I can never get my head around these units of measure. Often referenced in terms of resolution of the eye or a telescope. What the hell is an arcsecond?
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Imagine a clock.
Imagine the angle that a hand of that clock would sweeps in a minute. Or a second.
In actual fact an arcminute is 1/60th of a degree, which is 1/360th of a full circle. An arcsecond is 1/60th of an arcminute.
So if you imagined putting a giant clock on the floor, and a clock hand was sweeping across it, the bits that it “points to” during that time are expressed in arcminutes and arcseconds.
A circle can be divided into 360 wedges, which we call degrees.
Each degree in turn can be divided into 60 arcminutes, and each arcminute can in turn be divided into 60 arcseconds.
An arcminute is basically 1/60th of a degree.
From math class you probably know that a circle is split up in to 360 ‘degrees’.
Well if we want to measure smaller angles, we split each degree in to 60 ‘arcminutes’.
And for ever smaller angles we split each arcminute in to 60 ‘arcseconds’.
So there are 60 arcseconds in an arcminute. 60 arcminutes in a degree, and 360 degrees in a circle.
The same way we split hours of time in to minutes and seconds, we split degrees of angle in to arcminutes and arcseconds.
Why is a circle 360°? Because its an antiprime. It can be devided evenly with many numbers like: 2, 3, 4, 5, 6, 8, 9 and their products. Its a highly composite number. So when we are dividing circles having 360 for the whole is comfortable. Unlike grad which makes it 400 to lose all this advantage just because the right angle should be 100.
Why same reason why our timekeeping is in base 60. 60 mins in an hour and 60s in a min. 60 is also highly composite.
So instead of writing small angels like 12.48829° we can keep this nice property and devide 1° into 60′ arcminutes. And an arcminute into 60″ arcseconds. So 1″ is 1/3600 of 1°.
Degrees are useful as a human way of measuring angles, same reason why we don’t measure time as “seconds since the big bang” or 21.68158h. We don’t want to fuck around with decimals so lets use highly composite numbers.
If you are mathematically working with angles, you’ll use radians anyway.
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