APOD: Apollo's Analemma (2013 Sep 22)

[APOD Robot]

Apollo's Analemma

Explanation: Today, the Sun crosses the celestial equator heading south at 20:44 Universal Time. An equinox (equal night), this astronomical event marks the first day of autumn in the northern hemisphere and spring in the south. With the Sun on the celestial equator, Earth dwellers will experience nearly 12 hours of daylight and 12 hours of darkness. To celebrate, consider this remarkable record of the Sun's yearly journey through planet Earth's sky, made with planned multiple exposures captured on a single piece of 35 millimeter film. Exposures were made at the same time of day (9:00am local time), capturing the Sun's position on dates from January 7 through December 20, 2003. The multiple suns trace an intersecting curve known as an analemma. A foreground base exposure of the Temple of Apollo in ancient Corinth, Greece, appropriate for an analemma, was digitally merged with the film image. Equinox dates correspond to the middle points (not the intersection point) of the analemma. The curve is oriented at the corresponding direction and altitude for the temple, so the Sun's position for the September equinox is at the upper midpoint near picture center. Summer and winter solstices are at analemma top and bottom.

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[geckzilla]

Let me get this straight. On a nice day, the base exposure is taken and captures both the sun and the foreground. Subsequent exposures are then meant only to capture the sun and add on to the base exposure? The gaps, I assume, are from periods of cloud cover.

[Beyond]

Looks like an over-lap at the top left.

[Chris Peterson]

Let me get this straight. On a nice day, the base exposure is taken and captures both the sun and the foreground. Subsequent exposures are then meant only to capture the sun and add on to the base exposure? The gaps, I assume, are from periods of cloud cover.

Actually, I think the foreground image was made when the Sun wasn't in the frame at all. Looks as if it's with the Sun somewhat behind the camera. All the Sun images have the foreground so underexposed that essentially nothing is contributed.

Based on Anthony's comments in the past, I'm not even sure the foreground image was made at the same location as the analemma. Seems like a vulnerable location to leave a camera, or even a camera mount for a year.

[alter-ego]

Let me get this straight. On a nice day, the base exposure is taken and captures both the sun and the foreground. Subsequent exposures are then meant only to capture the sun and add on to the base exposure? The gaps, I assume, are from periods of cloud cover.

Actually, I think the foreground image was made when the Sun wasn't in the frame at all. Looks as if it's with the Sun somewhat behind the camera. All the Sun images have the foreground so underexposed that essentially nothing is contributed.

Based on Anthony's comments in the past, I'm not even sure the foreground image was made at the same location as the analemma. Seems like a vulnerable location to leave a camera, or even a camera mount for a year.

The temple view is from the SW. Although the shape and orientation of the analemma may be correct for the temple's location, it's absolute position wrt the temple does not seem possible. The sun is (nominally) behind the camera for the foreground image. As described, I interpret the film image as containing only the sun images. The temple could be a ccd image which was digitally merged with the sun images. I agree that the camera could easily have been at a different location. This is a nice picture, just not actually possible as framed.

[Anthony Barreiro]

Happy equinox! I love the rich golden light at 37 degrees north at this time of year, and how quickly the sunset and sunrise times change.

My dear friend Bubbles made this analemma that tracks the Sun through the tropical zodiac (e.g. the September equinox is the beginning of Libra). There is a link to an interactive version that lets you move the Sun around to different dates.

By the way, I had an "aha" moment when I realized that the Moon's libration is analogous to the Sun's analemma. The Moon's north-south libration is caused by the Moon's inclined orbit relative to the Earth's orbit around the Sun (the ecliptic), while the noonday Sun's north-south movement in the sky is caused by the inclination between the Earth's plane of rotation (the equator) and the plane of her orbit around the Sun (the ecliptic). The Moon's east-west libration is caused by her elliptical orbit around the Earth, and the Sun's east-west movement at mean solar noon is caused by the Earth's elliptical orbit around the Sun.

[alter-ego]

... and the Sun's east-west movement at mean solar noon is caused by the Earth's elliptical orbit around the Sun.

Speaking just about the Sun's apparent motion, only the asymmetry of the figure "8" shape is due to the eccentricity of the Earth's orbit. Both the east-west and north-south solar movements are due to the obliquity of the ecliptic. If the Earth's orbit were perfectly circular, the analemma would still be there. Only the shape and orientation would be different.

Edit:
Below you can see the components to the analemma - the vertical axis is degrees and the horizontal axis minutes of time.

