APOD: Analemma over Taipei (2022 Jun 21)

[APOD Robot]

Analemma over Taipei

Explanation: Does the Sun return to the same spot on the sky every day? No. A better and more visual answer to that question is an analemma, a composite of images taken at the same time and from the same place over the course of a year. The featured analemma was compiled at 4:30 pm many afternoons from Taiwan during 2021, with the city skyline of Taipei in the foreground, including tall Taipei 101. The Sun's location in December -- at the December solstice -- is shown on the far left, while its location at the June solstice is captured on the far right. Also shown are the positions of the Sun throughout the rest of the day on the solstices and equinoxes. Today is the June solstice of 2022, the day in Earth's northern hemisphere when the Sun spends the longest time in the sky. In many countries, today marks the official beginning of a new season, for example winter in Earth's southern hemisphere.

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[RocketRon]

Strictly speaking, winter officially begins on the 1st June in many southern hemisphere countries.
And usually feels it.
Good falls of snow on the ski fields in Australia already, winter has been underway for a good 3 weeks.
hth.

[RocketRon]

Great photo btw.

Analemmas must be one of astronomy's most intriguing aspects = the equation of time.

[rj rl]

I'm a bit confused as to why the two equinox lines don't conincide. Shouldn't they?

[RocketRon]

Possibly not at exactly the same time of day.

The 2 lines do cross though - so that time could be calculated/observed.

[RocketRon]

And the analemma has a 'long end' and a 'short end.'

During summer, that hemisphere has more daylight hours, accounting for the long end.
If observed from the other hemisphere, the analemma would be a mirror image
So, on average, they would coincide - sorta.

[Dan]

The reason it is not a perfect "8" is because the Earth's orbit is not 100% circular. It is an "ellipse".

When farther away from the sun (by a few million kms), the Earth moves just that much slower, hence the spacing is stretched out. Consequently, during northern winter months, the Earth moves just that much faster.

The best tans come from down below.

[Sa Ji Tario]

Strictly speaking, winter officially begins on the 1st June in many southern hemisphere countries.
And usually feels it.
Good falls of snow on the ski fields in Australia already, winter has been underway for a good 3 weeks.
hth.

What is observed is the climatic winter, the astronomical winter began today at 09:13 UTC, the moment of culmination of the solstice with the longest night in the southern hemisphere and the longest day in the northern hemisphere

[pferkul]

I'm a bit confused as to why the two equinox lines don't coincide. Shouldn't they?

I had the same question. I could imagine some slight misalignment, but they're not close at all.

[alter-ego]

I'm a bit confused as to why the two equinox lines don't coincide. Shouldn't they?

I had the same question. I could imagine some slight misalignment, but they're not close at all.

No, the equinox points do not coincide. Earth's orbital eccentricity creates the asymmetric figure 8 as pointed up earlier. For a perfectly circular orbit (eccentricity = 0), the equinox points would coincide at the center of the figure 8 (intersection point).

[alter-ego]

I'm a bit confused as to why the two equinox lines don't coincide. Shouldn't they?

I had the same question. I could imagine some slight misalignment, but they're not close at all.

No, the equinox points do not coincide. Earth's orbital eccentricity creates the asymmetric figure 8 as pointed up earlier. For a perfectly circular orbit (eccentricity = 0), the equinox points would coincide at the center of the figure 8 (intersection point).

Oh, I'm not sure if I'm answering your specific question.
My previous statement is technically correct, but I was only considering the endpoints. The APOD image does have a more obvious problem which you may have been asking about - the sun tracks are not overlapped. Assuming the remaining two sun tracks are for both equinoxes then ignoring the exact timing differences between the actual equinoxes and the image acquisitions, the equinox sun tracks will follow the same declination = 0°. Therefore, the tracks will overlap, but won't have the same endpoints, i.e. the same DEC, but different RA. In the APOD, certainly the track overlap error much too large.
As seen in an analemma viewed due south, the equinox suns intersect the analemma very near symmetrically (east/west), at least much more so than in the APOD. Looks like the southernmost equinox track is closer to correct, so the northern track is way off. As you can see, even when the equinox sun tracks are overlapped, track endpoints aren't the same.
 

