The Analemma Program is a feature of the Astronomical League. where an analemma is that figure-8 in the Pacific Ocean on sufficiently old globes. So, what does that represent?
That figure 8 traces the daily path of the Sun in 24-hour snapshots the Local Mean Noon. On any given meridian, such as your location, the sun arrives at close, but not precisely at 24-hour intervals every day. The effect is called the Equation of Time and is plotted as the longitudinal component of the analemma, added to the latitudinal position of the noon sun.
This paper is part of my Commonplace book.
My device is a small box, large enough to serve as an "in-basket" or hold the accumulation of 8.5 x 11" papers. The gnomon is a letter "I" from the art supply store with its upper wings clipped.
A little arithmetic. The paper at 11", will have to accomodate the longest shadow of the year,
so phi, the latitude plus i, the "obliquty of the ecliptic", or tilt of the earth's axis ( ~23.5 ), plus 90 degrees,
plus beta, the elevation of the sun at the winter solstice, equal pi, or 180.
Therefore, beta = PI/2 - (phi + i). Hence at approximately 40 deg north,
beta = 90 - (40+23.5) = 90 - 63.5
beta = 27.5 degrees.
and given 25 cm. of paper to work with, the height, h of the point in the gnomon is 25 * tan(beta),
height ~= 13 cm.
For the record, my site:
Wednesday, 27th – first observation.
[anasite]: image/
Not without further learning about observation taking.
enlarge it sufficiently to produce a spot of light. Time for a ![site photo][anasite]
"yaw" axis for lack of a better term. the patio isn't perfectly flat. So, depending on where I mark the sun's projection, the least pressure may tilt the observing box. A lighter touch may be required. Today's quote:
>_NW Corner is down._
Tuesday, 26th
Having built my device, I was eager to try it out. Today has been quite sunny, as it is now at 1:40 pm. But not at local noon. From my notepad:
>_Clouds o/h. (& 3 hawks looking for "coyote kill"?), "an otherwise sunny day"._
From my longitude of -74.472413 (google maps), I calculate my local noon at 11h 57m 53s.
The cloud cover was about 50% and covered my observing site, the corner on my patio, for at least 10 minutes on either side of 12:57:53 EDT.
I did notice from the shadow of the gnomon, that my analemma will have a bias on the paper, since the patio, along with the house is about 10 degrees to the east, producing a central line that far to the left.
[emchrono]: http://www.emeraldsequoia.com/ "Emerald Sequoia"
Tuesday, 30th – 14th
Monday, 29th – 13th
no reason #13 has to be lucky. there are two points on the paper. the one on the right is the "observation", albiet 70 sec. late! the one on the right is a guess as to what it might have been.
i took it because the elevation is likely a reliable measurement, the azimuth will be in question by the stated latency +/- any other inaccuracy. oh yes, Pat and i were hanging more pictures and it looked overcast. the sun didn't really peek thru the clouds, but the aperture's ellipse was evident.
Friday, 26th –12th
A stable bridge. A good reading. NE of #11 and NNW of #10, fitting a curve between them. Quite overcast yesterday. Excuse for not taking the data off the sheet: see the software diary, where I was busy, very on the Python course. And busier today.
Wednesday, 24th – 11th observation
The clouds taketh away, the clouds giveth. I hustled home from swimming at 12.30 with little hope for an observation. At 11.48 Pat observed the sun is out. So, I took #11 using the pool bridge technique. Today's was a little NW of yesterdays.
Thinking about recording the data already collected, I hit on using an RDB table in the program directory. Since I also have a time-stamping facility, `rdput`, I don't need to otherwise record the time I entered the observation, other than the day. So, here's the plan of record:
And I was going to begin today, but let's just open the file for starters, and record the first N on a cloudy day, likely tomorrow.
Tuesday, 23rd – 10th observation, equinox
The autumnal equinox was 5:29, last pm. The sky was cloudy most of the afternoon. It offered a tantalizing peek about 10 min. before local mean noon, with a grey oval at about 5 minutes. Sunday was overcast. I think we were busy Saturday, which says I can take a day off when I've had observations in 2 of the previous 4 days.
Also, the latest data-point making exercise: set a pool-shooters bridge with my left hand, and guide the right hand which holds the pencil down on the left index finger. The bridge, formed with the thumb, index, and middle fingers, holds the box on the patio quite firmly, as well. Still questions of azimuth alignment to consider as a study. Maybe too, translate these first 10 data points to X, Y, readings on the page and get started with the analysis.
The excitement builds.
Friday, 19th – 9th observation
Henceforth I'll number them, and maybe keep an index on the side or separate piece of paper?
Taday's reading moved a little more NE of the previous; some due to the westward movement of the sun, some possibly to the experimental error of the boxes rotation about the zenith.
Thursday, 18th – 8th observation
Just a small dot about 1 mm NW of yesterday's. This is still in line with the overall trend, though it represents a tiny reversal from yesterday. But now we're bounding the experimental error.
Wednesday, 17th – 7th observation
The ellipse of the apperture's projection is growing on the smaller axis. This only means the axis of the hole itself is closer to the sun's elevation.
After a week in MN, attending mom's 94th (!) birthday celebration, approx 96 (+/- 5) mm since the prior observation.
Today I tried holding my right wrist with my left hand. I noticed in going down to the paper, the paper seemed to bow up, so the mark has a tail to the northeast.
Also, apart from the observation, the [Mauna Kea chronograph][emchrono]
shows the Equation of time (it's convention means "the sundial is ahead") is increasing, from just over 2 minutes when I started, to now about 5 minutes. This makes sense to a first order observation, since the 'noon point' is moving north-east, indicating the sun is arriving earlier each day.
