Physics Photo of the Week
April 27, 2012
Animated Analemma
This time-lapse photograph is the
longest time-lapse I have ever attempted. The Sun was
photographed through a special filter roughly once a week at
8:30 am Eastern Standard Time throughout a whole year.
The resultant photo is a multiple exposure of all the
photographs made throughout the year. Rather than one
piece of film, the resultant image was a sum of many digital
camera images. The empty scene was photographed early
in the year on a winter afternoon. Each image of the
Sun was photographed through a filter that only showed the
Sun on a dark background.
Because the digital 
camera
could not be left out in the weather, a special jig was made
attached to a wooden post (also used for bird feeders) that
clamped the camera in the same place and orientation each
time the camera was mounted. A timer was programmed to
trip the camera when I had to be away at work.
I first encountered a photograph of the analemma by
Dennis DeCicco on the cover issue issue of Sky and Telescope in
1977. The most dramatic feature of the analemma is
basically the height of the Sun in the sky at a specified
time throughout the seasons. Because of the tilt of
the Earth's axis, the Earth's north pole points away from
the Sun in December and towards the Sun in June reaching the
extreme positions on the solstice dates. The solid
line at the eqinox date in March is a time exposure from
sunrise until about 8:20 am. The Sun's path at the
equinox represents the celestial equator - a projection of
Earth's equator onto the sky. A similar time exposure
showing the Sun's path was also made on the June solstice.
The "figure eight" appearance of the analemma is
due to the fact that Earth's orbit is
elliptical, not perfectly circular. In December the
Earth is closest to the Sun and advances in its orbit
significantly faster due to the stronger gravitational
attraction to the Sun by being closer to the Sun.
Because the Earth rotates at a constant rate, the Sun
appears to rise earlier than average because the Earth
advances further in its orbit around the Sun in one day when
the Earth is close to the Sun. The opposite occurs in
June when the Earth is further from the Sun. Hence the
analemma is widest in the season when the Earth is closest
to the Sun. The latest sunrise can be seen to occur in
the analemma a couple of weeks after the winter solstice -
that is when the Sun at 8:30 am EST is closest to the
horizon. Of course, in the mountains near Warren
Wilson College the horizon is far from horizontal.
The Sun's path is a bit rough in this
analemma. This is attributed to slight
mis-alignment of the camera each day that a photo was
taken. The camera clamp was mounted on a wooden post
(also used to hang bird feeders). The wooden post
warps at different angles between wet and dry spells.
Because the Sun's diameter is only 1/2 degree, a 1 degree
warp can significantly mis-align the camera's
pointing. Mounting the clamp on a steel post should
minimize the mis-alignments. Gaps in the
analemma occurred during vacation (in July) and bad weather
near the September equinox.
Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department. These photos feature interesting phenomena in the world around us. Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation. Atmospheric phenomena are especially welcome. Please send any photos to dcollins@warren-wilson.edu.
All photos and discussions are copyright by Donald Collins or by the person credited for the photo and/or discussion. These photos and discussions may be used for private individual use or educational use. Any commercial use without written permission of the photoprovider is forbidden.
Click here to see the Physics Photo of the Week Archive.