[pferkul]

I had the same question. I could imagine some slight misalignment, but they're not close at all.

No, the equinox points do not coincide. Earth's orbital eccentricity creates the asymmetric figure 8 as pointed up earlier. For a perfectly circular orbit (eccentricity = 0), the equinox points would coincide at the center of the figure 8 (intersection point).

Oh, I'm not sure if I'm answering your specific question.
My previous statement is technically correct, but I was only considering the endpoints. The APOD image does have a more obvious problem which you may have been asking about - the sun tracks are not overlapped. Assuming the remaining two sun tracks are for both equinoxes then ignoring the exact timing differences between the actual equinoxes and the image acquisitions, the equinox sun tracks will follow the same declination = 0°. Therefore, the tracks will overlap, but won't have the same endpoints, i.e. the same DEC, but different RA. In the APOD, certainly the track overlap error much too large.
As seen in an analemma viewed due south, the equinox suns intersect the analemma very near symmetrically (east/west), at least much more so than in the APOD. Looks like the southernmost equinox track is closer to correct, so the northern track is way off. As you can see, even when the equinox sun tracks are overlapped, track endpoints aren't the same.
 
Equinox Points on Analemma.jpg

Thanks. Since the sun tracks of the image do not overlap, are you saying the problem is that the wrong sun tracks were depicted?

To ask the question another way: From a fixed vantage point, will the sun set at the same point on the horizon on Mar. 21 and Sep 21? If I were designing a Mayan temple 1000 years ago and wanted the sun at sunset to shine down a secret corridor at the equinox, would it work on both equinoxes?

[johnnydeep]

The analemma always confuses the hell out of me, and I suspect it always will. The above discussion didn't help me much either [ EDIT: I mean, rationally, I know how it's constructed, but why exactly it looks like a figure eight is my mental block. ]

[gwrede]

Congratulations, APOD!

This is one of the most educating APOD pictures of the last couple of years!

Kudos also to the photographer, who so brilliantly and painstakingly showcased us subtleties about solstices most of us have never realized!

Excellent work, all!

[johnnydeep]

Congratulations, APOD!

This is one of the most educating APOD pictures of the last couple of years!

Kudos also to the photographer, who so brilliantly and painstakingly showcased us subtleties about solstices most of us have never realized!

Excellent work, all!

Did you also see the similar linked-to APOD in the description - https://apod.nasa.gov/apod/ap190621.html ? It's even nicer looking IMHO. Whether it's more instructive or not is not for me to appreciate.

[Meiying Lee]

Watching the sun appear one by one on the correct figure 8 is really exciting!
[youtube]https://youtu.be/59MW1aqO7L4[/youtube]

[Meiying Lee]

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.

[RocketRon]

What is observed is the climatic winter, the astronomical winter began today at 09:13 UTC, the moment of culmination of the solstice with the longest night in the southern hemisphere and the longest day in the northern hemisphere

The longest night in 2022 in the sthn hemisphere was on June 15th.

This is because of that equation of time.
The sun flits about all over the place at the ends of that analemma

[orin stepanek]

On the first photo; Lee actualy has the Sun's photo! nICE!

[alter-ego]

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.

Very nice follow up, and yes! a beautiful capture of the analemmas over Taipei!!
What you describe now makes sense if your wording is as I read it.

The APOD description says the 4 days of sun tracks were the solstices and equinoxes. Your description simply states you took the track images on four days of spring, summer, autumn and winter - not claiming any were taken at the solstices or equinoxes. Is this true?
I'm clarifying because the only aspect that appears off was the APOD claim that the sunset tracks were made on both equinoxes because the sun does not deviate from 0° declination in less than a day. This contradicts the large separation error between both the spring and autumn sun tracks and the tracks end positions. You description, however, does not conflict with the image.

Yes, and equinoxes will not occur at the intersection point in the figure 8, but the space tracks will overlap on the equinoxes. Endpoint sun positions will be separated by ~16 minutes of time, → 15min÷60min x15° = 4°, whereas the separations of the endpoints in your posted image ≈ 6.5°.

