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Diagram of an analemma looking east in the northern hemisphere. The dates of the sun's position are shown. This analemma is calculated, not photographed.

In astronomy, an analemma (pronounced /ˌænəˈlɛmə/, Greek for the pedestal of a sundial) is a curve representing the angular offset of a celestial body (usually the Sun) from its mean position on the celestial sphere as viewed from another celestial body relative to the viewing body's celestial equator. For instance, knowing that Earth's average solar day is almost exactly 24 hours, an analemma can be traced by plotting the position of the Sun as viewed from a fixed position on Earth at the same time every day for an entire year. The resulting curve resembles a figure of eight. This curve is commonly printed on globes. It is possible, though challenging, to "photograph" the analemma, by leaving the camera in a fixed position for an entire year and snapping images on 24-hour intervals (or some multiple thereof).

There are three parameters that affect the size and shape of the analemma: obliquity, eccentricity, and the angle between the apse line and the line of solstices. For an object with a perfectly circular orbit and no axial tilt, the Sun would always appear at the same point in the sky at the same time of day throughout the year and the analemma would be a dot. For an object with a circular orbit but axial tilt similar to Earth's, the analemma would be a figure of eight with northern and southern lobes equal in size. For an object with eccentricity similar to Earth's, but no axial tilt, the analemma would be a straight east-west line along the equator.

The vertical component (on a globe or map) of the analemma is the declination, or how far north or south from the equator an observer sees the sun directly overhead. The horizontal component is the equation of time, or the difference between solar time and local mean time. This can be interpreted as how "fast" or "slow" the sun is compared to clock time.

An analemma that includes an image of a total solar eclipse is called a tutulemma — a term coined by photographers based on the Turkish word for eclipse.^[1]

Earth's analemma

Analemma for Earth as seen from the northern hemisphere with altitude and azimuth to the same scale.

Analemma for Earth.

Owing to the tilt of Earth's axis (23.439°) 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 clock time each day. Depending on one's geographical latitude, this loop will be inclined at different angles.

The figure on the left is an example of an Earth analemma as seen from the northern hemisphere. It is a plot of the position of the sun at 12:00 noon at Royal Observatory, Greenwich, England (latitude 51.4791°N, longitude 0°) during the year 2006. The horizontal axis is the azimuth angle in degrees (180° is facing south). The vertical axis is the altitude in degrees above the horizon. The first day of each month is shown in black, and the solstices and equinoxes are shown in green. It can be seen that the equinoxes occur at altitude φ = 90° − 51.4791° = 38.5209°, and the solstices occur at altitudes φ ± ε where ε is the axial tilt of the earth, 23.439°. The analemma is plotted with its width highly exaggerated, which permits noting that it is slightly asymmetrical (due to the two-week misalignment between the apsides of the Earth's orbit and its solstices).

From the northern hemisphere, the analemma is oriented with the smaller loop appearing higher in the sky and the larger loop lower in the sky. This orientation is reversed in the southern hemisphere. From the equator, the analemma lies horizontally, with the smaller loop to the north and the larger loop to the south.

See equation of time for an in-depth description of the east-west characteristics of the analemma.

Other analemmas

Analemma for Mars

On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different^[2] due to the interplay between the tilt of each body's axis and the elliptical shape of its orbit.

In the following list, "day" and "year" refer to the synodic day and sidereal year of the particular body:

• Mercury: Because the day is exactly two years long (due to orbital resonance), the method of plotting the sun's position at the same time each day would only yield a single point. However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information. The resulting curve is a nearly straight east-west line.
• Venus: There are slightly less than two days per year, so it would take several years to accumulate a complete analemma by the usual method. The resulting curve is an ellipse.
• Mars: teardrop
• Jupiter: ellipse
• Saturn: technically a figure 8, but the northern loop is so small that it more closely resembles a teardrop
• Uranus: figure 8
• Neptune: figure 8
• Pluto: figure 8

See also

• Analemmatic sundial
• Armillary sphere
• De architectura
• On the Dioptra
• Analemma (Ptolemy)

References

External links

• Analemma Series from Sunrise to Sunset
• Earth Science Photo of the Day (2005-01-22)
• The Equation of Time and the Analemma — by Kieron Taylor
• The Use of the Analemma — from an inset from Bowles's New and Accurate Map of the World (1780)
• Figure-Eight in the Sky — contains link to a C program using a more accurate formula than most (particularly at high inclinations and eccentricities)
• The Analemma for Latitudinally-Challenged People — explains rising and setting analemmas as viewed from different latitudes and provides more depth on analemma.
• Analemma.com — dedicated to the analemma.
• Calculate and Chart the Analemma — a web site offered by a Fairfax County Public Schools planetarium that describes the analemma and also offers a downloadable spreadsheet that allows the user to experiment with analemmas of varying shapes.
• Analemma Sundial Applet — includes lots of reference charts.
• Analemmas — by Stephen Wolfram based on a program by Michael Trott, Wolfram Demonstrations Project.
• Analemma in Verse by Tad Dunne

• Astronomy Picture of the Day
  • 2002-07-09 — Analemma
  • 2003-03-20 — Sunrise Analemma
  • 2004-06-21 — Analemma over Ancient Nemea
  • 2005-07-13 — Analemma of the Moon
  • 2006-12-23 — Analemma over the Temple of Olympian Zeus
  • 2006-12-30 — Martian Analemma at Sagan Memorial Station (simulated)
  • 2007-06-17 — Analemma over the Ukraine
  • 2007-10-02 — Tutulemma: Solar Eclipse Analemma
  • 2007-12-04 — Analemma over New Jersey (movie)
  • 2008-12-21 — Analemma Over the Porch of Maidens
  • 2009-12-20 — Tutulemma: Solar Eclipse Analemma