Analemma explained

I have already thought a lot about the analemma.
It is logical that the sun speeds up and slows down due to the different diameters of the circles of latitude in order to complete one revolution in 24 hours.

But the sun does not change speed linearly.
If the sun would do that linearly, we should see the analemma as a straight line in the sky.
But we can see this elegant loop.

When the sun changes its speed, it does not do so linearly.
Above the 14th parallel south, the sun orbits twice on its way between the tropics (as at any other latitude).

When it is above the 14th parallel on November 1st, it crosses the meridians earlier and on its way north it is slower at the same latitude in mid-February.
There is a half-hour time difference in between.

These changes in speed are known.
If you read Time and date (dot) com correctly you can recognize the pattern...

Our Creator has clearly shown us that he exists.
He made it the way he wanted it.
Wonderful.

I made a little video about this. (no audio)
Bilingual; German in yellow and English in white.


My sources:

https://github.com/pmh099/navigation-spreadsheets

https://www.nauticalalmanac.it/en/

https://TheNauticalAlmanac.com/2019_Bowditch-_American_Practical_Navigator.html

As with my Gleason distance calculator, the spreadsheet shown in the video is in the G-Drive folder

https://drive.google.com/drive/folders/1TloiUPaKlGP4jPYsFCnLwlWBAWalUJzW

The late, great Rob Skiba used stellarium's own data and showed that indeed the Sun travels faster south of the equator than it does when it circles north of the equator.

In trying to understand the analemma, I realized an important point.

The height of the sun does not really change; however, my previous calculations did not produce a meaningful pattern.

If you calculate a right-angled triangle using a cathetus and the angle to the hypotenuse, you can use the tangent of the angle to determine the height of the triangle.
If the base line is wider, the height increases for the same angle. Flatter angle - less height.

If you try to determine the height of the sun at different latitudes using the angles given by timeanddate_com, you have a problem.
You get different values.

If you see the sun from point A with a certain angle of inclination, you should get the same height from another point.
But that is not the case.

In the Nautical Almanac there are several tables for the correction of sextant measurements.
On page 281, one of the tables contains a column “Refraction”

The moisture contained in the air deflects the light downwards.
The further away the sun is, the lower it appears.

The more moisture there is in the atmosphere, the larger it appears to us.

Rob Skiba has illustrated the problem very well:
Flat Earth and Atmospheric Magnification (short version)
https://www.youtube.com/watch?v=sWJdZXlPZb8

If you look at the refraction values, you can see that the deviation is only slight at very steep angles.
When calculating the altitude of the sun, I therefore have 6.5 degrees of latitude from the zenith point on the Tropic of Cancer at 23.5° north to 30° north.
This gives an angle of inclination of 83.5°.

For locations at latitude 50° north, for example, timeanddate outputs a vertical angle of 40 degrees when the sun is above the equator.
63 degrees for the sun above 23.5° north.

So if you subtract the number of degrees of latitude from 90 that you are away from the zenith of the sun, you get the vertical angle.
This angle would also be determined by a captain with a sextant.
However, this measurement must be processed with the corretion tables.





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I have illustrated the calculation in Figure 1.



This way I arrive at 4036 km altitude of the sun.
That is about 57 degrees of latitude on Gleason's map.

In the following pictures I let the observation point move to the south.
(15° N; equator; 15° S, 30° S; 45° S; 60° S)




Figure 2: 15 degrees north; minus ~12 km
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Figure 3: Equator; minus ~52 km
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At 15° N and at the equator, the refraction does not yet have a clear effect.
From 15° South a clearly recognizable difference to the height of the initial calculation becomes visible.



Figure 4: 15 degrees south; minus ~612 km
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Figure 5: 30 degrees south; minus ~1235 km
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Figure 6: 45 degrees south; minus ~2127 km
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Figure 7: 60 degrees south; minus ~3363 km
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At the end of the calculation series, the sun reaches its greatest altitude of 6.5 degrees when crossing the meridian.
With simple triangulation, this is 673 km.

Of course, it is still over 4000 km above us.
Refraction makes it appear so low.

For the distances between the latitudes, I assume ~70.7412 km for one degree.
This value is calculated from 6366.707 km radius of the equator divided by 90.
(On the globe, this value would be 111.12 km for one degree, because 90 degrees would run from the North Pole in a wide arc to the equator...)

Rob Skiba said something very nice at the end of his video:
If he (Rob) could figure it out, then our creator definitely knew it when he gave us these beautiful sunsets....

Time and date gives the same times for the meridian crossing as the Nautical Almanac.
When the sun is exactly south, T&D call it Solar Noon.



February, April and November 2024 in direct comparison.
Half an hour difference between February and November and in April the sun crosses the zero meridian on the hour.
The sun changes its speed.

The angular velocity of the sun is a constant 15 degrees an hour - one degree every 4 mins.

What causes this motion is unknown ,or we are uninformed about this but it is constant.

Triangulation to an object in motion is impossible. This is why navigation centres on the pole star .

The AE map is not a flat earth map . Any map showing latitude lengthening towards the North is the product of imagination . Giovanni Cassini and Phillipe de la Hire triangulated over 8 degrees of latitude across the Paris meridian France in the late 17th century .

