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
--------------------------------------------------------