Wednesday, 10th – 6th observation
After considering marking the edges of the elipse I thought I'd stick with a single point in the center. So, I count down from 8 seconds from 11:57:45 – "eight, seven, six, … " with my eyes on the second hand and speak the rest as I aim the pencil at the center, and try to settle on one point. Also, with my left hand, I press gently on the NE corner of the observing box wresting my right wrist on the south base, trying not to disturb the horizontal base. Today's reading looks fine, relative to #5 on the seventh, which i'm now labeling.
Sunday, 7th – 5th observation
A little messy on the point today. Here's the correction: just get a small dot as close to the center of the aperture's eliptical projection. The mark it later, either bolder or with a vertical hash mark. Yesterday's concern is unresloved, other than note the "regression to the mean" seems to have taken hold tody
Saturday, 6th – 3rd, 4th observations
yesterday's reading almost fell on top of thursday's
today's was a surprising bit to the right of the two prior. my intial guess is there are two problems:
the "square" of the box to the concrete of the patio. i'm using the two rulers, wedged into the earth at edges to achieve the square, and
the "square" of the paper to the edge of the box.
for the moment, i'm ruling my time-keeping. last night, i down-loaded the [Emerald Chronometer][emchrono] which gives routine updates from a NTP server. So, we'll see if the azimuth variation continues, or not.
btw. another great feature of the Chronometer is it's UTC feature, which is available on four of it's 16 different time pieces: Geneva, Mauna Kea, Terra, and Vienna, just to give you a sense of the inspiration.
Thursday, 4th – 2nd observation
after a family weekend of all weekends – Katie's wedding to Justin Hoffman – where there were any number of good observing days, today I got the 2nd reliable observation.
A data point. The point of the sun has moved ~7.8 (+/- 0.1) mm since the first reading.
I also recevied (8/31) a letter from the Project Mentor: [Lowell Martin](mailto:fwas_lam@yahoo.com), filed in my Astronomy folder with detailed instructions.
Friday, 24th – 24th obs, a minute late
Two really overcast days. And today, the sun was breaking thru, but for about 4, 5 minutes up to the moment, it clouded over again. So, the observation was a minute late, within a very few seconds.
Monday, 20th – 23nd obs
Sunday, 19th – 22nd obs
I've marked the observation, on the paper with a '.' as a superscript: i.e. #22^^.^^, and again noting the difference in azimuth.
Friday, 17th – 21st obs
Tuesday, 14th – 20th obs
The observation ellipse is now longer than wide: 8 x 5 mm. I wonder what that says about the meridinal allignment. Better look at that next time.
Sunday, 12th – 19th obs
Reese and Jessie saw the observation equipment, Reese sticking around for the moment of. He got the idea of the sun's elevation, but maybe not too sure about how fast it was moving.
And after, we recorded the observations thru today.
Thursday, 9th – 18th obs
The vote today on anomalistic azimuth is yes. A good reading, but to get it, I broke the west-edge ruler. But digging in a bit seems to allow a surer alignment. The thought occurs I'll be able to solve for an azimuthal error probability
Wednesday, 8th – 17th obs
I was about to declare #16 an anomaly. That's the good news; the bad news it wasn't. I really have to check my azimuthal alignment much more carefully. In any case, today's was still further to the NW, now two days in a row. As a result of the distraction, my reading was a second or two late.
Interestingly, the box frame isn't glued tightly on the south side. Consequently the slight slit between the south- and east-facing sides shows the noon sun as a crack along the east side of the box.
Monday, 6th – 16th obs
The observation ellipse more circular today; that's the good news. The other news is the strangness of the azimuth reading, suggesting either the square of the box to the pavement, OR the time synch of the iphone clock. I can check that, but not now.
Saturday, 4th – 15th obs
The sun broke thru with less than 5 min. to spare. We were upstairs and Pat saw it brightening after a rainey night and morning.
The observation ellipse is now approaching a circle; which it may never quite reach.
And time to record and reduce the last three observations
Friday, 3rd – a too-cloudy day
The sun broke thru 3-4 minutes before noon, and even closer (> 2 min) after noon (local mean solar). But, not at noon. So, no readings today.
Monday, 24th – 27th?, 28th, 29th, and 30th obs
I believe I made them on Tuesday, 18th, and Wednesday 19th respectively, or a day earlier. My operation was on 11/11 and the catheter came out on 11/20. Today looks promising. So it was. where's the 27th? Let's say Monday, 10th.
Saturday, 8th – 26th observation – after mostly cloudy, rainy days
it's starting to show the depth of the sun, and according to the clock, the equation of time in now +16 minutes. this means we'll start to see the swing on the way back after Dec 21,22.
Tuesday, 4th – 25th observation – after a week in Houston.
nominal. and collected the last three obs to the reading.rdb
Tomorrow
Tuesday, 16th – 34th, 35th obs
no. 32 was Monday, 35 today.
yesterday I set a water glass (?) on the data sheet, wrinkling it a bit. it seems the biggest error can be in the vicinity of the mark point. using the plastic rulers and judicious placement of my "pool bridge" technique seems to minimize any effect.
Saturday, 13th – 32nd, 33rd obs
no. 32 was on Monday, 33rd today. the sun was clouded over at the moment. I took an observation a minute late, and extrapolited the point, so there.
Thursday, 4th – 31st obs
The first sunny in a week. And time to collect the last 5, 6 observations.
I'm now reducing the data, from date, horz, and vert in `reading.rdb` in my Dropbox `commonplace/analemma` with a local script in `analib`, to produce `azEl.rdb` with date, azmu, and elev. Some of the assumptions are in the readings: "obs 0" has the height of the gnomon's aperture. I expect to model and solve for: