Analemma
Encyclopedia
In astronomy
, an analemma (icon; from Greek ἀνάλημμα "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
. The term is commonly applied nowadays to the figure traced in the sky when the position of the Sun is plotted at the same time each day over a calendar year from a particular location on Earth.
s, usually in the eastern Pacific Ocean, the only large tropical region with very little land. 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), see section below.
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 solstice
s. Viewed from 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 significant axial tilt, the analemma would be a figure of eight with northern and southern lobes equal in size. For an object with an eccentric orbit but no axial tilt, the analemma would be a straight east-west line along the celestial equator.
The north-south component of the analemma is the declination
, or the latitude at which the Sun is directly overhead. The east-west 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 portmanteau coined by photographers based on the Turkish word for eclipse.
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 solstice
s and equinox
es are shown in green. It can be seen that the equinoxes occur at altitude , and the solstices occur at altitudes 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).
The analemma is oriented with the smaller loop appearing north of the larger loop.
See equation of time
for a more detailed description of the east-west characteristics of the analemma.
over New England in the USA.
He made 44 exposures on a single frame of film all taken from the same location with a solar filter. The foreground showing a house is thus a superposition of all the images throughout the year. Since then most photographers take a single foreground image and superimpose the multiple sun images on top if it.
On Earth, the analemma appears as a figure eight
, but on other solar system bodies it may be very different because of 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:
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, an analemma (icon; from Greek ἀνάλημμα "pedestal of a sundial
Sundial
A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a...
") is a curve representing the angular offset of a celestial body (usually the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
) from its mean position on the celestial sphere
Celestial sphere
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...
as viewed from another celestial body relative to the viewing body's celestial equator
Celestial equator
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space...
. The term is commonly applied nowadays to the figure traced in the sky when the position of the Sun is plotted at the same time each day over a calendar year from a particular location on Earth.
Description
Since the Earth's mean 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 clock time every day for an entire year. The resulting curve resembles a figure of eight. This curve is commonly printed on globeGlobe
A globe is a three-dimensional scale model of Earth or other spheroid celestial body such as a planet, star, or moon...
s, usually in the eastern Pacific Ocean, the only large tropical region with very little land. 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), see section below.
There are three parameters that affect the size and shape of the analemma: obliquity
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...
, eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
, and the angle between the apse line
Apse line
In astrodynamics, apse line is an imaginary line defined by an orbit's eccentricity vector. It is strictly defined for elliptic, parabolic, and hyperbolic orbits...
and the line of solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...
s. Viewed from an object with a perfectly circular orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
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 significant axial tilt, the analemma would be a figure of eight with northern and southern lobes equal in size. For an object with an eccentric orbit but no axial tilt, the analemma would be a straight east-west line along the celestial equator.
The north-south component of the analemma is the declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
, or the latitude at which the Sun is directly overhead. The east-west component is the equation of time
Equation of time
The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...
, or the difference between solar time
Solar time
Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time and mean solar time .-Introduction:...
and local mean time
Local mean time
Local mean time is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude...
. 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 portmanteau coined by photographers based on the Turkish word for eclipse.
Earth's analemma
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
Northern Hemisphere
The Northern Hemisphere is the half of a planet that is north of its equator—the word hemisphere literally means “half sphere”. It is also that half of the celestial sphere north of the celestial equator...
. It is a plot of the position of the Sun at 12:00 noon at Royal Observatory, Greenwich
Royal Observatory, Greenwich
The Royal Observatory, Greenwich , in London, England played a major role in the history of astronomy and navigation, and is best known as the location of the prime meridian...
, England (latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
51.4791°N, longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
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 solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...
s and equinox
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...
es are shown in green. It can be seen that the equinoxes occur at altitude , and the solstices occur at altitudes where ε is the axial tilt
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...
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).
The analemma is oriented with the smaller loop appearing north of the larger loop.
See equation of time
Equation of time
The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...
for a more detailed description of the east-west characteristics of the analemma.
Photography of the Earth's analemma
The first analemma photograph ever made was created in 1978 /1979 by photographer Dennis di CiccoDennis di Cicco
Dennis di Cicco is an American amateur astronomer who lives in New England. He has discovered numerous asteroids from his backyard observatory in Sudbury, Massachusetts . He is also the senior editor of Sky and Telescope magazine, where he has been a member of the editorial staff since 1974...
over New England in the USA.
He made 44 exposures on a single frame of film all taken from the same location with a solar filter. The foreground showing a house is thus a superposition of all the images throughout the year. Since then most photographers take a single foreground image and superimpose the multiple sun images on top if it.
Other analemmas
Figure 8
Figure 8 may refer to:* 8 , in Arabic numeralsIn entertainment* Figure 8 , by American singer-songwriter Elliott Smith* "Figure of Eight" from the album Flowers in the Dirt by Paul McCartney...
, but on other solar system bodies it may be very different because of 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
Synodic day
A synodic day is the period of time it takes for a planet to rotate once in relation to the body it is orbiting ....
and sidereal year
Sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...
of the particular body:
- MercuryMercury (planet)Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
: Because orbital resonanceOrbital resonanceIn celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
makes the day exactly two years long, the method of plotting the Sun's position at the same time each day would yield only a single point. However, the equation of timeEquation of timeThe equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...
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. - VenusVenusVenus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...
: 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. - MarsMarsMars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...
: teardrop - JupiterJupiterJupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
: ellipse - SaturnSaturnSaturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
: technically a figure 8, but the northern loop is so small that it more closely resembles a teardrop - UranusUranusUranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...
: figure 8 - NeptuneNeptuneNeptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...
: figure 8 - PlutoPlutoPluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...
: figure 8
See also
- Analemmatic sundial
- Armillary sphereArmillary sphereAn armillary sphere is a model of objects in the sky , consisting of a spherical framework of rings, centred on Earth, that represent lines of celestial longitude and latitude and other astronomically important features such as the ecliptic...
- De architecturaDe architectura' is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects...
- On the Dioptra
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 SchoolsFairfax County Public SchoolsThe Fairfax County Public Schools system is a branch of the Fairfax County government which administers public schools in Fairfax County and the City of Fairfax...
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 WolframStephen WolframStephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine.- Biography :...
based on a program by Michael Trott, Wolfram Demonstrations ProjectWolfram Demonstrations ProjectThe Wolfram Demonstrations Project is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience. It consists of an organized, open-source collection of small interactive programs called Demonstrations, which are meant to visually and...
. - Analemma in Verse by Tad Dunne
- Astronomy Picture of the DayAstronomy Picture of the DayAstronomy Picture of the Day is a website provided by NASA and Michigan Technological University . According to the website, "Each day a different image or photograph of our universe is featured, along with a brief explanation written by a professional astronomer."The photograph is not necessarily...
- 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 Ukraine
- 2007-12-04 — Analemma over New Jersey (film)
- 2008-12-21 — Analemma over the Porch of Maidens
- 2009-12-20 — Tutulemma: Solar Eclipse Analemma
- 2010-12-31 — Analemma 2010