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Analemma was also a book by Ptolemy.

The analemma photographed, looking east in the northern hemisphere. The dates of the sun's position are shown.

In astronomy, an analemma (IPA: /ˌænəˈlɛmə/, Latin 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 (usually the Earth). 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 8. 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 8 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 of the analemma is the declination, or how far north or south from the equator the sun appears 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.

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 (23.45°) 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.

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

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

The analemma for Mars

On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different[1]. The variation is 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. An interesting phenomenon occurs because of the relationship between Mercury's day and year (see Mercury (planet)#Orbit and rotation).
• 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

• Analemma calendar

• Astronomy Picture of the Day, 2002 9 July: Analemma
• Astronomy Picture of the Day, 2003 20 March: Sunrise Analemma
• Astronomy Picture of the Day, 2004 21 June: Analemma over Ancient Nemea
• Astronomy Picture of the Day, 2005 13 July: Analemma of the Moon
• Astronomy Picture of the Day, 2006 23 December: Analemma over the Temple of Olympian Zeus
• Astronomy Picture of the Day, 2006 30 December: Martian Analemma at Sagen Memorial Station (simulated)
• Analemma Series from Sunrise to Sunset
• 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)
• The Analemma for Latitudinally-Challenged People explains rising and setting analemmas as viewed from different latitudes. It provides more depth than most analemma sources. PDF format. 1,433 Kb.
• Analemma.com is dedicated to the analemma.
• Calculate and Chart the Analemma is 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.