I certainly think your description is right, and you were not attempting to image the sunset tracks on the equinoxes.
Thanks again for a new view of the analemma. The link JohnnyDeep posted above is more instructive with all the annotations, but beauty is in the eye of the beholder right?

[Meiying Lee]

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.

Very nice follow up, and yes! a beautiful capture of the analemmas over Taipei!!
What you describe now makes sense if your wording is as I read it.

The APOD description says the 4 days of sun tracks were the solstices and equinoxes. Your description simply states you took the track images on four days of spring, summer, autumn and winter - not claiming any were taken at the solstices or equinoxes. Is this true?
I'm clarifying because the only aspect that appears off was the APOD claim that the sunset tracks were made on both equinoxes because the sun does not deviate from 0° declination in less than a day. This contradicts the large separation error between both the spring and autumn sun tracks and the tracks end positions. You description, however, does not conflict with the image.

Yes, and equinoxes will not occur at the intersection point in the figure 8, but the space tracks will overlap on the equinoxes. Endpoint sun positions will be separated by ~16 minutes of time, → 15min÷60min x15° = 4°, whereas the separations of the endpoints in your posted image ≈ 6.5°.

I certainly think your description is right, and you were not attempting to image the sunset tracks on the equinoxes.
Thanks again for a new view of the analemma. The link JohnnyDeep posted above is more instructive with all the annotations, but beauty is in the eye of the beholder right?

Yes, because of the weather in Taipei, there is no way to shoot the sunset trajectory smoothly on the spring equinox, autumn equinox, summer solstice or winter solstice. This photo marks the dates of the various suns.

[alter-ego]

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.

Very nice follow up, and yes! a beautiful capture of the analemmas over Taipei!!
What you describe now makes sense if your wording is as I read it.

The APOD description says the 4 days of sun tracks were the solstices and equinoxes. Your description simply states you took the track images on four days of spring, summer, autumn and winter - not claiming any were taken at the solstices or equinoxes. Is this true?
I'm clarifying because the only aspect that appears off was the APOD claim that the sunset tracks were made on both equinoxes because the sun does not deviate from 0° declination in less than a day. This contradicts the large separation error between both the spring and autumn sun tracks and the tracks end positions. You description, however, does not conflict with the image.

Yes, and equinoxes will not occur at the intersection point in the figure 8, but the space tracks will overlap on the equinoxes. Endpoint sun positions will be separated by ~16 minutes of time, → 15min÷60min x15° = 4°, whereas the separations of the endpoints in your posted image ≈ 6.5°.

I certainly think your description is right, and you were not attempting to image the sunset tracks on the equinoxes.
Thanks again for a new view of the analemma. The link JohnnyDeep posted above is more instructive with all the annotations, but beauty is in the eye of the beholder right?

Yes, because of the weather in Taipei, there is no way to shoot the sunset trajectory smoothly on the spring equinox, autumn equinox, summer solstice or winter solstice. This photo marks the dates of the various suns.
1630-3ab.png

Very, very nice
Those of us that like data, mixed in with new, artful, sunset and sunrise analemma composites, this should really like this. I certainly do!
Great job Meiying!
Thank you very much for sharing the annotated image!!

[Meiying Lee]

Very nice follow up, and yes! a beautiful capture of the analemmas over Taipei!!
What you describe now makes sense if your wording is as I read it.

The APOD description says the 4 days of sun tracks were the solstices and equinoxes. Your description simply states you took the track images on four days of spring, summer, autumn and winter - not claiming any were taken at the solstices or equinoxes. Is this true?
I'm clarifying because the only aspect that appears off was the APOD claim that the sunset tracks were made on both equinoxes because the sun does not deviate from 0° declination in less than a day. This contradicts the large separation error between both the spring and autumn sun tracks and the tracks end positions. You description, however, does not conflict with the image.

Yes, and equinoxes will not occur at the intersection point in the figure 8, but the space tracks will overlap on the equinoxes. Endpoint sun positions will be separated by ~16 minutes of time, → 15min÷60min x15° = 4°, whereas the separations of the endpoints in your posted image ≈ 6.5°.

