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

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