Why Does the Sun Rise and Set In a Straight Line?

[jumboseafood]

In this video: https://www.youtube.com/watch?v=j1-6d5-V3f4

They claim on a round earth the sun should make an arc in the sky. Here are the diagrams used to explain this.

But instead he shows the sun setting and rising in the straight lines


What mistakes is he making here?

 

[Mick West]

The "sun path" (the line that the sun travels across the sky from sunrise to sunset) is essentially the same as a "star path", or a moon path, or a planet path. While the relative positions of things vary a little from day to day, you can essentially think of everything being fixed to the "celestial sphere" which is a way of visualizing the stars and planets as being painted on the inside of a far-away sphere that the Earth is in the center of.

Do the stars move in straight lines? Well, we can check this out using time-lapse photos. A lot of the time people will take photos of the celestial poles (North or South, depending on where they live) so you get photo like this.

(Source)

Notice even here, looking north, as you move closer to the west (the left of the photo, where the stars are setting) the path seems to straighten out.

If we look more towards the west (where the sun sets), we see the star trails appear to be setting in straight lines.

This photo (source) is in the southern hemisphere, so the "center" of the rotation is the southern celestial pole.

The paths here are all EXACTLY as predicted by the standard model of the solar system. Unfortunately, it can be hard to understand unless you put a little effort into it.

 

[Mick West]

Perhaps a useful way of looking at this is this 360° video:
Source: https://www.youtube.com/watch?v=SGuTOfCTs98


If it's working correctly you should be able to move the view around. Pause it at around 30 seconds in and move the view around. You can see the circular paths around the poles (the south pole being below the horizon) and the increasing straighter paths as you get closer to east-west. The east-west path is the one the sun takes.

 

[Mick West]

Another one, this does not shows the trails, but it's a 360° view including a sunset and sunrise, so you can see the path of the sun is the same as the East-West stars. Watch if full-screen for the best effect, and try finding the sunset and sunrise and watching the path the sun takes, and the path the stars take, and compare with the stars that are more of the north or south.
Source: https://www.youtube.com/watch?v=NvTs-FANx1Y

 

[Mick West]

And while the sun's settin path may LOOK straight, it rarely is perfectly straight. The only time that happens is when the axis of the earth is tilted at right angles the sun - i.e. at the equinoxes. The the sun rises directly in the east, and sets directly in the west. It's still going in a circle, but, like the east-west stars, you are looking at it's circle edge-on. A multiple exposure taken in the middle of summer (or winter) will actually show the slight curve expected.
https://physics.weber.edu/schroeder/ua/SunAndSeasons.html

Multiple-exposure photo of the setting sun, showing that it follows the same diagonal path that a star would, as seen from a mid-northern latitude. This photo was made on June 21, when the sun set considerably north of due west.

Content from external source

 

[Mick West]

With considerble effort, you can capture the path of the sun through the year using a technique called "Solargraphy" using a pinhole camera to take a VERY long exposure (6-12 months) which gives the sun's path every day (except for gaps due to clouds) on a single exposure photograph. These often use a cylinder to capture the image, giving a panorama style image which creates a curve.

However some appear to use a conventional box pinhole camera, allowing you to see the actual paths as they would appear with a rectilinear camera. Like these:
https://stevenduncanart.com/portfolio-item/adelaide-solargraphy/

 

[Mendel]

What mistakes is he making here?

The main mistake is not realizing when you just disproved your own cosmology. ;-P
On Flat Earth, the sun is said to move in a circle parallel to the surface, so it should appear to slow down as it is setting, and its path should curve sideways toward the north. I have filmed car lights from a motorway bridge to demonstrate the effect. The fact that the sun does not do that means Earth is not flat.

You can track the apparent path of the sun by tracking the shadow of the tip of a sundial (can be as simple as a pencil stuck in a pizza box). This setup as the advantage that you can experiment with it using a flashlight and a dark room.

 

[DavidB66]

I was puzzled by this question myself a month or so ago. Intuitively it seemed (to me, anyway) that if the sun rises in the east and goes down in the west, it cannot follow a straight line path throughout the day: it must either have an angular change of direction in the centre, or more likely follow a continuous curve. And yet time-lapse films or photo sequences often seem to show a straight path, at least around sunrise and sunset.
After much painful thought, and some reading, I came to the same general conclusions as Mick. The only time the whole path appears exactly straight is at an equinox. At other times of year the path may approximate more or less closely to a straight line. There is a connection between this problem and the theory of sundials. A line through the tip of a sundial's gnomon and the tip of its shadow at any given time indicates the direction of the sun at that time. It is well established that on an equinox the tip of the shadow traces a straight line throughout the day. At other times of the year (at least between the tropics and the polar circles) it traces a hyperbola, which approximates more closely to a straight line the closer the date is to an equinox. Also, the curve of a hyperbola approximates more closely to a straight line the further it is from the vertex of the hyperbola, which in the case of a sundial means when the time of day is closer to sunrise or sunset. There is a useful diagram and discussion in this webpage: http://mathshistory.st-andrews.ac.uk/HistTopics/Sundials.html [Added: I wrote this before seeing the comment by Mendel, who also draws attention to the sundial comparison. He got there before me!]
Another complication is the type of camera and the way the images are taken. I noticed some 'solargraphy' images of the kind mentioned by Mick, and was puzzled that the path of the sun did not seem straight even at an equinox. I suspected that it was due to some peculiarity of the technique, and as Mick points out, the image is projected onto a curved surface. (A strip of film is bent around the inside of a cylinder.) These solargraphs should not be taken as representing what would appear to the naked eye or to a normal camera.

