APOD: Three Sun Paths (2023 Jun 21)

[APOD Robot]

Three Sun Paths

Explanation: Does the Sun follow the same path every day? No. The Sun's path changes during the year, tracing a longer route during the summer than the winter. Pictured here, the Sun's arc was captured from noon to sunset on three days, from highest in the sky to lowest: summer solstice, equinox, and winter solstice. The images were taken near Gatto Corvino Village in Sicily, Italy in 2020 and 2021. The path and time the Sun spends in the sky is more important in determining the season than how close the Earth is to the Sun. In fact, the Earth is closest to the Sun in January, during northern winter. Today is a solstice, so today the Sun is taking its longest path of the year across the sky in Earth's northern hemisphere, but the shortest path in the southern hemisphere.

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[MarkBour]

Lovely plots!

If the dots are accurate, and I assume they are, then they're a bit of a surprise to me.
I thought the path would always look like a part of an ellipse, but the shapes are a bit different than that.
Note how the path on the summer solstice, especially, seems to get nearly linear near the horizon.
***
Ah, I guess it's really hard to determine exactly what to expect here, since I think the overall shot is partially panoramic, so it will warp things so they can be seen nicely in a flat image.

[Ann]

Lovely plots!

If the dots are accurate, and I assume they are, then they're a bit of a surprise to me.
I thought the path would always look like a part of an ellipse, but the shapes are a bit different than that.
Note how the path on the summer solstice, especially, seems to get nearly linear near the horizon.
***
Ah, I guess it's really hard to determine exactly what to expect here, since I think the overall shot is partially panoramic, so it will warp things so they can be seen nicely in a flat image.

This is the analemma, the apparent path of the Sun across the sky over the year. Image: J.C. Casado.

---

Ann

[Cousin Ricky]

If the dots are accurate, and I assume they are, then they're a bit of a surprise to me.
I thought the path would always look like a part of an ellipse, but the shapes are a bit different than that.
Note how the path on the summer solstice, especially, seems to get nearly linear near the horizon.
***
Ah, I guess it's really hard to determine exactly what to expect here, since I think the overall shot is partially panoramic, so it will warp things so they can be seen nicely in a flat image.

I’m pretty sure it’s the camera lens, as mapping a 3-D world onto a 2-D image always involves distortion, and the wider the field of view, the more the distortion. It’s the same principle as mapping a round Earth onto a flat map.

You can see similar distortions of constellations in many nighttime wide angle photos on APOD.

[jisles]

Depends on the observer's latitude. On the equator the Sun's daily path across the sky is longer at the equinoxes than at the solstices. That's because it traces half a great circle at the equinox and half a small circle at the solstice.

John

[Chris Peterson]

Depends on the observer's latitude. On the equator the Sun's daily path across the sky is longer at the equinoxes than at the solstices. That's because it traces half a great circle at the equinox and half a small circle at the solstice.

The ecliptic always defines a great circle. I don't see how the latitude of the observer can change that.

[JWP456]

It's worth noting that the appearance of the "arc" of the sun's path plotted on a photograph on a given day at a given location depends on the angle of elevation of the camera axis (a line perpendicular to the focal plane through the center of the lens). So for example if at the location of the photo in today's APOD on an equinox the camera axis rather than being level was raised 53 degrees (the complement of the latitude at that location), and the camera was rotated slightly in the E-W direction to account for the change in declination over the course of a day (about 12 minutes), the "arc" of the sun's path would be a straight line, and the horizon in the photo, by contrast, would appear as an arc.

[JWP456]

Depends on the observer's latitude. On the equator the Sun's daily path across the sky is longer at the equinoxes than at the solstices. That's because it traces half a great circle at the equinox and half a small circle at the solstice.

The ecliptic always defines a great circle. I don't see how the latitude of the observer can change that.

If one thinks of the path along which the sun is directly overhead on the summer solstice in the northern hemisphere, for example, that would be a circle of nearly equal latitude, i.e. a small circle, so I think if one is referring to the apparent motion of the sun over the course of a day it is not incorrect to describe it's path as following a small circle (+ or- the change in declination during the day) when it's declination is greater or less than zero.

