Analemma's

This figure is depicted on many globes:



If you could record the position of the sun in the sky at the same time every day, (let’s say sometime around noon and subtracting one hour if you are observing daylight saving time) you would notice that the sun takes a rather strange path. You might notice that at certain times throughout the year the sun's position not only varies higher and lower (North and South) as you would expect with the change of the seasons, but also slightly east and west. This figure-8 path that the sun makes in the sky is called the analemma.



The sun takes this strange path for two reasons completely independent from the other.

1. The Earth is tilted on its axis 23.5° in relation to the plane of its orbit around the sun.
2. The Earth does not orbit the sun in a circle, but in an ellipse.

It is simply the sum of these two effects that causes the analemma.

More information can be found about the analemma on Wikipedia.
Also, here is a website that shows animations and explains how this works in case you have any trouble.

The explanation for this phenomena is coherent with the RE model of a round earth tilted on an axis with an elliptical orbit. What kind of FE earth model could show this?

It's obviously a perspective effect in FET, just like the rising and setting of the sun and moon.

It's obviously a perspective effect in FET, just like the rising and setting of the sun and moon.

To my understanding that perspective effect for sinking ships and the rising/setting of the moon has a lot to do with the surface of the horizon. Clearly, this is not on the horizon.
 

At the North Pole, the analemma would be completely upright (an 8 with the small loop at the top), and you’d only be able to see the top half of it. If you headed south, once you drop below the Arctic Circle, you’d be able to see the entire analemma, and it would start to tilt to one side the closer to the horizon you photographed it. By time you got down to the equator, the analemma would be completely horizontal. Then, as you continued to go south, it would continue rotating so that the small loop was beneath the large loop in the sky. Once you crossed the Antarctic Circle, the analemma, now nearly completely inverted, would start to disappear, until only the lower 50% was visible from the South Pole.

As winter transitions into summer, that arc gets higher and higher in the sky, peaking at its highest point during the summer solstice, and then declining back down to its low point as summer transitions back into the winter. The Earth’s axial tilt — responsible for this phenomenon — explains why the Sun moves along this direction (drawn in white) of the analemma:



So on a planet like Mercury, where the axial tilt is less than one degree, the Sun’s position in the sky doesn’t change from day-to-day, and so an analemma on Mercury is just a single point! But something else must be going on; Mars, which has almost the same axial tilt as Earth, has an analemma that looks like this:



If the Earth’s orbit were a perfect circle, and the Earth always moved at the same speed around the Sun, our analemma would simply be a line and the Sun would simply move along that line, reaching one end on the Summer Solstice and the other end on the Winter Solstice. But, no planet’s orbit is a perfect circle.

When a planet (with an elliptical orbit) is closest to the Sun (perihelion), it moves fastest. When a planet is farthest from the Sun (aphelion), it moves more slowly.



What this means is that the Earth moves different amounts through the sky as it rotates, which is important. You see, the amount of time it takes the Earth to rotate once is not 24 hours. It actually takes 23 hours, 56 minutes, and 4 seconds. Why are our days 24 hours, then? Because, on average, the Earth revolving around the Sun adds an extra 3 minutes and 56 seconds to each day. But during some days (like in March), it appears that the Sun is moving more slowly, so that 24 hours later — what we record as a day — the Sun has shifted its position in the sky.

The Earth’s axial tilt also contributes to the Sun’s apparent motion in not just the up-down direction, but also in the “side-to-side” motion. The following (1-3) contribute to the shape while producing the sum (4).

1. the effect of eccentricity (what I talked about above) [top left image below]
2. the effect of axial tilt (something that most planets have) [top right image below]
3. the combined effects of both of these (which gives us our equation of time) [bottom left image below]
4. the overall path of the analemma, which aligns neatly with the equation of time. [bottom right image below]

This is some truly outstanding educational material rottingroom, thanks!

Please demonstrate that this shape could only happen on a globe and no other shape.

Please demonstrate that this shape could only happen on a globe and no other shape.

"It's impossible to prove a negative" -- Various FEers
"Please demonstrate that this shape [is impossible on a flat Earth]" -- Tom Bishop

Can't prove a negative, Tom. Rottingroom has given why this shape happens for the round-earth model. He's not saying it's impossible on a flat Earth, he's asking how it's possible on a flat Earth. It's up to you guys to give a reason for it.