Analemma Components

[Uwe]

"Equinox dates correspond to the middle points (not the intersection point) of the analemma."
That I didn't know, or did not thought about, thanks for bringing it to my attention and the matching link.
*Thumbs up for APOD!*

[Ayiomamitis]

"Equinox dates correspond to the middle points (not the intersection point) of the analemma."
That I didn't know, or did not thought about, thanks for bringing it to my attention and the matching link.
*Thumbs up for APOD!*

Uwe,

The cross-over point between the two loops occurs twice during the year and which means one imaging the analemma has a "back-up" date in the event the imaging of the cross-over point is missed the first time around due to the weather.

More specifically, the cross-over point first occurs around April 12-13 when the sun is moving upwards from the left side of the lower loop and towards the right side of the upper loop. The second cross-over occurs around August 31st and when the sun is moving downwards from the left side of the upper loop and towards the right-side of the lower loop.

The equinoxes, as mentioned in the APOD text, are the midpoint of the analemma extrema.

Anthony.

[Ayiomamitis]

Let me get this straight. On a nice day, the base exposure is taken and captures both the sun and the foreground. Subsequent exposures are then meant only to capture the sun and add on to the base exposure? The gaps, I assume, are from periods of cloud cover.

Actually, I think the foreground image was made when the Sun wasn't in the frame at all. Looks as if it's with the Sun somewhat behind the camera. All the Sun images have the foreground so underexposed that essentially nothing is contributed.

Based on Anthony's comments in the past, I'm not even sure the foreground image was made at the same location as the analemma. Seems like a vulnerable location to leave a camera, or even a camera mount for a year.

Chris,

Thanks again for interjecting and setting things straight. Your recollection is right on!

Anthony.

[Ayiomamitis]

Alter-Ego,

I have been trying for many years to gain access to the archaeological grounds during the day and also during the evening for various projects I have had in mind and, regrettably, without the slightest hint of success. To this end, I must seek a compromise and where I will complete the analemma from home and introduce the foreground as accurately as possible in relation to azimuth and altitude using a follow-up independent exposure, thus yielding a digital composite comprised of two images (analemma itself on a single frame of film plus the foreground of interest).

Also, as noted by Chris in his reply, even if I were allowed to leave the equipment on the grounds for the pursuit of the analemma, the tourist traffic is so great that the camera would not only be tampered with (ie. its alignment accidently "adjusted" by wondering hands) during the twelve-month exercise but, in all likelihood, be stolen. We have a record year in 2013 with tourism so far and which will approach 20 million visitors by year-end. One serious reason for this tourist activity are the beloved archaeological grounds. Now, imagine a camera sitting on a stand for the pursuit of the analemma with serious tourist traffic day after day.

You write that the view is from the southwest which means that one would then be looking northeast. Since the sun rises as far north as around 57 degrees azimuth (for my geographic location), I am not sure where the problem lies. This particular analemma is for 9:00:00 UT+2 which would place it slightly further south in relation to azimuth.

If there was any possibility of pursuing this exercise and which took three years to complete from the actual grounds, I can assure you I would have done it so as to avoid the digital composite involving the two underlying photos.

Anthony.

[Guest]

I've been checking accu weather's sunrise/sunset section.
yesterday the 21st it showed the daylight as 12 hours and 11 minutes.
today it's two minutes shorter, but still not exactly 12 hours.
at this rate it will be exactly 12 hours in about 3 or 4 more days.
How come it's not exactly 12 hours on the equinox?

[wonderboy]

I've been checking accu weather's sunrise/sunset section.
yesterday the 21st it showed the daylight as 12 hours and 11 minutes.
today it's two minutes shorter, but still not exactly 12 hours.
at this rate it will be exactly 12 hours in about 3 or 4 more days.
How come it's not exactly 12 hours on the equinox?

"Earth dwellers will experience nearly 12 hours of daylight and 12 hours of darkness."


Nearly is the operative word.

That being said, did the recent mega quakes in indonesia, japan and haiti not knock the earth back a bazillionth of a second, could that not slow down the equinox timings slightly?

Paul

[Guest]

equi - nox -- Equal Night. it doesn't say approximately equal night. aproxaequinox might.
It says equal. eleven minutes is more than 1/6th of an hour. try holding your breath for eleven minutes if you think that's a short time.
Or try waiting at gun point by a mugger for eleven minutes waiting for the police to show up.
eleven minutes is a long time.
And
It will be an equal day and night about next Wednesday.
Why isn't that date the equinox?
Yesterday should be called something else.

[geckzilla]

I didn't think the camera would be left at the site but rather somehow accurately placed each time. I didn't even think to consider it could much more easily be kept untouched at home. Oops.

[neufer]

I've been checking accu weather's sunrise/sunset section.
yesterday the 21st it showed the daylight as 12 hours and 11 minutes.
today it's two minutes shorter, but still not exactly 12 hours.
at this rate it will be exactly 12 hours in about 3 or 4 more days.
How come it's not exactly 12 hours on the equinox?