[Chris Peterson]

Depends on the observer's latitude. On the equator the Sun's daily path across the sky is longer at the equinoxes than at the solstices. That's because it traces half a great circle at the equinox and half a small circle at the solstice.

The ecliptic always defines a great circle. I don't see how the latitude of the observer can change that.

If one thinks of the path along which the sun is directly overhead on the summer solstice in the northern hemisphere, for example, that would be a circle of nearly equal latitude, i.e. a small circle, so I think if one is referring to the apparent motion of the sun over the course of a day it is not incorrect to describe it's path as following a small circle (+ or- the change in declination during the day) when it's declination is greater or less than zero.

I don't see that. We're always at the center of a (nearly) circular path, and all that changes is the tilt with respect to the horizon.

[JWP456]

The ecliptic always defines a great circle. I don't see how the latitude of the observer can change that.

If one thinks of the path along which the sun is directly overhead on the summer solstice in the northern hemisphere, for example, that would be a circle of nearly equal latitude, i.e. a small circle, so I think if one is referring to the apparent motion of the sun over the course of a day it is not incorrect to describe it's path as following a small circle (+ or- the change in declination during the day) when it's declination is greater or less than zero.

I don't see that. We're always at the center of a (nearly) circular path, and all that changes is the tilt with respect to the horizon.

I just commented because I thought jisles was talking about the apparent motion of the sun, which can be described as a function of the latitude of the place of observation and declination of the sun (and change in declination over some given time period). If one sets up an instrument such as a solar transit to follow this path (assuming the declination to not be equal to zero), the traced path or apparent motion of the sun would be a small circle if I'm not mistaken, i.e. follow a path between sunrise and sunset parallel to the earth's equator (+ or - the change in declination) rather than a great circle. Obviously I don't dispute that the trace of the plane of the ecliptic on the earth's surface is a great circle (if I'm stating that correctly), I just thought jisles was referring to apparent motion, and you and he are talking about different things.

[Chris Peterson]

If one thinks of the path along which the sun is directly overhead on the summer solstice in the northern hemisphere, for example, that would be a circle of nearly equal latitude, i.e. a small circle, so I think if one is referring to the apparent motion of the sun over the course of a day it is not incorrect to describe it's path as following a small circle (+ or- the change in declination during the day) when it's declination is greater or less than zero.

I don't see that. We're always at the center of a (nearly) circular path, and all that changes is the tilt with respect to the horizon.

I just commented because I thought jisles was talking about the apparent motion of the sun, which can be described as a function of the latitude of the place of observation and declination of the sun (and change in declination over some given time period). If one sets up an instrument such as a solar transit to follow this path (assuming the declination to not be equal to zero), the traced path or apparent motion of the sun would be a small circle if I'm not mistaken, i.e. follow a path between sunrise and sunset parallel to the earth's equator (+ or - the change in declination) rather than a great circle. Obviously I don't dispute that the trace of the plane of the ecliptic on the earth's surface is a great circle (if I'm stating that correctly), I just thought jisles was referring to apparent motion, and you and he are talking about different things.

Maybe. I simply don't understand how the concept of a small circle fits into this.

[orin stepanek]

Summer solstice at Stonehenge

Solstice Sun at Lulworth Cove; impressive photo! JMO!

Kitty surprised about solstice!

[Guest]

The APOD was about the Sun's daily path across the sky due to the Earth's daily rotation. (Not about the Earth's annual orbit about the Sun.) If the visible daily path wasn't partly cut off by the Earth's own body, it would be a great circle if the Sun were on the equator (at an equinox) and a small circle at other times. But the visible path is indeed interrupted by the Earth's own body, the amount of the obstruction varying with the latitude. At the Earth's equator with a sea horizon we can see a longer path at the equinox than at other times. That was my point.

John

[Guest]

I don't see that. We're always at the center of a (nearly) circular path, and all that changes is the tilt with respect to the horizon.

I just commented because I thought jisles was talking about the apparent motion of the sun, which can be described as a function of the latitude of the place of observation and declination of the sun (and change in declination over some given time period). If one sets up an instrument such as a solar transit to follow this path (assuming the declination to not be equal to zero), the traced path or apparent motion of the sun would be a small circle if I'm not mistaken, i.e. follow a path between sunrise and sunset parallel to the earth's equator (+ or - the change in declination) rather than a great circle. Obviously I don't dispute that the trace of the plane of the ecliptic on the earth's surface is a great circle (if I'm stating that correctly), I just thought jisles was referring to apparent motion, and you and he are talking about different things.

