by alter-ego » Wed Dec 21, 2016 6:31 pm
JohnD wrote:A very pretty thing, that I enjoyed so much, when the usual analemma pictures are static and boring, that I went to find out more about this figure, and why it has two differently sized loops The Wiki article is especially confusing!
https://en.wikipedia.org/wiki/Analemma
The paragraph "Solar analemma as seen from Earth" says that the smaller loop is on top from the Northern hemisphere, but below from the Southern. Is that true? I expected that there would be a smaller loop on top from either hemisphere, getting smaller as one approached the Poles and more equal as one approached the Equator, where the loops would be equal in size.
It's clear to me that the extreme of each loop marks the Solstice, but why are the Equinoxes not where the loops cross? That's in the analemma from the Royal Observatory, so I have to believe that!
John
So first, the analemma's shape is constant for all locations on earth, only the viewing perspective changes.
The small loop is always on the northern end of the analemma. The apparent flip between the northern and southern hemispheres is due to a 180° change in viewing direction. In the north one faces southward to view the analemma. In the south, one faces northward. In the northern hemisphere, if you face northward and lean backward you'll view the analemma with the big loop at the "top".
Second, the loops are different sizes due to earth's elliptical orbit.
Earth is closest to the sun during the northern winter months, so the apparent position of the sun is changing the fastest, thus how fast/slow the sun appears is greatest between these months. For a perfectly circular orbit, the analemma would be a symmetrical figure 8 with identical loops (the loops are due to the earth's tilted rotation axis, not ellipticity), and there would be equal times between the equinoxes and solstices, i.e. the crossing point would be the equinoxes. By definition, the equinoxes occur when the sun crosses the equator (0° declination). Because the orbit is elliptical, the crossing point actually occurs at ~9° declination. It doesn't take much ellipticity to dramatically change the analemma. In fact, both the analemma's slight east/west lean and loop asymmetry is entirely due to the orbital eccentricity.
Hope this helps.
[quote="JohnD"]A very pretty thing, that I enjoyed so much, when the usual analemma pictures are static and boring, that I went to find out more about this figure, and why it has two differently sized loops The Wiki article is especially confusing! https://en.wikipedia.org/wiki/Analemma
The paragraph "Solar analemma as seen from Earth" says that the smaller loop is on top from the Northern hemisphere, but below from the Southern. Is that true? I expected that there would be a smaller loop on top from either hemisphere, getting smaller as one approached the Poles and more equal as one approached the Equator, where the loops would be equal in size.
It's clear to me that the extreme of each loop marks the Solstice, but why are the Equinoxes not where the loops cross? That's in the analemma from the Royal Observatory, so I have to believe that!
John[/quote]
So first, the analemma's shape is constant for all locations on earth, only the viewing perspective changes.
The small loop is always on the northern end of the analemma. The apparent flip between the northern and southern hemispheres is due to a 180° change in viewing direction. In the north one faces southward to view the analemma. In the south, one faces northward. In the northern hemisphere, if you face northward and lean backward you'll view the analemma with the big loop at the "top".
Second, the loops are different sizes due to earth's elliptical orbit.
Earth is closest to the sun during the northern winter months, so the apparent position of the sun is changing the fastest, thus how fast/slow the sun appears is greatest between these months. For a perfectly circular orbit, the analemma would be a symmetrical figure 8 with identical loops (the loops are due to the earth's tilted rotation axis, not ellipticity), and there would be equal times between the equinoxes and solstices, i.e. the crossing point would be the equinoxes. By definition, the equinoxes occur when the sun crosses the equator (0° declination). Because the orbit is elliptical, the crossing point actually occurs at ~9° declination. It doesn't take much ellipticity to dramatically change the analemma. In fact, both the analemma's slight east/west lean and loop asymmetry is entirely due to the orbital eccentricity.
Hope this helps.