Analemma Traces Figure Eight Shaped Apparent Solar Path Across Sky

Summary: As an astronomical diagram, the analemma traces an elongated figure eight shaped apparent solar path across the sky for a year via a fixed spot on Earth.

“solar analemma @Taranto”: analemma taken with digicam Olympus FE-140 from Oria, Brindisi province, Apulia region, southern Italy; Ionian Sea scene imaged June 23 at Taranto, about 30 kilometers away; bronze Sailors Monument (Il Monumento ai Marinai), inaugurated Sunday, June 16, 1974, by Venetian sculptor Vittorio di Colbertaldo (1902-1979), imaged Sunday, June 23: Giuseppe Donatiello (gjdonatiello), Public Domain, via Flickr

The astronomical diagram known as analemma (Greek: ἀνάλημμα, analēmma, "support") traces the elongated figure eight shaped apparent solar path across the sky, as viewed daily throughout a year at the same clock time and from a fixed location on Earth.

The analemma reveals that, despite any appearance to the contrary, Earth’s sun does not occupy the same position in the sky at the same time from one day to the next. Earth’s significant axial tilt of around 23.4 degrees and eccentric, elliptical orbit account for the daily solar phenomena of same time but different position in the celestial dome.

Earth’s elliptical orbit accounts for varying distances between Earth and its sun. Elliptical orbits feature a pair of extreme points, known astronomically as apsides (Ancient Greek ἁψίς, hapsís, “arch, vault”).

The closest, center-to-center orbital distance between a celestial body, such as Earth, and sun is known as perihelion (Ancient Greek: περί, perí, “near” + ἥλιος, hḗlios, “sun”). Earth’s orbital perihelion occurs about two weeks after the December solstice.

Aphelion (Ancient Greek: ἀπό, apó, “from” + ἥλιος, hḗlios, “sun”) denotes the farthest, center-to-center orbital distance between a celestial body and the solar system’s sun. Earth reaches orbital aphelion two weeks after the June solstice.

The sun’s apparent position during the late spring month of May and summer’s three months forms the small loop of the solar analemma’s elongated, unequally sized, figure eight shape. During summer, the sun appears to rise ever higher in the sky and reaches its highest position around the summer solstice.

The sun’s apparent movements in the sky in winter, during the early and mid-spring months of March and April, and in autumn account for the solar analemma’s longer loop. The “fast sun” of Earth’s orbital perihelion, when Earth increases its orbital speed, and the “slow sun” of Earth’s orbital aphelion, when Earth decreases its orbital speed, flatten the bottom of the longer loop.

Location determines the solar analemma’s orientation. In the Northern Hemisphere, the small loop tops the broad, long loop. Contrastingly, the broad, long loop tops the small loop in the Southern Hemisphere.

At the North Pole, the solar analemma assumes an upright orientation and yields an incomplete figure eight, with only the top of the small loop visible. At the South Pole, the upright solar analemma is inverted, with an incomplete figure eight with only the bottom of the broad, long loop visible.

South of the Arctic Circle, the complete solar analemma displays. The small loop begins a tilt toward the horizon that increases with decreasing latitude toward the equator. The tilt keeps the small loop higher in the sky than the broad, long loop. The small-loop favoring tilt in the Northern Hemisphere’s solar analemma culminates in the figure eight’s horizontal orientation in the sky at the equator.

South of the equator, the solar analemma continues its display of both loops of the figure eight. Tilting of the figure eight resumes with increasing latitude southward, away from the equator. The tilt raises the broad, long loop to a higher position in the Southern Hemisphere’s sky than that of the small loop. The broad, long loop-favored tilt produces a complete inversion of the figure eight after crossing the Antarctic Circle southward toward the South Pole.

Nearness to sunrise or to sunset also determines the solar analemma’s eastward or westward tilt. In the morning, the solar analemma tilts toward the east. Later in the day, with the sun’s apparent path downward toward the horizon, the solar analemma tilts toward the west.

The takeaway for the solar analemma that traces a figure eight shaped apparent solar path across the sky over the course of a year is that Earth’s axial tilt, elliptical orbit and orbital velocity variations determine the astronomical diagram’s shape.

Earth's solar analemma contrasts with Mars's teardrop-shaped analemma, created by the Red Planet's orbit, which is more elliptical than that of Earth; Martian analemma traced via Opportunity rover, from inside Victoria Crater's Duck Bay alcove, between Earth dates Oct. 23-Dec. 11, 2007): NASA/JPL/Cornell/ASU/TAMU, Public Domain, via NASA APOD (Astronomy Picture of the Day) May 16, 2014

Acknowledgment

My special thanks to talented artists and photographers/concerned organizations who make their fine images available on the internet.

Image credits:

“solar analemma @Taranto”: analemma taken with digicam Olympus FE-140 from Oria, Brindisi province, Apulia region, southern Italy; Ionian Sea scene imaged June 23 at Taranto, about 30 kilometers away; bronze Sailors Monument (Il Monumento ai Marinai), inaugurated Sunday, June 16, 1974, by Venetian sculptor Vittorio di Colbertaldo (1902-1979), imaged Sunday, June 23: Giuseppe Donatiello (gjdonatiello), Public Domain, via Flickr @ https://www.flickr.com/photos/133259498@N05/30847625776/

Earth's solar analemma contrasts with Mars's teardrop-shaped analemma, created by the Red Planet's orbit, which is more elliptical than that of Earth; Martian analemma traced via Opportunity rover, from inside Victoria Crater's Duck Bay alcove, between Earth dates Oct. 23-Dec. 11, 2007): NASA/JPL/Cornell/ASU/TAMU, Public Domain, via NASA APOD (Astronomy Picture of the Day) May 16, 2014, @ https://apod.nasa.gov/apod/ap140516.html

For further information:

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Available @ http://www.planetary.org/blogs/emily-lakdawalla/2014/a-martian-analemma.html

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Available @ https://www.timeanddate.com/astronomy/perihelion-aphelion-solstice.html

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Available via U.S. Geological Survey (USGS) Publications Warehouse @ https://pubs.usgs.gov/pp/1395/report.pdf

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Available @ https://www.timeanddate.com/astronomy/solar-analemma.html

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