Friday, March 23, 2012


Well, it has already sprung, I guess, but still, there she is. It is now springtime, and I am much relieved to have shaken off winter. Not as much as you folks up in the white north, most likely, but relieved enough. Maybe I am destined to die in wintertime, because I feel it weakening me every year. Maybe it is the connection with my jungle ancestors (oh wait, they don't know wintertime in the jungle) or with my acer macrophyllum relatives. (who knows what that means, without having to look it up, besides my brother?) But that is over now. Soon it will be summer. I am really interested in watching the sun rise higher and higher each day, arcing overhead with the joy of a pollo. Oh, not a chicken! I mean Apollo! Does chicken (pollo) and Apollo have anything to do with each other?
So I am watching the sun and waiting for the light to come from overhead. Since I am at 20 degrees 45 minutes, that shouldn't be long. Here is a quiz. If the sun works in a sinusoidal curve from equator to tropic to equator to other tropic, based on the revolution around the sun (which we would assume is circular, but really it isn't) then what day does the sun reside directly over 20.75 degrees north lattitude?
You should note that the sun is directly over the equator on the equinoxes.
Except that all of that is not really true. It would be nice if it was, and that is what I base the quiz on, but the truth is more complicated, like leapyears and such. The earth doesn't go around in a circle, so the sun spends more time over the northern part of the sine curve than the southern (hence the colder south pole) (well, the fact that land is on the south pole also has something to do with that) So if you want to be exact, you need the almanac. But that's just the way it is. Part of the trick with Celestial navigation. But you can do all right with the navigation with a sine curve.
Ok, back to business. Hawaii is about the same lattitude (just a little south), so if I leave April 30, and get in before June 1, will I see the sun directly over my head during the passage?
I don't think it will be that impressive, but I've never seen a directly overhead sun. The closest I've come was probably in Vietnam last June, when I was about 10 degrees north, and the sun was still to the north of me.
Or in Costa Rica in March a few years ago, I was at 8 degrees, and the sun was at 0. Close, but not perfect.
So I am happy with the returnation of the sun to the northern lands (sorry for you folks down under).


mlloyd said...

Full of trixy questions/statements! I'm betting you're not feeling blue anymore =) Alas, the big leaf maples are not yet leafing out in the great white north (although Cliff Mass almost guarantees that we'll not see any more white stuff for this year). I have no idea the answer to your other quiz question, I just wanted to point out that your brother is not the only one who might not need to look up the scientific name in a book.

kava crosson-elturan said...

It is definitely feeling fally down under. We still have leaves though.

T. Abe Lloyd said...

Being precluded from the first quiz, I'll weigh in on the second. I think the math would be:
20.75 = 22.5*sin(theta)
which comes out to 67 days after the spring equinox.

I have a little reservation for this answer because I feel like there should be two solutions since the sun will pass directly over head, continue northward until the Summer solstice, and then pass directly overhead again on its way south towards the fall equinox. I can't figure out how to get the second solution (Shouldn't I have a parabolic equation?). Actually, I can't intuitively derive the second overhead passing by taking subtracting my first answer from half a year (182.625-67.25) = 115 days after the Spring equinox.

T. Abe Lloyd said...

Well the second passing of the sun over your latitude should actually be 112 days after the spring equinox, according to the sine equation I posted in the last comment. My logic for subtracting half a year turns out not to work, but I'm not sure why. Maybe because my answer is wrong in the first place???

T. Abe Lloyd said...

Oops, I just realized that the tropic of Cancer is roughly 23.5 degrees, not 22.5. I will have to revise my answer to 62 days from the spring equinox. (May 19th I think)