 26 November 2021 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 22:40, 7 January 2022 (UTC)
 * International System of Units Logo.png

Infobox for arcminute but not for arcsecond
The article is meant to cover both the arcminute and the arcsecond, but the infobox only covers the arcminute.

Wootery (talk) 18:58, 5 June 2022 (UTC)

Vandalism!
The article seems to have been vandalized. Worse yet, the INCORRECT definition here is the first definition brought up in a number of browsers! An arc minute is 1/60th of a degree! Not 1/3600th!!! The subsequently derived numbers are also, therefore wrong. It seems to be an intentional vandalism, since the definition of an arcsecond is identical (and correct).174.130.71.156 (talk) 21:21, 8 March 2023 (UTC)