Analemma Program Introduction

Analemma Observing Program Coordinator:

Lowell Martin
4251 FM 2181 – Suite 230 / #357
Corinth, TX 76210
Email: fwas_lam at yahoo dot com
Ph: (940)-453-6692

Introduction

Just about everyone knows that the Sun’s altitude at culmination, the highest point above the observer’s horizon, varies through the year – high in the summer, and low in the winter. However, outside of navigators, cartographers and astronomers, it is not commonly realized that the Sun’s apparent angular velocity also varies – sometimes “fast” (west of the meridian at Local Noon), and sometimes “slow” (east of the Meridian at Local Noon). 

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 

Rules and Regulations

To qualify for the AL’s Analemma Observing Program Certificate and pin, you need only be a member of the Astronomical League, either through an affiliated Club or as a Member at Large, generate an analemma, and analyze the data of the analemma by completing the four “activities” listed below in their prescribed order. 

  • 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).

DO NOT ATTEMPT DIRECT OBSERVATIONS OF THE SUN! Due to hazards associated with direct observation of the Sun, only indirect observations will be accepted. Submissions using direct observations of the Sun will be rejected. Looking at the sun can cause permanent damage to your eyes.

Though not necessary to observe on specific days, both the Vernal and Autumnal Equinox, both the Summer and Winter Solstice, and the days of perihelion and aphelion should be noted on the analemma. The Observer’s Latitude, Longitude, and Local Observing Time should also be noted.

Some pre-observing activity is required:

  • Select your observing site. The site must allow full-year observation of the Sun – either a ray through a hole in an obstruction, or a shadow. You will need to obtain the site’s Latitude, Longitude, and Magnetic Variation (if you use a magnetic compass to identify true north/south). The purpose of “starting with the answer” for these pre-observing activities is to assure the observations will fit on the chosen media … nothing more; once the analemma is complete, the analysis of the analemma is to be completed with reference only to the analemma and measured dimensions of the observing apparatus.
  • Specify your Observing Time: Most observers will find it least complicated to record their observations at Local Noon; it can be calculated from the Observing Site’s Longitude, and should be calculated to the second. A source for accurate times (e.g., W W V or a cell phone) is required to assure that the observations are taken at the same clock time (even when using a small enclosure, being off by 15-20 seconds makes a small but noticeable change in the observed position of the Sun). Be sure to add 1 hour when Daylight Savings Time is in effect. 

Observers, who find it impractical to return to their observing location at Local Noon over the year, may choose between two alternatives:

  1. They may take 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. They should then complete the four Activities, in their prescribed order, using the calculated Local Noon points. For an overview of using non-Local Noon observations, click here (Appendix B).
  2. They may set-up a camera for unattended operation, photo­graph the area where they expect the indication to be, and determine the distances from the image. Observers are cautioned about several inherent weaknesses of this technique:
    1. 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 
    2. Automatic exposure control may washout surface markings used to locate the analemma point
    3. The Field of View will change if the camera is moved
    4. 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°

Observers are required to develop their technique for accurately determining distances to the individual analemma points.

Reminder: Observers using a photographic technique are required to collect a minimum of 100 data points, spread approximately uniformly throughout the year.

  • Specify your observing apparatus: If using a transmitted light ray or shadow for your observations, a box containing a sheet of paper can be constructed – for a procedure to build such a box, click here (Appendix A … there are many ways to cast a light ray or shadow; this is only one of them). The points of the analemma are to be marked during the year, with the points of Solstices, Equinoxes, and aphelion and perihelion identified on the analemma.

When the Analemma is complete, a number of parameters about the Earth and its journey around the Sun are to be calculated. The following four activities are to be done in their prescribed order:

  • Activity #1: with reference only to your analemma and measured dimensions of your observing apparatus, calculate (1) the tilt of the Earth’s axis off the normal (i.e., the perpendicular vector) to its orbital plane, and (2) your observing latitude.

For a recommended calculation procedure, click here (Appendix F)

  • Activity #2: with reference only to your analemma and measured dimensions of your observing apparatus, calculate the Sun’s path in the sky and produce a sketch or plot to depict that path. 

For a recommended calculation procedure, click here (Appendix G)

  • Activity #3: with reference only to your analemma and measured dimensions of your observing apparatus, calculate the Equation of Time curve across the year. 

For a recommended calculation procedure, click here (Appendix H).  

  • Activity #4: with reference only to your analemma and measured dimensions of your observing apparatus, calculate the eccentricity of the Earth’s orbit. 

For a recommended calculation procedure, click here (Appendix I).  

To receive your Analemma Observing Program certificate and Award Pin, mail the following to the AL Observing Program Coordinator (do not mail originals):

  • A description of your observing setup (with dimensions). This includes a description of your observing location (Latitude, Longitude, Magnetic Variation, if used) and Local Observing Time.
  • A copy of your analemma, with the points of Solstices, Equinoxes, and aphelion and perihelion identified
  • A description of how you derived the tilt of the Earth’s axis and your observing Latitude. If an observing time other than Local Noon was used, a description of how the data was transformed into Local Noon data is to be included as well. (Activity #1)
  • A copy of your sketch or plot of the Sun’s path in the sky, and a brief description of how you derived it (Activity #2)
  • A copy of your Equation of Time curve, and a brief description of how you derived it (Activity #3)
  • Your estimate of the eccentricity of Earth’s orbit, and a brief description of how you derived it (Activity #4)

Include with your submission, your name as you want it to appear on the certificate, address, phone number, email, and society affiliation. Upon verification of your observations, your certificate and pin will be forwarded to you or your club’s Awards Coordinator, whomever 

Analemma Observing Program Coordinator:

Lowell Martin
4251 FM 2181 – Suite 230 / #357
Corinth, TX 76210
Email: fwas_lam at yahoo dot com
Ph: (940)-453-6692

Additional Links

Printable version of this page
Appendix A – Construction of an Enclosure
Appendix B – Overview of Non-Local Noon Observing
Appendix C – Unattended Photography 
Appendix D – * * *   Reserved for Future Use   * * *
Appendix E – * * *   Reserved for Future Use   * * *
Appendix F – Activity #1 (Tilt of Earth’s Axis and Observer’s Latitude)
Appendix G – Activity #2 (Path of the Sun in the Sky)
Appendix H – Activity #3 (Equation of Time)
Appendix I  – Activity #4 (Eccentricity of Orbit)