I read in trigonometry class that 1 minute is equal to 1/60 degrees. So, 'minute' is an angular unit. But also 'arcminutes' are used to measure seperation between celestial objects and also equals to 1/60 degrees. Are they any similar? If not, then what's the difference?
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5$\begingroup$ "Minute" is a length of time. Your trig teacher meant to say arcminute. $\endgroup$– Daddy KropotkinJun 1, 2021 at 17:00
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20$\begingroup$ @DaddyKropotkin: "Minute" is not just a length of time: it can also mean the same as "arcminute"; this is confusing, but not incorrect. $\endgroup$– psmearsJun 2, 2021 at 11:19
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6$\begingroup$ @DaddyKropotkin To follow up on psmears comment: Minute, as used in measurement, is a magnitude adjustment just like "hekto", "mega" or "deci" - it specifically means one sixtyeth. It is also used figuratively: a minute adjustment, meaning "tiny". It is more than a measure of time. $\endgroup$– StianJun 2, 2021 at 12:45
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3$\begingroup$ @psmears and @ Stian Yttervik thank you both for clarifying $\endgroup$– Daddy KropotkinJun 2, 2021 at 12:49
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10$\begingroup$ @StianYttervik: Note that "minute" as in "a minute adjustment" is a different word (it's an adjective rather than a noun, and it is pronounced differently too). $\endgroup$– psmearsJun 2, 2021 at 12:57
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4 Answers
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This can get a bit confusing, because "arcminute" and "minute" are both sometimes used in celestial coordinate systems but mean two different things.
An arcminute is 1/60th of a degree, and an arcsecond is 1/60th of an arcminute. That's simple enough, and when talking about small angular distances, it's often much handier to refer to something as being, say, 140 arcseconds across, rather than 0.0389 degrees. So you're likely to see angular sizes or scales quoted in degrees, arcminutes and arcseconds.
If you're trying to state the position of an object on the sky, things get a little more complicated, thanks to the commonly-used equatorial coordinate system, which states an object's position on the celestial sphere in terms of its declination and its right ascension. The declination of an object is usually given in degrees, arcminutes and arcseconds. Its right ascension, on the other hand, is usually given in hours, minutes and seconds. Here, one "hour" corresponds to 1/24th of a circle, or 15 degrees. One minute is then 1/60th of an hour, and one second is 1/60th of a minute. So as units of angular separation in this context, an arcminute is different from a minute, and an arcsecond is different from a second.
answered Jun 1, 2021 at 17:23
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$\begingroup$ I actually made a riddle on Puzzling.SE about exactly this discrepancy several years ago. Looking at it after reading this question is probably a spoiler for the answer, but it was long enough ago so whatever. $\endgroup$ Jun 3, 2021 at 14:55
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Your trigonometry book isn't wrong: both "minute" and "arcminute" can refer to $\frac1{60}$ of a degree. It's certainly a very good idea to use the term "arcminute" when referring to $\frac1{60}$ of a degree, but it's not essential if there's no ambiguity, eg, in a static geometry problem where there's no mention of time.
The term "arcminute" is relatively new. According to Google Ngrams, "arcminute" and "arcsecond" started becoming popular around 1970-1980. FWIW, I went to high school in the 1970s, and I can't remember any of my books or teachers using those terms.
From the arcminute Ngram
Here's the arcsecond Ngram
The results for "arc minute", "arc-minute", etc, are similar.
However, the terms "minutes of arc" and "seconds of arc" were quite popular before that era, and it appears they have mostly been displaced by "arcminute" and "arcsecond".
As the Wikipedia Sexagesimal article mentions, people have been using the base 60 system to represent fractional quantities since the 3rd millennium BC. The Chaldeans (Babylonians) inherited it from the Sumerians, and they used it to record celestial positions.
The Babylonian Astronomical diaries span 7 centuries, and Babylonian data was one of the sources used in Ptolemy's Almagest. The trigonometry tables in the Almagest use base 60 both for the angles and for the values of the trig functions (Ptolemy trig tables used chord length, which is closely related to the sine function).
European mathematicians continued to use sexagesimal for recording and computing with fractional quantities up to the late 17th century, but it was gradually displaced by decimal fractions.
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4$\begingroup$ The word in latin was minuta/minutus, which means "made small". Likely it was convenient for them to define these 1/60ths as "small parts" and here we are - same root for the time division and the angle division, same measurement name. pars minuta prima, the first part made small. It is then fairly clear to see where also the second came from - dividing again into a "second" part. $\endgroup$– StianJun 2, 2021 at 12:52
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One minute has two definitions. One is 1/60th of an hour, or 60 seconds, while the other is 1/60th of a degree. Typically, one minute is shorthand for "arcminute." You can tell between the two by replacing the word with "60 seconds." If it makes sense, then it means that. If not, then it is one arcminute.
An exception is the use of "minute" as an adjective (means tiny), but it is obvious that when used in a sentence, you can distinguish its meaning.
answered Jun 1, 2021 at 17:05
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13$\begingroup$ I don't see how your proposed test can tell between the two - a minute can be replaced with "60 seconds" for both meanings of the words: [ 1 arcminute = 1 minute (of arc) = 60 seconds (of arc) = 60 arcseconds ] vs [ 1 minute (of time) = 60 seconds (of time) ] $\endgroup$– SteveJun 2, 2021 at 8:51
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3$\begingroup$ @Steve Exactly, I don't know why does this have so many upvotes. $\endgroup$– User123Jun 2, 2021 at 18:44
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Put into perspective, it becomes clear that the traditional terms are still competitive. I would prefer them.
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1$\begingroup$ This seems very similar to @PM2Ring's answer. What makes yours different? $\endgroup$ Jun 4, 2021 at 12:34
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$\begingroup$ The difference is the common scale, whereas theirs have no scale at all. The difference in noise at peak level made me suspect that the scales could be very different. It no longer "appears they have mostly been displaced by arcminute and arcsecond." $\endgroup$ Jun 7, 2021 at 17:58