Quote from: Tom Bishop on September 04, 2013, 03:54:06 PM

Please demonstrate that this shape could only happen on a globe and no other shape.

"It's impossible to prove a negative" -- Various FEers
"Please demonstrate that this shape [is impossible on a flat Earth]" -- Tom Bishop

Can't prove a negative, Tom. Rottingroom has given why this shape happens for the round-earth model. He's not saying it's impossible on a flat Earth, he's asking how it's possible on a flat Earth. It's up to you guys to give a reason for it.

If this shape is possible in other configurations of the earth, then it cannot be a proof that the earth is a globe. There is nothing specific about this shape telling us that the earth is round.

Quote from: Alex Tomasovich on September 04, 2013, 04:04:01 PM

Quote from: Tom Bishop on September 04, 2013, 03:54:06 PM

Please demonstrate that this shape could only happen on a globe and no other shape.

"It's impossible to prove a negative" -- Various FEers
"Please demonstrate that this shape [is impossible on a flat Earth]" -- Tom Bishop

Can't prove a negative, Tom. Rottingroom has given why this shape happens for the round-earth model. He's not saying it's impossible on a flat Earth, he's asking how it's possible on a flat Earth. It's up to you guys to give a reason for it.

If this shape is possible in other configurations of the earth, then it cannot be a proof that the earth is a globe. There is nothing specific about this shape telling us that the earth is round.

Where are we talking about proof of anything, Tom? You're getting quite defensive. The OP is simply asking how this works for a flat Earth.

The shape tells me that over the course of the year, frame by frame cut into 365 consecutive days, the sun makes a big figure 8 in the sky, indicating that sometimes the sun is rotating around the North Pole and at other times the sun is rotating around the South Pole. This suggests that the Flat Earth Bi-Polar model is correct.

The shape tells me that over the course of the year, frame by frame cut into 365 consecutive days, the sun makes a big figure 8 in the sky, indicating that sometimes the sun is rotating around the North Pole and at other times the sun is rotating around the South Pole. This suggests that the Flat Earth Bi-Polar model is correct.

Can you elaborate, please. Rottingroom has provided diagrams of the method behind the RE model. Or, if you don't have diagrams, just further explanation.

Recall these were taken at the same time of day throughout the year. The Bipolar model can explain why the sun would get closer to the horizon, sure, but why the figure-8? I would think it would be just a vertical line.

A perfect line does not occur because the sun does not travel at a constant speed throughout the year. What is being captured in the sun's analemma is the offset of motion. As the sun travels towards and away from the North Pole it speeds up and slows down, much like the needle on a record player as it approaches the center. We can see that at the ends of the figure 8 the spacing of the suns are closer together, indicating when the sun is the closest to the poles.

A perfect line does not occur because the sun does not travel at a constant speed throughout the year. What is being captured in the sun's analemma is the offset of motion. As the sun travels towards and away from the North Pole it speeds up and slows down, much like the needle on a record player as it approaches the center. We can see that at the ends of the figure 8 the spacing of the suns are closer together, indicating when the sun is the closest to the poles.

That's brilliant! Good job.

Not only does the flat earth model need to account for the figure 8 shape but it needs to account for the changing orientation of the figure 8 as one views this from different hemispheres.

So assuming we take these pictures at noon everyday:

North pole should be upright.
Northwestern hemisphere should be slanted (like a forward slash) with the smaller section of the figure 8 being on top.
Northeastern hemisphere should be slanted (like a back slash) with the smaller section of the figure 8 being on top.
The Equator should have the entire figure 8 on its side.
Southern hemisphere should be slanted (like a back slash) with the smaller section of the figure 8 on the bottom.
Southern hemisphere should be slanted (like a forward slash) with the smaller section of the figure 8 on the bottom.
South pole should be upside down compared to the upright North Pole depiction.

I'm not so sure these things can be accounted for with Tom's explanation. Really the same arguments as that of the placement of the star and how those are configured differently depending on the angular view.

As long as this topic is on hold awaiting more input, I wanted to mention a similar problem I came across, regarding the moon's travel.