Maybe. I simply don't understand how the concept of a small circle fits into this.

Well, jisles said:
"Depends on the observer's latitude. On the equator the Sun's daily path across the sky is longer at the equinoxes than at the solstices. That's because it traces half a great circle at the equinox and half a small circle at the solstice", and you responded:
"The ecliptic always defines a great circle. I don't see how the latitude of the observer can change that."
And while I don't disagree with your statement, and think jisles is oversimplifying, I think it is correct to say that the trace of the sun's path (the subject of today's APOD post), as seen by an observer from almost any place where the sun was visible at most times of the year, is not a great circle with the center of the earth it's center, but closely approximates the path of a star of the same declination as the sun at the time (except, of course, that the sun's declination is continually changing). So I think if one is talking about the apparent motion of the sun over the course of a day as observed from some point on the earth (which, again, is the subject of the post), it is not incorrect to describe it as usually approximating a small circle.

[alter-ego]

I don't see that. We're always at the center of a (nearly) circular path, and all that changes is the tilt with respect to the horizon.

I just commented because I thought jisles was talking about the apparent motion of the sun, which can be described as a function of the latitude of the place of observation and declination of the sun (and change in declination over some given time period). If one sets up an instrument such as a solar transit to follow this path (assuming the declination to not be equal to zero), the traced path or apparent motion of the sun would be a small circle if I'm not mistaken, i.e. follow a path between sunrise and sunset parallel to the earth's equator (+ or - the change in declination) rather than a great circle. Obviously I don't dispute that the trace of the plane of the ecliptic on the earth's surface is a great circle (if I'm stating that correctly), I just thought jisles was referring to apparent motion, and you and he are talking about different things.

Maybe. I simply don't understand how the concept of a small circle fits into this.

I'll try to simplify: Since the Sun's declination is essentially constant over the ~7½ hours of imagery, the Sun's declination circle is not a great circle when the horizon is flat (a great circle).
The simulated Stellarium APOD view below uses a stereographic projection (my favorite for visual representations) which shows the Sun due south intersecting the meridian and ecliptic. Here I also displayed the equatorial grid. The horizon, ecliptic and meridian are the visible great circles. The red dashed curve nominally traces the Sun's position /declination through the day. This path is not a great circle.
 

 
Regarding the APOD, projection and camera orientation are key drivers to apparent paths the Sun could take. In the next view, I plotted the Alt and Az in a linear X/Y plot (flat horizon) (green curve). I aligned the beginning and ending Sun positions to be reasonably overlapped with the APOD sun positions. It's clear this X/Y plot tracks the actual APOD solstice path very well indicating a rectangular horizontal coordinate grid with little distortion.
 

 
Below is the Stellarium stereographic projection of the solstice-Sun path against the (distorted) az/alt grid. Its shape is more what I'd expect instead of a flat-top hill. As said earlier, this curve is not a great circle. Same as before, I reasonably overlapped the beginning and ending X/Y Sun positions. The curves aren't even close. For this wide-field composite image, the horizontal coordinate grid shows significant distortion from the linear X/Y grid.
 

 
Edit: Labled two plots for readability.
 

[Chris Peterson]

I just commented because I thought jisles was talking about the apparent motion of the sun, which can be described as a function of the latitude of the place of observation and declination of the sun (and change in declination over some given time period). If one sets up an instrument such as a solar transit to follow this path (assuming the declination to not be equal to zero), the traced path or apparent motion of the sun would be a small circle if I'm not mistaken, i.e. follow a path between sunrise and sunset parallel to the earth's equator (+ or - the change in declination) rather than a great circle. Obviously I don't dispute that the trace of the plane of the ecliptic on the earth's surface is a great circle (if I'm stating that correctly), I just thought jisles was referring to apparent motion, and you and he are talking about different things.

Maybe. I simply don't understand how the concept of a small circle fits into this.

