It has always seemed to me that there
are large differences in the rate with which
nights shorten and lengthen depending on
their proximity to the last equinox. (Am I
getting solstices and equinoxes confused?
Anyway, you know what I mean.)
Is this true? If not, what is the right pattern?
If it is, why on earth?
That is, nights seem to me to get shorter very
slowly for the first three months of so after
Dec. 21st (and longer slowly for the first
three months after June 21st). As I get closer
to June nights seem to get shorter faster (and
longer faster as I get closer to Dec 21st).
This doesn’t make a lot of intuitive sense. You’d
expect these rates either to be constant or to
at least peak midway between the equinoxes.
Yes, you’re right that the rate of change of day length varies. See here (near the bottom of the page) for a graph. Day length varies as a sine curve, so that near the solstices (i.e. June and Dec) the day length changes slowly, and near the equinoxes (i.e. Mar and Sep) it changes quickly. Why it’s a sine curve gets into awkward 3D trigonometry…
I decided to acknowledge that eqn (2) should read
cos(H) = - tan(L) tan(D)
to save someone the trouble of doing this for me. I
knew that minus sign belonged somewhere…Joseph
There are some more calculations here, one of which explains what spherical triangle is used. A diagram would help.