Now astronomers admit that the moon travels round the earth once a month, while the globe is going round the sun. What then should be the path of the moon? Neither a circle nor an ellipse; but a series of cycloidal curves, a sinuosity like the track of the serpert. But my limited space demands brevity.

Look at the curvature and study it, and you will find out some curious phenomena which the moon ought to manifest if their theories [i.e. of globularists] were true; but which she [i.e. the moon], in spite of her supposed fickleness, refuses to manifest. Trace out the path of the moon through the various signs of the zodiac, in relation to the sun's fixed position. The moon would sometimes be very slow--sometimes very swift, very--sometimes stationary--and sometimes actually appearing retrograde!

Yet the daily speed of the moon never varies more than two or three degrees, and the moon's motion is always "direct" through the twelve signs--justifying the inspired statement of the Psalmist that the moon is "the faithful witness in the sky" (Ps 89). [From: The Sea-Earth Globe and its Monstrous Hypothetical Motions, by Zetetes, pp. 15-16]

So there you have a kind of corollary to the complaint that flat earth theorists haven't yet posted an explanation about the path traveled by the sun. Actually they did post something already, but indeed the moon apparently presents a problem for round earthers, by the smoothness of its movement.

As long as this topic is on hold awaiting more input, I wanted to mention a similar problem I came across, regarding the moon's travel.

Quote

Now astronomers admit that the moon travels round the earth once a month, while the globe is going round the sun. What then should be the path of the moon? Neither a circle nor an ellipse; but a series of cycloidal curves, a sinuosity like the track of the serpert. But my limited space demands brevity.

Look at the curvature and study it, and you will find out some curious phenomena which the moon ought to manifest if their theories [i.e. of globularists] were true; but which she [i.e. the moon], in spite of her supposed fickleness, refuses to manifest. Trace out the path of the moon through the various signs of the zodiac, in relation to the sun's fixed position. The moon would sometimes be very slow--sometimes very swift, very--sometimes stationary--and sometimes actually appearing retrograde!

Yet the daily speed of the moon never varies more than two or three degrees, and the moon's motion is always "direct" through the twelve signs--justifying the inspired statement of the Psalmist that the moon is "the faithful witness in the sky" (Ps 89). [From: The Sea-Earth Globe and its Monstrous Hypothetical Motions, by Zetetes, pp. 15-16]

So there you have a kind of corollary to the complaint that flat earth theorists haven't yet posted an explanation about the path traveled by the sun. Actually they did post something already, but indeed the moon apparently presents a problem for round earthers, by the smoothness of its movement.

Claiming that the moon's orbit around the Earth causes it to go retrograde around the Sun is evidence that the author hasn't done his/her homework. This is true of the majority of satellites in our system, but not for our sole Moon.

You see, the Moon does orbit the Earth every 28-ish days, which results in a mere 13 'lunar years' for every Earth year. This is really, really slow in comparison to the distance the Earth-Moon system travels around the sun. This means that if you traced the path of the Moon around the sun, the shape you get is convex.


The Moon is also really far away in comparison to the Earth, especially in comparison to how close both are to the Sun. This means that the Sun actually has over twice the gravitational pull on the Moon than the Earth does. This means that the Moon's path is actually more defined by the Sun than it is by the Earth!

My intuition tells me that the orbit would be wacky if the moon were going around a spinning and whirling earth. I've looked at " class="bbc_link" target="_blank" rel="noopener noreferrer">some animations on youtube, and while I don't know a way to prove it, I think the path through the zodiac would be more erratic, if the alleged system of various orbits were true.

Regarding your link, which I reproduce here, which addresses comparative moon orbit appearances, I think the error is that you are choosing the wrong perspective (and so is that author). The example given is of a car A passing a car B, which is then passed by car A, and so on, with the task being to draw the path of one of the cars. Will it be a crazy scribbly line, or will it be a nearly perfect circle? Seen from above, both cars will trace a near circle (assuming a circular track). But, if you look from car A out to a particular point in the stands, car B will be rather wild compared to that point. That's the comparison. You're in one of the cars, looking out at the stands, and taking the other car in relation to what you see. It won't be neat. But the moon, in fact, traces a neat path through the zodiac.

