The story of Arcminutes and Arcseconds



Once there was a hare and a tortoise (yeah yeah, your primary school friends). Now they are no longer in UKG, have grown up and now have started star-gazing.

Hare: Do you see that torti? Look there! There's the moon.
Tortoise: Yeah! He's all shiny and bright. Ready to be eaten with bread and butter.
Hare: And do you see the shiny star beside it? It's actually not a star. It's Venus.
Hare: Wo...ho Harry! Do planets too shine like stars?
Hare: They reflect, like the big shiny bright moon.
Tortoise: Aha...and do you see that Harry? The one over there.
The tortoise pointed his index finger towards a faint star in the deep sky.
Hare: Where? Is it over there?
Hare too tried to point towards exactly the same star as the tortoise.
Tortoise: Yeah! That one.
     I, the author, projected their tiny arms on the astronomical scale. It passed through deep space and when they finally reached the destination, lo, it was like one pointed in the east and one in the west (excuse the mild exaggeration).


But how come there be so big a gap for such a small difference in direction?
Let's see how.
When you are on a global scale, even a small difference can cause blunder.
How do we measure this small distance which is causing such huge difference? Let's take a millimeter scale.
  The direction in which Hare pointed varies, say 1mm from the direction of tortoise from the tip of their fingers.
  But as the distance from the two is increasing, the distance between the two directions is increasing too.


But as the starting point remains the same, the angle between the two remains a constant. So we can say that angular measurement is the required concept.


Angles are measures in units called degree and radians; radian is the standard unit. By standard unit, I mean internationally recognized one.
   Degrees can be converted to radians and radians to degrees
      1°= π/180 radians
      180°= 180× π/180= π radians
A high school protractor can measure as small an angle as 1°. We say it as: the least count of a high school protractor is 1°.
Least count: the smallest measurement which can be made accurately.
But in astronomical level, 1° is too big.
The smaller units are arcminutes and arcseconds denoted by 1' and 1".
      1°= 60'
      1'= 60"
1° contain 60 arcminutes in the same way that 1cm contains 10 mm.
1' contains 60 arcseconds.

Now that both hare and tortoise know the difference, they take the astronomical scales and make measurements and then report their results like:
     The star to the right of Venus is at an angle of 6° 48' 3".
And both laugh at each other.

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