At 07:06 PM 3/3/98 GMT, John Butler wrote:
>
>Just to say "thank you" to all of you who replied with such comprehensive and
>informative answers to my question. I will reply individually when I have
done
>justice to the replies, something that will require an ice pack and a very
>large pot of coffee :-)
>
>Cheers
>John Butler
Hi John,
A good question will always draw eager responses. We are like kids in a
class, waving our hand to get the teacher's attention because WE know the
answer. But we never got asked! Are schools still like that?
As further follow up I'd like to show what a powerful little equation the
sunrise formula is: Cos t = - tan d * tan L.
For L = 0, Cos t = 0, and t = 90 degrees or 6 hours from the noon zenith.
On the equator, the days are always 12 hours long.
For d = 0, cos t = 0 and t = 90 degrees. At the equinox when the sun is
over the equator, the days are 12 hours long at every latitude.
When d and L have the same sign, cos t is negative, so the solution is 180
- t.
When the sun is over your hemisphere, the days are always longer than 12
hours.
When the signs are different, cos t is + and t is less than 90 degrees.
When the sun is over the other hemisphere, the days are always less than 12
hours.
Cos t = -1 when L = 90 - d as tan(90-d)= 1/tan d. For the maximum solar
declination of 23.5 degrees, the latitude above which the sun does not set
is 90 - 23.5 or 66.5 degrees, the polar circle. The same logic applies for
cos t = 1, and defines the other polar circle above which the sun does not
rise.
To answer your original question, at any latitude between the polar circles
except the equator, the length of day increases with increasing declination
until the maximum declination of 23.5 degrees is reached on the solstice.
This is truly the longest day!
All this can be drawn from that one simple equation. Cos t = - tan d * tan L.
Remarkable. This equation deserves to be on a tee shirt, the ultimate
honour for science trivia! I can just picture it arching over a glowing
sunrise graphic.
Cheers, Roger Bailey