12 hours and 11 minutes is from when:
the first edge of the Sun hits the Eastern horizon to when
the last edge of Sun hits the Western horizon.

The 12 hours is based on the center of the Sun.

Day ~ 12 hr. + [7.5 * sec(Lat)] min.
Night ~ 12 hr. - [7.5 * sec(Lat)] min.

[Cousin Ricky]

equi - nox -- Equal Night. it doesn't say approximately equal night. aproxaequinox might.
It says equal. eleven minutes is more than 1/6th of an hour. try holding your breath for eleven minutes if you think that's a short time.
Or try waiting at gun point by a mugger for eleven minutes waiting for the police to show up.
eleven minutes is a long time.

Mother Nature does not respect our etymologies.

And
It will be an equal day and night about next Wednesday.
Why isn't that date the equinox?

Because next Wednesday is not a useful epoch; plus, it only applies to your latitude. If you haven't already, check the link from the text "nearly 12 hours."

Yesterday should be called something else.

If you come up with a new name, good luck getting it to stick.

[rstevenson]

equi - nox -- Equal Night. it doesn't say approximately equal night. aproxaequinox might.
It says equal. ...
And
It will be an equal day and night about next Wednesday.
Why isn't that date the equinox?
Yesterday should be called something else.

No, yesterday is called the Equinox. The day you're talking about is sometimes called the Equilux, to differentiate it from the Equinox. The Equinox is defined not as the day when there is an equal amount of day and night, but as the day when the Sun passes directly over the equator. See this Wikipedia article for a more complete explanation.

Rob

[Chris Peterson]

I've been checking accu weather's sunrise/sunset section.
yesterday the 21st it showed the daylight as 12 hours and 11 minutes.
today it's two minutes shorter, but still not exactly 12 hours.
at this rate it will be exactly 12 hours in about 3 or 4 more days.
How come it's not exactly 12 hours on the equinox?

12 hours and 11 minutes is from when:
the first edge of the Sun hits the Eastern horizon to when
the last edge of Sun hits the Western horizon.

The 12 hours is based on the center of the Sun.

That is one point.

But optically, days are always longer than they are geometrically because of atmospheric refraction. We see the Sun on the horizon while it is still geometrically below it, due to bending of light through the atmosphere. This effect is also responsible for a slight distortion (in fact, an uncertainty) in sunrise and sunset times.

[bkinmonth]

I'd heard the bit about leading/trailing edges and refraction before, and it made sense so I never really stopped to do the math. But now, according to the "nearly 12 hours" link, it says the total for refraction and "semidiameter" (what ever happened to "radius"? ) is 50 arc minutes. By my calculation it takes 3 1/3 minutes of time for the earth to turn 50 arc minutes. So that would seem to account for 6 2/3 minutes, which is not 11 minutes. What am I missing?

[Joe Stieber]

My dear friend Bubbles made this analemma that tracks the Sun through the tropical zodiac (e.g. the September equinox is the beginning of Libra).

The sun's position at today's equinox (Sept 22, 2013) is in Virgo, about 38 degrees west of the modern Libra border. It looks like your friend is using an astrological position of the sun that doesn't consider precession.

[Chris Peterson]

I'd heard the bit about leading/trailing edges and refraction before, and it made sense so I never really stopped to do the math. But now, according to the "nearly 12 hours" link, it says the total for refraction and "semidiameter" (what ever happened to "radius"? :ssmile: ) is 50 arc minutes. By my calculation it takes 3 1/3 minutes of time for the earth to turn 50 arc minutes. So that would seem to account for 6 2/3 minutes, which is not 11 minutes. What am I missing?

You are failing to account for latitude. At the equator, the Sun rises and falls perpendicular to the horizon on the equinoxes, which means that you can trivially relate the apparent angular speed of the Sun with the rotation rate of the Earth. As you move to higher latitudes, the angle of the rising and setting sun becomes shallower. At high latitudes, the day is longer than the night by a greater amount than at the equator.

[JohnD]

Please, juts go back and count the number of annalemmas (annalemmae?) that have been APODS.
Too many.
I realise that that you can only use pics that are submitted, or that you can find on the 'net and get permission to use, but annalemmas are really rather boring.

JOhn

[Beyond]

Please, juts go back and count the number of annalemmas (annalemmae?) that have been APODS.
Too many.
I realise that that you can only use pics that are submitted, or that you can find on the 'net and get permission to use, but annalemmas are really rather boring.

JOhn

That's because they are their own infinity loop. They just keep going around and around and around and around and around and around and around and around and around and around and around........

[geckzilla]

Please, juts go back and count the number of annalemmas (annalemmae?) that have been APODS.
Too many.

The discussion within this thread indicates otherwise.