I'll try to simplify: Since the Sun's declination is essentially constant over the ~7½ hours of imagery, the Sun's declination circle is not a great circle when the horizon is flat (a great circle).
The simulated Stellarium APOD view below uses a stereographic projection (my favorite for visual representations) which shows the Sun due south intersecting the meridian and ecliptic. Here I also displayed the equatorial grid. The horizon, ecliptic and meridian are the visible great circles. The red dashed curve nominally traces the Sun's position /declination through the day. This path is not a great circle.
 
Solstice Sun - Equatorial Grid, Ecliptic and Solar Path.jpg
 
Regarding the APOD, projection and camera orientation are key drivers to apparent paths the Sun could take. In the next view, I plotted the Alt and Az in a linear X/Y plot (flat horizon) (green curve). I aligned the beginning and ending Sun positions to be reasonably overlapped with the APOD sun positions. It's clear this X/Y plot tracks the actual APOD solstice path very well indicating a rectangular horizontal coordinate grid with little distortion.
 
APOD & Linear X-Y Plot of Solstice Sun Positions.jpg
 
Below is the Stellarium stereographic projection of the solstice-Sun path against the (distorted) az/alt grid. Its shape is more what I'd expect instead of a flat-top hill. As said earlier, this curve is not a great circle. Same as before, I reasonably overlapped the beginning and ending X/Y Sun positions. The curves aren't even close. For this wide-field composite image, the horizontal coordinate grid shows significant distortion from the linear X/Y grid.
 
Stellarium Simulation & Same Stretched X-Y Plot of Solstice Sun Positions.jpg
 
Edit: Labled two plots for readability.
 

I would argue that neither the concept of a great circle or a small circle, which are elements of solid trig, make any sense in the contexts of projections.

[MarkBour]

...
I'll try to simplify: Since the Sun's declination is essentially constant over the ~7½ hours of imagery, the Sun's declination circle is not a great circle when the horizon is flat (a great circle).
The simulated Stellarium APOD view below uses a stereographic projection (my favorite for visual representations) which shows the Sun due south intersecting the meridian and ecliptic. Here I also displayed the equatorial grid. The horizon, ecliptic and meridian are the visible great circles. The red dashed curve nominally traces the Sun's position /declination through the day. This path is not a great circle.
 
Solstice Sun - Equatorial Grid, Ecliptic and Solar Path.jpg
 
Regarding the APOD, projection and camera orientation are key drivers to apparent paths the Sun could take. In the next view, I plotted the Alt and Az in a linear X/Y plot (flat horizon) (green curve). I aligned the beginning and ending Sun positions to be reasonably overlapped with the APOD sun positions. It's clear this X/Y plot tracks the actual APOD solstice path very well indicating a rectangular horizontal coordinate grid with little distortion.
 
APOD & Linear X-Y Plot of Solstice Sun Positions.jpg

Below is the Stellarium stereographic projection of the solstice-Sun path against the (distorted) az/alt grid. Its shape is more what I'd expect instead of a flat-top hill. As said earlier, this curve is not a great circle. Same as before, I reasonably overlapped the beginning and ending X/Y Sun positions. The curves aren't even close. For this wide-field composite image, the horizontal coordinate grid shows significant distortion from the linear X/Y grid.
 
Stellarium Simulation & Same Stretched X-Y Plot of Solstice Sun Positions.jpg
 
Edit: Labled two plots for readability.

Well, I felt a little guilty that my basic surprise at the shape of the paths kicked off such a discussion. But now I'm happy that alter-ego could account for it and explain it! I'm not saying I fully understand the explanation, yet.

I like the last photo of the three, it shows that a Stellarium simulation with stereographic projection gives the shape I had expected. Apparently alter-ego had the same expectation. Then, knowing that some sort of distortion was at play -- there always has to be some distortion to map surroundings onto a flat image -- I just left it there, not knowing anything else to do with it.

So, the path in the APOD, as alter-ego showed, matches showing the Sun's path in "a linear X/Y plot", with a "rectangular horizontal coordinate grid with little distortion". Is that what one gets if one takes a series of shots, rotating as the Sun moves across the sky, and then simply stitches them together into a panoramic image? That's kind of what it sounds like.

I also like the description that the path came out looking kind of like a "flat-top hill" that alter-ego used.