Embedded Files
Analemma Observing Program
Participants in the Analemma Observing Program will monitor the Sun’s motion throughout the year and note changes in the Sun’s position, both in altitude and azimuth. They will then, with reference only to their analemma and observing apparatus:
Calculate their observing latitude and the tilt of the Earth’s axis
Sketch or plot the path of the Sun on the Celestial Sphere
Calculate the Equation of Time
Calculate the eccentricity of the Earth’s orbit
For non-photographic techniques, the analemma should be formed by a minimum of 50 observations spread approximately evenly throughout the year (i.e., about one per week).
For photographic techniques, the analemma should be formed by a minimum of 100 observations spread approximately evenly throughout the year (i.e., about two per week).
I'd like to use photographic techniques.
Steve Boerner
Astronomical League Member-at-Large
sboerner@charter.net
My location:
+38.631490 N latitude
90.552686 W longitude
Magnetic Variation
1° 40' W changing by 0° 4' W per year (not used)
Some pre-observing activity is required:
1. Select your observing site. The site must allow full-year observation of the Sun
2. Specify your Observing Date and Time
3. Readings within three hours of Local Noon, and use a published (e.g., map-derived) value for their Observing Latitude to calculate how their points would have appeared at Local Noon.
4. A camera may be setup for unattended operation.
Observers are required to develop their technique for accurately determining distances to the individual analemma points.
Additonal information:
Gnomen height, calculations, and picture:
Raspberry Pi3 Information:
crontab entry to start analemma.sh shell script
analemma.sh shell script to take a single image:
Options for fswebam explained:
What I plan to eventually submit:
(May 2022)
On this page...
AL provided text is in white
My text is is yellow.
Right click on pictures to enlarge in a new window.
My proposed setup:
Camera pointed west showing protected location.
(explanation below)
I've wanted to work on the Analemma Program since it was first announced, but knew the only way I could do it was from my house. The difficulty was that our lot and house presented problems with finding a spot to place the apparatus. The house has no south or east facing windows. Southwest and west windows face 50 foot tall trees in the back yard. For a while I even thought about trying to do something at my son's townhouse when he lived in England, but it didn't work out. Our house itself blocks the front yard and the fifty foot trees in the back prevented using it there. Short of climbing up to the third story roof there was no possible location with power. I was stumped.
Last year (2020) the huge tree in the lower right corner fell and hit my neighbor's house during a storm. It opened up a possible location where the rear 20'x20' addition meets the house proper. The proposed location is on the second story with easy hands-on access through a window. The roof has a pitch at that point so the apparatus needs to be adjusted with a bulls eye level and shims. I see this leveling as the most significant source of error as I progress.
(view of trees in the back when facing south)
(north is up the first and third pictures.)
The house is at an angle of 135 degrees from true north. The location should allow observations between 10 a.m. and 2 p.m. CST although the trees may be an issue as they fully leaf out in the summer or through limbs when the is low in the south in winter. The only way to tell is to try.
(yellow dot is the location of analemma)
I plan collect data via imaging. The location provides easy access for a cheap Logitech webcam by running the cable into an unused bedroom between the sill and sash of a window.
I'm not 100% sure that the apparatus location will be shadow free at local noon daily throughout the year. If not I will adjust the capture time earlier in the day and make mathematical corrections.
My location:
+38.631490 N latitude
90.552686 W longitude
Correction for local noon = (90.552686 - 90) minutes * 60 clock minutes
from clock time 15 degrees
= 0.552686 degrees * 4 minutes/degree
= 2.210744 minutes after 12:00
= 12:2.210744 p.m.
= 12:02:12.64464 ~ 12:02:13 p.m
Hopefully not needed.
The Internet suggests that St. Louis averages 202 sunny days throughout the year so I should be good.
Observers are cautioned about several inherent weaknesses of this technique:
These images will likely contain distortion (i.e., scaling factors will vary across the image) due to curvilinear perspective; wide-angle lenses should not be used as they increase the severity of this effect.
Automatic exposure control may washout surface markings used to locate the analemma point.
The Field of View will change if the camera is moved.
The accuracy of locating individual analemma points decreases as the camera angle shallows (here, “camera angle” refers to the angle downward from horizontal that the camera is pointing … 0° denotes pointing horizontally, and 90° denotes pointing vertically downward); observers should not attempt to use camera angles less than 60°.
My plan is to have a Logitech C110 webcam (located outside 24/7/365) connected to a Raspberry Pi 3 running Linux (located inside). I will use an app called fswebcam to take and save images. The app will be called by cron at a specific time based on the local noon time at my location (12:02:13 CST).
T
NTP Internet time will be used and should always be less than one second off.
The observation time depends on how far the location is from the center of the time zone. The center of the Central time zone is 90 degrees.
Images will be captured daily at 12:02:13 p.m. CST.
How I will address the issues:
Test shot showing no pincushion or bullseye. The squares are 1"x1". (Note: the lower left edge is distorted due to paper curling up). After trying a few squares the average number of pixels is 72.5/inch. I'll spend more time calibrating this in the future.
