The analemma is a term in astronomy used to describe the plot of the different positions of the Sun in the celestial sphere recorded at a the same time of day (at 24 hour intervals) and from the same location on successive days through the calendar year. This appears as a figure of eight. If the course of the earth around the sun were a precise circle and if the earth's polar axis stood perpendicular to the plane of its orbit, the sun would always appear at the same point in the sky at the same time of day throughout the year and no analemma would be seen. If the orbit were circular, but the polar axis tilted as it is, the northern and southern lobes of the figure of eight would be equal in size; if the polar axis were not tilted but the orbit had its current eccentricity then the analemma would be a straight east-to-west line. It is possible to construct an analemma by taking a photograph of the sun each day of the year at the same time and place and with a camera positioned in exactly the same way each time.

Explanation

The analemma for Earth

Plotting the analemma with the width exaggerated shows that it is slightly asymmetrical due to the misalignment of apsides and solstices.

Due to the earth's tilt on its axis (23.5°) and its elliptical orbit around the sun, the relative location of the sun above the horizon is not constant from day to day when observed at the same time on each day. Depending on one's geographical latitude, this loop will be inclined at different angles.

The vertical coordinate of a point corresponding to a date corresponds to the declination of the sun on that date, while the horizontal coordinate indicates whether the sun is "fast" or "slow" compared to mean time as measured by clocks.

The deviation between solar time and mean time is known as the equation of time and is due to the variation in the length of the synodic day, which is due to variation in the distance between the earth and the sun. (See aphelion, perihelion.)

Plotting the analemma with the width exaggerated shows that it is slightly asymmetrical due to the misalignment of apsides and solstices.

Analemma on other planets

The analemma for Mars

On Earth, the analemma shows a "8"-shape figure, but on Mars it has a teardrop shape. Other planets also have analemmas with various shapes [1].

External links

• Figure-8 in the Sky
• Astronomy Picture of the Day, 2002 July 9: Analemma
• Astronomy Picture of the Day, 2003 March 20: Sunrise Analemma
• Astronomy Picture of the Day, 2004 June 21: Analemma over Ancient Nemea
• Stunning Analemma Series from Sunrise to Sunset
• Analemma.com: free download of SunGraph software for analemmae (incorrectly claims Mercury and Venus lack analemmae)
• Analemma explanation by John Holtz
• Earth Science Photo of the Day, Jan 22, 2005
• The Equation of Time and the Analemma, by Kieron Taylor
• An article by Brian Tung, contains link to a C program using a more accurate formula than most (particularly at high inclinations and eccentricities)