Astrophotography by Anthony Ayiomamitis

Conquering the Solar Analemma Challenge

Why are Mediterranean summers much warmer than winters? Why are days during the summer longer than those in winter? Why does the Northern Hemisphere experience summer when the Southern Hemisphere is going through winter with precisely the opposite effect six months later?

The answer to these seemingly simple questions has to do with the fact that the earth spins about an axis not perfectly vertical but tilted 23.45° relative to a perpendicular defined by the orbital plane traced out by Earth's annual motion around the sun and due to an orbit around the sun which is not perfectly circular but slightly elliptical in nature.

For example, because of the elliptical nature of the planet’s orbit around the sun, our planet travels at a faster rate when is closest to the sun (perihelion) in January than at aphelion in July when it is furthest away. This differential rate in motion is responsible for the sun being observed slightly to the left or slightly to the right of the local meridian at noon for 361 out of 365 days each year. In fact, the sun can be observed to lie on the local meridian at noon on only four days each year, namely, April 12th or 13th, June 21st, August 30th and December 21st. For the 361 days when the sun is observed to be slightly to the left or right of the meridian, the sun can require up to an extra 16 minutes to reach the local meridian (this effect is commonly referred to as the “Equation of Time”).

Similarly, the tilt in the planet’s axis of rotation relative to its orbital plane is the reason why we experience seasons and explains why the sun is observed to rise to higher declinations at noon in the summer and much lower declinations during the winter.

These two physical characteristics about our planet lead to the sun reaching the meridian on different times and at different declinations over the course of a year. When these cumulative deviations over time are analyzed more closely, we notice that it forms a pattern similar to the figure “8” loop commonly referred to as the “analemma”.

More generally, an analemma is the figure "8" loop that results when one observes the position of the sun at the same time during the day over a period of one year and not necessarily only at local noon. When the observation is during the initial part of the day, the analemma will be slanted from left to right; in contrast, when the observation of the sun is during the latter part of the day, the analemma will be slanted in the opposite direction and from right to left.

The first successful attempt in photographing this constant change in declination in combination with the “Equation of Time” was in 1979 when American and Sky&Telescope Senior Editor Dennis di Cicco photographed the analemma from his home in Massachusetts. What is perhaps of greater interest is that only six other times since the pioneering work in 1979 has anyone also managed to successfully image the solar analemma as a multi-exposure on a single piece of film. The complete list of successfully produced analemmas includes three efforts from the US and one each from Canada, Russia, Britain and Denmark. Of these seven efforts, it is very strange that no one has imaged the analemma as it would appear precisely on the southern meridian with efforts having being concentrated on the analemma as observed in early morning where the analemma is inclined from left to right (the angle of inclination is dependent on one’s geographical latitude).

This small number of successfully produced analemmas is an indication of how challenging such a task it represents and why the imaging of the analemma is considered perhaps the most difficult and demanding astrophotography project that one can pursue. Aside from requiring significant analysis and preparation prior to starting the imaging of the sun over local skies lasting twelve months in duration, one must also exercise discipline, organization and accurate procedural matters in order to assure that a properly framed and structured analemma will be produced at the end of the twelve months.

By studying the sun's azimuth on a second-by-second basis, it was established that the vertical analemma corresponded to an exposure schedule for precisely 12:28:16 UT+2, for it is at this time that azimuth for the summer and winter solstice line-up perfectly. The ephemeris of the sun at this time was also used to examine the range in altitude from January 1st to December 31st in order to arrive at an imaging schedule for the analemma. More specifically, the altitude was identified for the upper apex (June 21) and the cross-over points (Aug 30); this range was divided by seven so as to derive an offset that could be successively subtracted from the altitude on June 21st so as to identify the corresponding dates with that target altitude for imaging. A similar approach was adopted for the lower loop where a divisor of 14 was applied to the range in altitude between the cross-over point (Aug 30) and the lower apex (Dec 21).

A Baader solar filter (ND5.0) which permits for the transmission of 0.001% of the visible light to pass through was used in front of a Canon FD 24mm camera lens. This particular focal length lens was used since the range of the sun in both altitude and azimuth (as per the ephemeris in the previous paragraph) represents approximately 60% of the lens' field of view which allows for some error in the proper orientation of the camera with respect to both altitude and azimuth. A cellular phone was calibrated to the Atomic Clock over the Internet at the start of each imaging day so that the shutter could be tripped at the precise second of interest. Software calculations suggested an exposure of 1/250th sec for ISO 200 film; this exposure was purposely increased by three stops to 1/30th sec in order to account for days when the sun is lower in the sky and, therefore, not as intense and/or when very thin clouds were present.

My initial attempts at tackling this challenging imaging exercise started on the summer solstice of 2001 when I attempted to image a perfectly vertical analemma on the southern meridian as well as various other versions of the analemma. However, this first attempt came to a quick stop six months into the project due to bad weather which caused me to miss two key exposures in December/2001 including the vital apex point on the lower loop. This is something that proved to be a blessing in disguise, for it allowed me to restart in January/2002 and, therefore, enabled me to produce two analemmas representing the motion of the sun across local the sky over twelve consecutive months of the same calendar year (each of the other seven successfully completed analemmas spanned two calendar years).

Regrettably, 2002 was also characterized with nine failed analemmas due to very slight movement of the film within the camera chamber. Each of these analemmas was immediately restarted for a third annual marathon with favourable results finally realized twelve months later and thereafter (see here).

Note: The above text is available as a brief article in Interstellarum (Aug/2011, pg 15).