The automatic exposure control actually makes the gnomen's shadow point easier to see.
The image was taken at local noon and shows the north south line. North is at the tip end of the gnomen's shadow.
I'm worried about snow shifting the apparatus. I believe I will be able to both detect the movement, reset the platform, and/or make corrections. Time will tell.
I've mounted the webcam directly above and perpendicular to the base. The camera is pointed straight down.
he saved images will be periodically copied to a Win10 laptop for analysis. The individual images will be loaded into Adobe Photoshop and zoomed to the 400% so that the individual pixels show on the screen. With the I
My gnomen and 13" tall camera support (1"x2") are mounted to a waste piece of ceramic tile I found out in the garage. The webcam is mounted above the center of the expected analemma height and centered on the ceramic tile. The tile is aligned N/S using both a compass and gnomen shadow at local noon on a given day. The camera has a "weather cover" to keep it dry and protected.
My apparatus relies heavily on 3D printed PETG parts for the gnomen(s), camera support, and weather shade. PETG should be stable outside for the course of the program. The gnomen is designed to allow accurate realignment if weather causes it to move.
nfo tab showing, I'll place the mouse pointer on the tip of the gnomen's shadow. I will read the X,Y coordinates for the tip of the gnomen's shadow and the base of the gnomen. The information will be recorded in a spreadsheet. The gnomen's base position should not change (error check for movement). I will also run a calibration using the "graph" above to determine a conversion between x,y coordinates and position in cm from the base of the gnomen. If my initial plan doesn't work I'll resort to an application (MB Ruler) that I can use to measure the distance and angle from the junction of the gnomen and plane of the base.
By plotting the x,y position of the gnomen's shadow vs. the day an analemma should be produced.
5.00 inches above the base/gnomen intersection to give
Hi Sun: 1.40"
Lo Sun: 9.25"
Equator: 4.00"
Shadow length: 7.85"
02 12 * * * /home/pi/analemma.sh
Script contents:
sleep 11
fswebcam -p YUYV -d /dev/video0 -r 1280x720 -D 5 -S 40 --top-banner --title "Analemma Observing Program" --set brightness=30% --set "Background Compensation"=1 --set sharpness=80 --timestamp "%m-%d-%y@%H:%M:%S(%Z)" --scale 1280x960 -F 10 --png 9 --font luxisr:30 /home/pi/images/"`date -u +%F"@"%T%Z`".png
fswebcam
Screen shot of gnomen from Tinkercad.com.The gnomen was designed so it slips onto one of the corners of the ceramic tile base with a snug fit. It should remain in place for a year. The design should allow for exact realignment if necessary.
This causes the RPi to run the analemma.sh shell script at 12:02 p.m. (CST). cron is only able to go to the minute level so the analemma.sh script needs to deal with seconds.
Line by Line Action:
sleep 11 is needed to get the pictures time stamped at 13 seconds after the script starts or 12:02:13 p.m.
The RPi is configured to run using UTC.
fswebcam
-p YUYV
-d /dev/video0
-r 1280x720
-D 5
-S 100
--top-banner --title "Analemma Observing Program"
--set brightness=30%
--set "Background Compensation"=1
--set sharpness=80
--timestamp "%m-%d-%y@%H:%M:%S(%Z)"
--scale 1280x960
-F 10
--png 9
--font luxisr:30
/home/pi/images/"`date +%F"@"%T-%Z`".png
call fswebcam
set the color space to YUYV
choose the correct camera
set the resolution to 1280x720*
wait 5 second for the RPi to stabalize the camera
skip the first 100 frames to average exposure
create banner for the top of the image
set brightness of image
set backlight level
set sharpness to 80
set timestamp for the banner on picture
set the scale to 1280x960 for squares to be square
take and stack 10 frames
set the quality level of saved pngs to maximum
set the font to be used in the banner
save in png format (i.e.2021-05-13@13:02:12-UTC.png) in /home/pi/images
Sample images taken on sunny days (near solstices, equinoxes, perihelion, aphelion, others?)
A table containing the yearly x,y pixel and cm locations of the tip of the gnomen at local noon (12:02:13 p.m. CST).
An analemma plotted with x,y pixel data.
An alalemma plotted with cm x,y data.
My observing latitude and the tilt of the Earth’s axis calculations.
A sketch or plot the path of the Sun on the Celestial Sphere
Equation of Time graph
Eccentricity of the Earth’s orbit calculations
At the start of the project I saved images in both jpg and png formats. I quickly changed to png only. I'll also adjust various fswebcam options to improve picture quality.
*I have to pick one of the preset camera resolutions or it defaults to 352x288 thus the 1280x720 above. The 1280x740 produces squished images and needs to be resized later to 1280x960 to accurately reproduce the squares on the graph paper.
Sample picture(s)
Shadow at (439,569) Base at (309,569)
Shadow is 130 pixels long or 1.79" long in x
Shadow at(430,562) Base at (309,566)
The shadow is 121 pixels long or 1.67" long in x
(I messed with it during the week)
Well all that looked nice and should have worked, but it turns out that there is nowhere on my lot that gets direct sunlight for the full year. The location
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