So! While Tom has answered your analemma regarding the sun, you have no good answer for a similar point about the moon!

As Alex pointed out to you the shape produced is not that of a perfect circle, it is convex with 13 points because the moon makes its lunar orbit 13 times a year. A 13 pointed shape is a "moonshot" away from a perfect circle.

I'm not sure how you arrive at the guess that a vantage point from afar would produce a wild orbit. As I see it in my head, there should be no issues.

Also Tom, while clever was only able to explain the suns side to side movement in the analemma. The slanting, upright or flat path of the analemma when viewed from different locations has not been explained for a FE.

As Alex pointed out to you the shape produced is not that of a perfect circle, it is convex with 13 points because the moon makes its lunar orbit 13 times a year. A 13 pointed shape is a "moonshot" away from a perfect circle.

I'm not sure how you arrive at the guess that a vantage point from afar would produce a wild orbit. As I see it in my head, there should be no issues.

Also Tom, while clever was only able to explain the suns side to side movement in the analemma. The slanting, upright or flat path of the analemma when viewed from different locations has not been explained for a FE.

Not a very effective answer, rotter!  I didn't claim a perfect circle, and I'm not speaking of a vantage point from afar, but from within one of the two moving (or supposedly moving) objects. As for Tom, he can get around to the analemma later, I shouldn't wonder.

Quote from: rottingroom on September 05, 2013, 05:38:50 PM

As Alex pointed out to you the shape produced is not that of a perfect circle, it is convex with 13 points because the moon makes its lunar orbit 13 times a year. A 13 pointed shape is a "moonshot" away from a perfect circle.

I'm not sure how you arrive at the guess that a vantage point from afar would produce a wild orbit. As I see it in my head, there should be no issues.

Also Tom, while clever was only able to explain the suns side to side movement in the analemma. The slanting, upright or flat path of the analemma when viewed from different locations has not been explained for a FE.

Not a very effective answer, rotter!  I didn't claim a perfect circle, and I'm not speaking of a vantage point from afar, but from within one of the two moving (or supposedly moving) objects. As for Tom, he can get around to the analemma later, I shouldn't wonder.

I suppose my skimming led me to believe out to the stands meant from afar. Even then, I don't see why you would see a wild path. You can use this model to see how the shape is produced by playing around with the sliders. Then, if you turn the Earths speed all the way down you can attempt to observe how this might look from Earth and notice that from Earth it goes at a constant regular path around the Earth.

By the way I was able to use this site to produce a model that looked like Alex's. You have to download Wolfram Demonstration to use it yourself and it's free.

You have to use the settings from Snapshot 2 to get a too scale diagram the Earth-Moon-Sun system.

I suppose my skimming led me to believe out to the stands meant from afar. Even then, I don't see why you would see a wild path. You can use this model to see how the shape is produced by playing around with the sliders. Then, if you turn the Earths speed all the way down you can attempt to observe how this might look from Earth and notice that from Earth it goes at a constant regular path around the Earth.

Skimming??!! My gorgeous prose, you dare to skim? 

I have seen the slider modeling site, and I still believe that if you choose a spot on the earth, and look out at the gently moving zodiac, the moon, in the currently popular model, would trace quite a squiggly path through the zodiac, rather than the very gentle path it does trace. Remember that the point is not to see from afar the circles or near-circles that are alleged (or contrived in the cars-on-racetrack example), but rather to look from a spot on the earth, out at the zodiac, tracking the location of the moon in relation to the zodiac. I think it would perform a squiggle. So this is a good example of how science can be precise but answer the wrong question. And anyway the earth isn't moving in the first place, nor is it a sphere. So the moon moves gently because that is its course through the heavens. Not because it happens to trace a near-circle as a result of gravity from two larger bodies with everything spinning madly about.

Alex, using this model I cannot produce the same convex shape you showed us if I use 13 for the lunar orbit.

Maybe because this model doesn't show an accurate representation of the moons distance from Earth. There is a slider but no way to tell what distance would be correct.

Yeah that slider is pretty useless. It doesn't even say what units it's using. D8< In reality, the moon is 0.00257 times the distance from the Earth to the sun, or about .26% Even pushing that slider all the way over doesn't look like it's that close. Just about, but not quite.