I certainly think your description is right, and you were not attempting to image the sunset tracks on the equinoxes.
Thanks again for a new view of the analemma. The link JohnnyDeep posted above is more instructive with all the annotations, but beauty is in the eye of the beholder right?

Yes, because of the weather in Taipei, there is no way to shoot the sunset trajectory smoothly on the spring equinox, autumn equinox, summer solstice or winter solstice. This photo marks the dates of the various suns.
1630-3ab.png

Very, very nice
Those of us that like data, mixed in with new, artful, sunset and sunrise analemma composites, this should really like this. I certainly do!
Great job Meiying!
Thank you very much for sharing the annotated image!!

Many thanks! This is a video of the sun appearing in sequence, also dated.

Click to play embedded YouTube video.

[rj rl]

I had the same question. I could imagine some slight misalignment, but they're not close at all.

No, the equinox points do not coincide. Earth's orbital eccentricity creates the asymmetric figure 8 as pointed up earlier. For a perfectly circular orbit (eccentricity = 0), the equinox points would coincide at the center of the figure 8 (intersection point).

Oh, I'm not sure if I'm answering your specific question.
My previous statement is technically correct, but I was only considering the endpoints. The APOD image does have a more obvious problem which you may have been asking about - the sun tracks are not overlapped. Assuming the remaining two sun tracks are for both equinoxes then ignoring the exact timing differences between the actual equinoxes and the image acquisitions, the equinox sun tracks will follow the same declination = 0°. Therefore, the tracks will overlap, but won't have the same endpoints, i.e. the same DEC, but different RA. In the APOD, certainly the track overlap error much too large.
As seen in an analemma viewed due south, the equinox suns intersect the analemma very near symmetrically (east/west), at least much more so than in the APOD. Looks like the southernmost equinox track is closer to correct, so the northern track is way off. As you can see, even when the equinox sun tracks are overlapped, track endpoints aren't the same.
 
Equinox Points on Analemma.jpg

yep, this is what I was wondering about! Your post and Meiying's explanations made it clear.

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.
合併1ab.png

beautiful photos, congratulations on your work being selected for an APOD!

[Meiying Lee]

No, the equinox points do not coincide. Earth's orbital eccentricity creates the asymmetric figure 8 as pointed up earlier. For a perfectly circular orbit (eccentricity = 0), the equinox points would coincide at the center of the figure 8 (intersection point).

Oh, I'm not sure if I'm answering your specific question.
My previous statement is technically correct, but I was only considering the endpoints. The APOD image does have a more obvious problem which you may have been asking about - the sun tracks are not overlapped. Assuming the remaining two sun tracks are for both equinoxes then ignoring the exact timing differences between the actual equinoxes and the image acquisitions, the equinox sun tracks will follow the same declination = 0°. Therefore, the tracks will overlap, but won't have the same endpoints, i.e. the same DEC, but different RA. In the APOD, certainly the track overlap error much too large.
As seen in an analemma viewed due south, the equinox suns intersect the analemma very near symmetrically (east/west), at least much more so than in the APOD. Looks like the southernmost equinox track is closer to correct, so the northern track is way off. As you can see, even when the equinox sun tracks are overlapped, track endpoints aren't the same.
 
Equinox Points on Analemma.jpg

yep, this is what I was wondering about! Your post and Meiying's explanations made it clear.

In 2021, I spent a whole year in Taipei recording the position of the sun at 7:30 am and 4:30 pm. In the northern hemisphere, the summer solstice of the sun analemma in the morning is at upper left, and the winter solstice at lower right. As for the sun analemma in the afternoon, the tilt direction is different from that in the morning. The summer solstice is at upper right, and the winter solstice at lower left. Whether it is in the morning or in the afternoon, sun analemma has a small circle above and a large circle below. It is also worth noting that the intersection of the figure-8 did not form at vernal equinox or at autumnal equinox. In addition, I recorded four days of sunrise and sunset tracks respectively in spring, summer, autumn and winter, and combined them with sun analemma. The degree of inclination of sunrise or sunset can be used to determine the latitude of the shooting location.
合併1ab.png

beautiful photos, congratulations on your work being selected for an APOD!

Thank you very much! I am really happy that the sky in Taipei can be on APOD.