All you astro people (and math freaks)

[Rick Measham]

I'm not sure how many of you subscribe to MJD's Perl 
Quiz-of-the-week, but this week it concerns datetime and what he 
calls 'Greek Time'. Basically midnight = midnight and noon = noon. 
However 6pm (greek) = sunset. This means that night hours are longer 
in winter and day hours are longer in summer.

In his question, he assumes that each period (night/day) should be 
evenly divided into 12 parts. However this stinks to me! Surely in 
the middle of winter, the hour before sunrise shouldn't be a heap 
longer than the hour after? Surely the lengths of hours should slowly 
decrease towards noon and then increase again towards midnight. I 
figured this is a sine wave.

However when I thought about it I realised it wasn't. But what is the 
conversion? At the equinoxes, it (should) be a straight line graph. 
However as sunrise gets later, it becomes a half-sine-wave. The skew 
based on sunrise/set times.

The question is this: How does one turn a sine wave into a straight 
line slowly? There must be a mathematical function that allows us to 
create a formula to get the 'percentage of daylight' at any point in 
the day. (I'm not talking observed daylight but some theoretical 
daylight that puts 50% at sunrise and set)

Cheers!
Rick
--

There are 10 kinds of people:
  those that understand binary, and those that don't.

  The day Microsoft makes something that doesn't suck
is the day they start selling vacuum cleaners

Write a wise proverb and your name will live forever.
   -- Anonymous

Re: All you astro people (and math freaks)

[Eugene van der Pijll]

Rick Measham schreef:
 In his question, he assumes that each period (night/day) should be 
 evenly divided into 12 parts. However this stinks to me! Surely in 
 the middle of winter, the hour before sunrise shouldn't be a heap 
 longer than the hour after? Surely the lengths of hours should slowly 
 decrease towards noon and then increase again towards midnight. I 
 figured this is a sine wave.

That would perhaps be nicer for us computer-owning people, but that
wasn't how it was implemented in ancient times. It is really much easier
to have only two different hour lengths per day. You only need two
different clepsydras that way.

And many people only used the day-hours; there were few public events in
the evening or night: no electric lights. So nights were spent mostly at
home, where the time of day was not important.

So you could also define an hour as 1/12th of the day, and accept that
a day isn't 24 hours exactly. But who cares, noone stayed up the whole
night then.

Eugene