and pictures by Anthony AYIOMAMITIS
Marathon Attempt (III)
the sun's position across the sky is virtually identical from year
to year when looking at the coordinates for a specific date and
time, differing by a few arc-seconds at best, a complete ephemeris
was regenerated as a precautionary measure from Jan 1, 2002 to Dec
31, 2002 for each of the eleven desired analemmas. The analysis
during the first run was based on the ephemeris for the 06:00:00 UT
analemma as that was the first analemma undertaken.
this second odyssey at generating the complete set from sunrise to
sunset, a more conservative approach was adopted by using the
ephemeris for the perfectly vertical analemma on the meridian
(10:28:16 UT) and by applying precisely the same type of analysis
as the first run for the identification of the first half of each
loop (the "S"-shape referred to earlier). This approach is
not only more conservative but perhaps more accurate for the simple
reason that the second half of the analemma schedule and each loop
is immediately extracted by simply lining up target dates and
matching altitudes from the first half.
As was the case with the
analysis during the first attempt, a small number of the newly
scheduled imaging dates permitted for some flexibility due to the
fact that the computed altitude (radix + offset) fell between two
available dates (ex. July 26 or July 27, 2002, Table 2)
which permitted for an extra day in honoring that particular imaging
Furthermore, the ratio of multiple exposures between
the summer and winter loops (12:28) is now in agreement with the
ratio of the vertical distances (14.45░:32.41░); during the first
run when the schedule was established using the ephemeris of the
06:00:00 UT analemma, the ratio was visually set to 12:28 which did
not agree with the ratio of the corresponding vertical distances
analemma of 8h UT over Epha´stos' temple, Athens.
Similarly, if a multi-exposure did deviate by the
self-imposed maximum of +1 day when imaging the first half of each
loop, the schedule for the complementary side was adjusted
accordingly due to a firm desire to simultaneously assure perfect
horizontal and/or vertical symmetry. With respect to the time of
exposure, the shutter was tripped at the precise second with
absolutely no allowance for error.
With the guiding hand of
my second attempt at generating the complete set of analemmas from
sunrise to sunset was much more problem-free as I was able to
eventually adhere to my regimen of shooting the sun (sort of speak)
at precisely the new set of precise dates and times (Table
2) over the course of one calendar year without the slightest
problem as a result of any further earthquakes or seriously adverse
weather for seven of the eleven analemmas.
Of course, the major
obstacle encountered during the first run, namely the accidental
film advances with the Canon AE-1 bodies, would resurface for two of
my double-analemma cameras (11:00:00-12:00:00 and 13:00:00-14:00:00
UT), thus necessitating yet additional restarts three
months into the project and forfeiting yet another 44 (4 analemmas
and 11 exposures each) multiple exposures.
The only deviation from the shooting schedule occurred for my
two extreme analemmas which encountered a physical obstruction (a
mountain range) around the winter apex point (Figures 3 and 13),
thus necessitating the forced omission of several
total multi-exposures. This is something which I had
suspected in mid-October/2001 and a detailed analysis of the
mountain's profile as a function of altitude did not permit for any
creative adjustment in the shooting schedule (+1 day etc) so as to
work around the obstruction, for the sun during these two dates was
a mere 1.5░ below the mountain's profile with little movement in
altitude during this period of the season.
By an incredible stroke
of luck, a scheduled exposure for each of these analemmas coincided
with the solar disk being partially obstructed by the mountain
(thank you Apollo !) which made the problem quite self-evident to the
observer of the completed analemma. The local weather for both of
these inflexible dates was, again fortunately, also accommodating
(thank you Apollo !). Nevertheless, Murphy's Law struck a second time
for these two analemmas as I would also loose the much-desired apex
point (winter solstice) on the lower winter loop!
analemma of 9h UT over Hera's temple (700 BC).
My initial plans called for an extra multi-exposure for each
analemma involving the actual physical landscape as viewed through
the lens. However, this was something that was eventually bypassed
so as to make the creation of the composite depicted in Figure 14
Nevertheless, upon the completion of each analemma, the
roll of film was advanced by one frame for the shooting of the
associated landscape for future reference, and which has the added
benefit of also providing a point of reference for the photo lab in
the proper cutting of the film following development. The foreground
images presented in the composite analemmas were shot during January
and February, 2003, when the sun is relatively quite low over the
horizon and a much richer shade of blue for the background sky can
be acquired without having to resort to using any filters, thus
making the analemma more pronounced.
Not to leave any aspect of this project untouched and
bordering on something that could best be described as a Sisyphean
task extraordinaire, I am also currently imaging what I believe to
be the first triple analemma (129 total multi-exposures) on a single
piece of film as well as the first analemma similar in appearance to
a bead necklace (see Table 1).
The triple analemma is to be centered by the special case
vertical analemma (10:28:16 UT) alluded to above as well as the
analemmas at + 40 min (09:48:16 UT and 11:08:16 UT) which will just
fit perfectly (68.3░ x 47.8░ arc coverage) on a single piece of 35mm
film using my Canon FD 24mm f/2.8 lens (74░ x 53░ arc coverage in
My initial aspirations for the triple analemma
involved the meridian case flanked by the analemmas at + 1 hr
(09:28:16 and 11:28:16 UT) but this was not possible as the
physical range in azimuth slightly exceeds the corresponding range
available with my 24mm wide angle lens.
A further analemma on the meridian also in progress involves
imaging during every 0.6░ movement (or more) in either azimuth
and/or altitude (139 total images) so as to generate a completed
analemma similar in appearance to a bead necklace (the solar disk
has an apparent diameter of approximately 0.5░).
The two points
representing winter and summer solstice - Dec 21/02 and Jun 21/03,
respectively - as well as the intersection of the two loops (Aug
30/03) will be included automatically.
Ignoring these three fixed
points, the greatest proportion of the remaining 136 images will be
due a movement of 0.6░ or greater in altitude (#1),
representing 124 out of 136 images, whereas the balance (12 out of 136) will be due to
There exist no examples where both conditions (0.6░ movement in
each of azimuth and altitude) occur simultaneously.
Similarly, 86 of
the 139 multi-exposures will be spaced two days apart whereas a
further 27 multi-exposures will be spaced three days apart between
Yet a third analemma on the meridian in progress as well is
based on a weekly shooting schedule and whose sole purpose is to
illustrate the relative "slow" or "fast"
movement of the sun during the different seasons. If the interval
between multi-exposures is precisely the same, the relative rate of
the sun's movement across the sky can be assessed more accurately.
By keeping the three key reference points of the analemma fixed
(summer solstice, cross-over, winter solstice), a weekly imaging
schedule is easily generated without a need to adjust any of the key
dates. The sole exception to the 52 planned multi-exposures is the
one extra day between the winter solstice and the scheduled image
immediately prior to it (Dec 13/02).
the Earth movements
of the horizontal and vertical movements of the Earth axis
summation as seen from the Sun.
As described in the following section, the Canon A-1 is
ideally suited for the imaging of the solar analemma as it makes
this exercise completely problem-free and, to this end, two of the
three above analemmas now in progress which are very aggressive in
nature - 129 and 139 multiple-exposures each on a single frame of 35
mm film - involve my two faithful Canon A-1 cameras purchased over
15 years ago.