## Thank the Sumerians

Over five thousand years ago, the Sumerians in the area now known as southern Iraq appear to have been the first to develop a penchant for the numbers 12, 24, 60 and 360.

It is easy to see why. 12 is the first number that is evenly divisible by six smaller numbers:

12 = 1×12, 2×6, 3×4 .

24 is the first number that is evenly divisible by eight smaller numbers:

24 = 1×24, 2×12, 3×8, 4×6 .

60 is the first number than is evenly divisible by twelve smaller numbers:

60 = 1×60, 2×30, 3×20, 4×15, 5×12, 6×10 .

And 360 is the first number that is evenly divisible by twenty-four smaller numbers:

360 = 1×360, 2×180, 3×120, 4×90, 5×72, 6×60, 8×45, 9×40, 10×36, 12×30, 15×24, 18×20 .

And 360 in a happy coincidence is just 1.4% short of the number of days in a year.

We have 12 hours in the morning, 12 hours in the evening.

We have 24 hours in a day.

We have 60 seconds in a minute, and 60 minutes in an hour.

We have 60 arcseconds in an arcminute, 60 arcminutes in a degree, and 360 degrees in a circle.

The current equatorial coordinates for the star Vega are

α2019.1 = 18h 37m 33s
δ2019.1 = +38° 47′ 58″

Due to precession, the right ascension (α) of Vega is currently increasing by 1s (one second of time) every 37 days, and its declination (δ) is currently decreasing by 1″ (one arcsecond) every 5 days.

With right ascension, the 360° in a circle is divided into 24 hours, therefore 1h is equal to (360°/24h) = 15°. Since there are 60 minutes in an hour and 60 seconds in a minute, and 60 arcminutes in a degree and 60 arcseconds in an arcminute, it follows that 1m = 15′ and 1s = 15″.

Increasingly, you will see right ascension and declination given in decimal, rather than sexagesimal, units. For Vega, currently, this would be

α2019.1 = 18.62583h
δ2019.1 = +38.7994°

Or, both in degrees

α2019.1 = 279.3875°
δ2019.1 = +38.7994°