# the seasons **URL:** \ **Category:** Factual Questions\ **Created:** [February 1, 2003, 2:24pm UTC](https://boards.straightdope.com/t/the-seasons/152094 "2003-02-01T14:24:27Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![fhapgood](https://avatars.discourse-cdn.com/v4/letter/f/dbc845/32.png) [@fhapgood](https://boards.straightdope.com/u/fhapgood)\ **Post date:** [February 1, 2003, 2:24pm UTC](https://boards.straightdope.com/t/the-seasons/152094/1 "2003-02-01T14:24:27Z")
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. Yet that doesn’t seem to be my experience. ---
**Author:** ![raygirvan](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@raygirvan](https://boards.straightdope.com/u/raygirvan)\ **Post date:** [February 1, 2003, 7:22pm UTC](https://boards.straightdope.com/t/the-seasons/152094/2 "2003-02-01T19:22:09Z")
Yes, you’re right that the rate of change of day length varies. See [here](http://www.islandnet.com/~see/weather/almanac/arc_1998/98feb04.htm) (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… ---
**Author:** ![fhapgood](https://avatars.discourse-cdn.com/v4/letter/f/dbc845/32.png) [@fhapgood](https://boards.straightdope.com/u/fhapgood)\ **Post date:** [February 1, 2003, 7:56pm UTC](https://boards.straightdope.com/t/the-seasons/152094/3 "2003-02-01T19:56:06Z")
> [@](#): > > \*Originally posted by raygirvan \* > \*\*Yes, you’re right that the rate of change of day length varies. See [here](http://www.islandnet.com/~see/weather/almanac/arc_1998/98feb04.htm) (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… \*\* That’s what I wanted to know. I guess I’m not going to find out, huh? ---
**Author:** ![raygirvan](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@raygirvan](https://boards.straightdope.com/u/raygirvan)\ **Post date:** [February 1, 2003, 8:25pm UTC](https://boards.straightdope.com/t/the-seasons/152094/4 "2003-02-01T20:25:12Z")
This [Usenet posting](http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=pW3668q.jabartlo%40delphi.com) by Joseph Bartlo goes through the calculation. As I said… ---
**Author:** ![fhapgood](https://avatars.discourse-cdn.com/v4/letter/f/dbc845/32.png) [@fhapgood](https://boards.straightdope.com/u/fhapgood)\ **Post date:** [February 1, 2003, 9:01pm UTC](https://boards.straightdope.com/t/the-seasons/152094/5 "2003-02-01T21:01:36Z")
> [@](#): > > \*Originally posted by raygirvan \* > \*\*This [Usenet posting](http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=pW3668q.jabartlo%40delphi.com) by Joseph Bartlo goes through the calculation. As I said… \*\* Thanks! ---
**Author:** ![raygirvan](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@raygirvan](https://boards.straightdope.com/u/raygirvan)\ **Post date:** [February 2, 2003, 2:45am UTC](https://boards.straightdope.com/t/the-seasons/152094/6 "2003-02-02T02:45:04Z")
Aargh! I just read the following message: _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](http://www.math.niu.edu/~rusin/uses-math/position.sun/solar.position), one of which explains what spherical triangle is used. A diagram would help.