Analemma

:Analemma "was also a book by Ptolemy".

In astronomy, an analemma (IPA: 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 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.

Earth's Analemma

Owing to the Earth's tilt on its 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 time on 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. It is a plot of the position of the sun at 12:00 noon at Royal Observatory, Greenwich, England (latitude 51.4791 deg north, longitude 0) during the year 2006. The horizontal axis is the azimuth angle in degrees (180 degrees 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 degrees, and the solstices occur at altitudes φ±ε where ε is the axial tilt of the earth, 23.439 degrees. The analemma is plotted with width highly exaggerated, which permits noticing that it is very slightly asymmetrical (because of the two-week misalignment of the apsides of the Earth's orbit and its solstices).

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

Other analemmas

[
Mars]

On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different. [ [http://www.analemma.com/Pages/OtherAnalemmas/OtherAnalemmas.html Other Analemmas] ] 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 (because of 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

References

ee also

* Analemma calendar

External links

* [http://antwrp.gsfc.nasa.gov/apod/ap020709.html Astronomy Picture of the Day, 2002 9 July: Analemma]
* [http://antwrp.gsfc.nasa.gov/apod/ap030320.html Astronomy Picture of the Day, 2003 20 March: Sunrise Analemma]
* [http://antwrp.gsfc.nasa.gov/apod/ap040621.html Astronomy Picture of the Day, 2004 21 June: Analemma over Ancient Nemea]
* [http://antwrp.gsfc.nasa.gov/apod/ap050713.html Astronomy Picture of the Day, 2005 13 July: Analemma of the Moon]
* [http://antwrp.gsfc.nasa.gov/apod/ap061223.html Astronomy Picture of the Day, 2006 23 December: Analemma over the Temple of Olympian Zeus]
* [http://antwrp.gsfc.nasa.gov/apod/ap061230.html Astronomy Picture of the Day, 2006 30 December: Martian Analemma at Sagan Memorial Station (simulated)]
* [http://antwrp.gsfc.nasa.gov/apod/ap070617.html Astronomy Picture of the Day, 2007 17 June: Analemma over the Ukraine]
* [http://antwrp.gsfc.nasa.gov/apod/ap071002.html Astronomy Picture of the Day, 2007 2 October: Tutulemma: Solar Eclipse Analemma]
* [http://antwrp.gsfc.nasa.gov/apod/ap071204.html Astronomy Picture of the Day, 2007 4 December: Analemma over New Jersey (movie)]
* [http://www.perseus.gr/Astro-Solar-Analemma.htm Analemma Series from Sunrise to Sunset]
* [http://members.aol.com/jwholtz/analemma/analemma.htm Analemma explanation by John Holtz]
* [http://epod.usra.edu/archive/epodviewer.php3?oid=228384 Earth Science Photo of the Day, Jan 22, 2005]
* [http://myweb.tiscali.co.uk/moonkmft/Articles/EquationOfTime.html The Equation of Time and the Analemma, by Kieron Taylor]
* [http://astro.isi.edu/games/analemma.html An article by Brian Tung, contains link to a C program using a more accurate formula than most (particularly at high inclinations and eccentricities)]
* [http://www.math.nus.edu.sg/aslaksen/projects/tsy.pdf 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.
* [http://www.analemma.com/ Analemma.com] is dedicated to the analemma.
* [http://www.wsanford.com/~wsanford/exo/sundials/analemma_calc.html 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.
* " [http://demonstrations.wolfram.com/Analemmas/ Analemmas] " by Stephen Wolfram based on a program by Michael Trott, The Wolfram Demonstrations Project.