Babylonian Astronomers and Angular Measure

From the Babylonian astronomers circa 500 BC (No-39), the circle is divided into 360 equal bits: i.e., 360°. Each degree is divided into 60 arcminutes and every arcminute into 60 arcseconds: 

       1°=60'=3600''     , where ' is the arcminute symbol;

       1'=60''               , where '' is the arcsecond symbol.

This sexagesimal system began with ancient Sumerians maybe before 2000 BC perhaps because its easy to divide 60: 60 has 12 whole number factors: 

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

Of course, the 60 division passed over into time-keeping too: 60 minutes in the hour; 60 seconds in the minute.

The Babylonians used the strict sexagesimal system only it seems for math and astronomy: they had other base systems: e.g., the 10-base system just like everyone else in the world unquestionably because of an anatomical peculiarity of primates (Ne-17).

Alas, the French Revolution that gave us the metric system completely overlooked angular measure, and so we're stuck with degrees, arcminutes, and arcseconds.

Alien Angular

Now everyone's hand is a bit different---we are all unique---but just approximately at arm's length 

    1 finger = 1° 
    1 fist = 10° 
    1 spread hand = 18°

(Se-18). You'll find these results a convenient what judging angles on the sky. How far apart are stars? How high is a star above the horizon? What is the angular diameter of the Moon? The last is a real question. Go out and measure it with your fingers on a good night.

Why angles on the sky? Well it is by angular coordinates that you find objects on the sky.

The sky has NO APPARENT DEPTH, except that it's far. There is no simple way to tell distances by eye or even by simple geometric ways available to the ancients.

Even today distance measurements are relatively hard---relative to angular measurements.

Even the ancients could measure angles fairly accurately---when they weren't being sloppy that is---and today sub-arcsecond accuracy is pretty common: i.e., angles measured to less than 1/3600 of a degree.

Angular positions on the sky using an angular coordinate system is how astro bodies are located.

Angular Diameter

For example, the Sun and the Moon have very different sizes: the Sun diameter is about 400 times the Moon's diameter, but the Sun is about 400 times further away than the Moon.

The upshot is the Moon and Sun have almost the same angular diameter on the sky. The Moon and Sun both have angular diameters of about 0.5 degrees.

More exactly as seen fro the Earth's center using mean distances and radii we find di_moon=0.515127 degrees=30.9076' and di_sun=0.533121 degrees=31.9872'.

Angular Velocity Angular velocity.

If you have angular position, you can have ANGULAR VELOCITY. For example say that the angular speed is a constant, then the angular speed just equals any change in angle divided by the corresponding change in time: d_theta/dt =Delta_theta/dt =angular velocity.

  1. What is the angular speed of the Earth around the Sun? Or from Earth's perspective, what is the angular speed of the Sun around the Earth measuring the Sun relative to the ``fixed stars''? Behold 

           d_theta/dt=360 degrees/365.25 days = about 1 degree/day  .

    Actually it's a little less than 1 degree per day. The ancient Babylonians may even have chosen the degree size in order to make the angular speed of the Sun about 1 degree per day, but who knows.

  2. But if they did, why not 365 degrees in a circle? Well 360 is so easy to divide: so many whole number factors: 

        1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 40, 45,

      60, 90, 120, 180, and 360:  22 factors in all.

    Some people arn't fond of trailing decimal digits.