 

[Mendel]

The path of the sun is only curved with reference to a straight horizon; but the horizon is curved in itself, too!
Mount a camera horizontally and swivel it, and you will create a panoramic image where the horizon is a straight line, and the sun's path bends. Affix the camera to an equatorial mount, as used for astronomy, which provides an axis of rotation parallel to the globe's, and the sun's path will appear straight as an arrow (but the horizon will appear bent).

The reason for this is that, what would be straight lines on a plane, are great circles on a sphere -- they can appear parallel in one place, intersect in two others, and still be always "straight".

 

[Mick West]

The path of the sun is only curved with reference to a straight horizon; but the horizon is curved in itself, too!
Mount a camera horizontally and swivel it, and you will create a panoramic image where the horizon is a straight line, and the sun's path bends. Affix the camera to an equatorial mount, as used for astronomy, which provides an axis of rotation parallel to the globe's, and the sun's path will appear straight as an arrow (but the horizon will appear bent).

The sun's path IS curved though, just, somewhat like the horizon viewed from altitude, not a lot. Ignoring the horizon, if you just take a timelapse of the sun's path with a rectilinear camera (like, roughly, an iPhone) then it's going to be slightly curved in that image (unless it's on an equinox)

 

[Mick West]

The sun's path IS curved though

To kind-of clarify that, the Sun’s path is curved, in the sense that if you hold a straight edge up to it, and all straight edges are straight in the image, then the suns path is curved in that image. Much like the horizon.

 

[180out]

The Sun, sitting in it’s position at the center of our solar system, doesn’t rise and set; the Sun appears to rise and set because Earth spins on its axis.

 

[Mendel]

The sun's path IS curved though, just, somewhat like the horizon viewed from altitude, not a lot. Ignoring the horizon, if you just take a timelapse of the sun's path with a rectilinear camera (like, roughly, an iPhone) then it's going to be slightly curved in that image (unless it's on an equinox)

If you do a cylindrical projection where the axis of the cylinder is aligned with the globe axis, it ought to be straight (and the horizon ought to be bent). Basically, use a pinhole camera with a semicircular projection surface and put the pinhole in the center of the diameter. I think what happens is the horizon gets twisted for our usual perspective (unless you project onto a half-sphere and not a half-cylinder). ;-p

I followed a youtuber a while ago who tried to verify that the lit part of the moon always points at sun, and with a half-moon, in the evening the lit part of the moon would still point up while the sun was lower in the sky that the moon. If you swivel the camera, or take a panoramic image, the moon doesn't seem to point at the sun! He didn't give up, and eventually used a stick to verify that the moon was pointing at the sun if you followed the direction across the "dome". On the panoramic photograph, you'd have had to draw a curve, but in reality, the connection was straight.

If you draw two great circles on a sphere, they're both straight, but their relative angles are shifting along their length. This is what happens here, and it happens at the equinox, too. (If the sun rises and sets, and the horizon is straight in our frame of reference, then the path of the sun must change angles. Except the horizon isn't even a great circle.)
For 12 hours, the sun curves ("appears to curve") one way, and the other 12 hours, it curves back. This is why, if the sunrise/sunset occurs near 6am or 6pm local solar time, the sun path curvature against the horizon is the least. This is also why the moon appears to rotate (it doesn't if you use an equatorial mount).

 

[Vic Thornley]

For the model of a flat earth to work in respect of the sun, you must show how half of the world is in daylight, the other in darkness. All at any one time, half of it MUST be lit. This also has to take into account seasonal day lengths whilst still maintaining only half lit up at any time.

Another point to note is that on the two equinoxes, if you are stood on the equator looking due east, the sun rises due east and continues straight up till it is directly above you. If you swivel round to face due west, the sun descends in a straight line down to set. This path puts it at 90 degrees tilted to a circular path it would have on a flat plain. Why is this so difficult to understand for some people.

 

[DavidB66]

I came across an article which discusses the path of the sun, and how it appears in time lapse images, including the question whether or when the path is curved:

Keen-eyed students will often notice that the equinox path appears to be a straight line in the photograph, while the two solstice paths appear to curve outwards a little. When I first noticed the curve in the summer photo, I casually assumed it was a projection effect or wide-field distortion of some kind, and I ignored it. But when I finished the winter sequence and finally combined all three photos, it struck me that I was actually recording the sun’s different declination circles in the sky. The sun’s apparent path through the sky on any given day is always a circle, but we view the circle from different perspectives in different seasons. At the equinoxes, we view the circle from the inside, from the circle’s exact center, so we don’t notice the curve at those times, but during summer and winter, we view the sun’s circle off-center, from a little to one side or the other, so at those times we perceive the curve of the circle.

The article includes a composite image showing time lapses of the sun's sunrise path at the summer and winter solstices, and the fall equinox, taken from the same location in California:


It will be seen that the curvature at the solstices is slight. I suspect that it would be more noticeable from higher latitudes.

The original article is here:

https://www.astronomyforthinkers.com/articles/tilted-sunrise/