Quote from: rottingroom on September 05, 2013, 06:26:04 PM

I suppose my skimming led me to believe out to the stands meant from afar. Even then, I don't see why you would see a wild path. You can use this model to see how the shape is produced by playing around with the sliders. Then, if you turn the Earths speed all the way down you can attempt to observe how this might look from Earth and notice that from Earth it goes at a constant regular path around the Earth.

Skimming??!! My gorgeous prose, you dare to skim? 

I have seen the slider modeling site, and I still believe that if you choose a spot on the earth, and look out at the gently moving zodiac, the moon, in the currently popular model, would trace quite a squiggly path through the zodiac, rather than the very gentle path it does trace. Remember that the point is not to see from afar the circles or near-circles that are alleged (or contrived in the cars-on-racetrack example), but rather to look from a spot on the earth, out at the zodiac, tracking the location of the moon in relation to the zodiac. I think it would perform a squiggle. So this is a good example of how science can be precise but answer the wrong question. And anyway the earth isn't moving in the first place, nor is it a sphere. So the moon moves gently because that is its course through the heavens. Not because it happens to trace a near-circle as a result of gravity from two larger bodies with everything spinning madly about.

Odes, put yourself in the center car for that one example. The other is, in essence, orbiting you. If you tracked it with your head, you'd see it moving around you against the background of viewing stands at an even pace.

By the way, unrelated but I've just played around a bit with a lot of the models on this Wolfram Demonstrations site and it's pretty fun and interesting. I highly recommend it 

The object is not to track the moon, but to see where the moon is in relation to a background. So I wouldn't trace the passing car with my head, but I'd look out at the stands. The metaphor breaks down because in reality the stands themselves are turning somewhat. In other words, the earth is flat and still, while the sun, moon, and stars are on various turning layers. Their movement is quite even. If the moon were going around the earth and both moving around the sun, the moon would take up a squiggly path, not a straight one. The old intuition is correct. Science came along and shifted the perspective and said "No, it's a near-circle." And in their model, so it is. But from earth, the moon would not trace a near-circle, against the zodiac, if the moon were rotating around the earth, and both the earth and moon were rotating around the sun.

By the way, unrelated but I've just played around a bit with a lot of the models on this Wolfram Demonstrations site and it's pretty fun and interesting. I highly recommend it 

I bet it is fun! But I hate installing stuff. I did enjoy the sliders on the one web page.

The object is not to track the moon, but to see where the moon is in relation to a background. So I wouldn't trace the passing car with my head, but I'd look out at the stands. The metaphor breaks down because in reality the stands themselves are turning somewhat. In other words, the earth is flat and still, while the sun, moon, and stars are on various turning layers. Their movement is quite even. If the moon were going around the earth and both moving around the sun, the moon would take up a squiggly path, not a straight one. The old intuition is correct. Science came along and shifted the perspective and said "No, it's a near-circle." And in their model, so it is. But from earth, the moon would not trace a near-circle, against the zodiac, if the moon were rotating around the earth, and both the earth and moon were rotating around the sun.

I see what you mean by against the zodiac now. Phew, I'm just not familiar with much of that type of terminology. In any case, do you have some source that shows any observations of the zodiac moving with the moon?

Also, you point out that against the zodiac the moons movement would be wild but keep in mind that on your human scale these celestial objects seem to move very slowly. There are, as you said, different layers of motion here:

The stars making their own motions which by themselves barely move from that distance.

There is the moons orbit which takes nearly a month to orbit the earth.

Then there is the earths orbit around the sun which takes an entire year to complete.

Then finally the earths rotation about the polar axis in a day. This final motion is the most apparent and from this perspective it would appear that the moon and stars make some similar motion to each other. This perspective created from this motion effects stars and the moon along the same plane.

Besides doesn't what you refer to as the zodiac show that a spherical earth is a reasonable conclusion? If you rotate yourself about a room and look into the "stands" then all the objects in the room rotate together from your perspective.If some fly were also buzzing about your head then it too would be rotating with the more static objects in the room. That fly would be moving independently and there would noticeable differences but your rotation would have the fly having some movement similar to that of the stands.