The task was given to these true scientists by the French Royal Academie of Science in a test of Newtons theory of gravity which predicts an oblate spheroid as the shape Earth.

They used triangulation using the stars, which do not move in relation to each other but revolve around Polaris . Latitude shortened towards the pole by a factor of 1/800.

The equinoctial circle is not at zero degrees. I don't think the tropics are 23.4N ( although the value could be correct for the Northern tropic) and 23.4S, why are you showing the figure of 23.5 for both? Globe earth has earth tilting at 66.6 degrees and earth travelling around the sun at 66,600 mph.

I extrapolated the standard value of the globe latitude .111.12km north to the pole and calculated the height of Polaris using Cassini's factor with the result that the height of the  pole star was around 3960mls. Earth radius.

Polaris has a yearly small rotation of radius 0.66 degrees. This explains the analemma and tides( see Rowbotham's "Zetetic Astronomy")

That number crops up alot in the heliocentric globe nonsense.

Don't take this as severe criticism but everything we have been told is bs.

I don't have much time hence I try to be short and to the point , sorry if it appears argumentative.

Can provide more detail if you require any

Just to clarify.

Zetetic astronomy was written in the 19th century. There are no photographs of the analemma from that time that I have come across and it is not mentioned in the book as I recall.

The tides of the open seas are are explained within that book as being a result of the motions of the sun around the plain causing changes in the atmospheric pressure acting on the lads and open seas. These are daily rhythmic fluctuations .

The analemma has a longer yearly period corresponding to suns cyclical journey between the tropics. I suspect the orbit of Polaris is also caused by motions of the continental masses in response to these cyclic changes in pressure too.

I say this because star trails always centre upon Polaris wherever it's position in orbit. This points to the observer viewing from a moving land not motion of the celestial dome

There are much longer cycles too. Isostatic rebound - said by scientists to be a rhythmic  raising/lowering of landmasses which are recovering from the pressures exerted upon them by the ice ages .

All these motions tell us the land rests upon a fluid substance - the waters beneath that religions speak of.

The Mohorovicic discontinuity is the scientific name of the boundary between the underlying fluid and the oceanic basins and continental land masses.

Hope this helps in your understanding of the solar analemma.

Reading a book , "Full Meridian of Glory" by P. Murdin , turns out the original value of one degree of latitude across Paris as measured by Cassini and Picard in 1670 was actually 111.092 metres and not 111.220 of the supposed standard .

I calculated all that stuff in error. The good thing about that is that it shows all that 666 crap , and hence ,the solar system model is a diabolical con ,speaking biblically.

No - the sun does not have a constant speed.
The analemma proves it very impressively.
The sun changes its speed in a north-south direction due to the different circumferences between the tropics; in addition, it sometimes moves faster and sometimes slower at the same latitude.
With this non-constant movement, our Creator paints a sign of his existence in the sky. We cannot explain how he accelerates or decelerates the sun. He simply does it.

Navigation to moving celestial bodies by triangulation should not be possible?
For captains on the high seas, sextant measurements are routine and they use the nautical yearbook.
At least until the introduction of electronic solutions.
These yearbooks are still on board as a backup in case the electronic systems fail.
The calculation of celestial bodies was already known to the ancient Egyptians.

The map and the fact that on the Gleason Map you can find the places on exactly the coordinates you enter into a modern navigation system is also a fact.
I trust this map more than French scientists who calculated a flattened globe and an equator that is not at 0° seems to me to be a somewhat daring idea...

Back to the analemma:

Also on time&date day & night world map the zenith position of sun and moon is given at a certain date/time.




In the screenshot I have entered February 10 and November 3 at 0:00 on Time&date and additionally in the German and English version of the xls.table.
As you can see, the deviation of the meridian crossing of the sun at 180 degrees longitude is + 16 min, 27 sec and - 14 min, 10 sec.
Half an hour difference in three and a half months.
Latitude and longitude as well as the sun and moon both show the same coordinates of the zenith.

A sun orbiting exactly in a 24-hour rhythm would cross this 180th degree of longitude every day of the year at exactly 0:00 UTC time.

When Rowbotham wrote his book, he was probably unaware of these time differences...
Today, this information is more easily accessible, although sometimes hidden from our eyes.
Sailors navigating with the Nautical Almanac are aware of these differences and take them into account in their calculations, as well as refraction, humidity and air pressure.

If you were to drive a stake into the ground at any point on the earth to create a sundial with an analemma design, the shadow will point slightly to the west in February, as the slow sun is still in the east at 12:00 noon (and vice versa for fast November).
Without this time deviation, the shadow of the stake would only be a straight line on the ground when the sun passes the meridian. Shorter in summer and longer in winter.

The suns angular velocity is shown in Skiba's video that you posted . It is constant. The time taken to circle the plain is constant wherever the sun is on its journey between the tropics.

http://spiff.rit.edu/classes/phys235/solar_path/solar_path.html. Globe model obviously.

4 degrees per hour. 365.25 days per year.

That we have the solar analemma not showing as a straight line across a meridian means that the movement of earth causes the analemma because the stars and constellations do not change their relative positions .

A sextant can show nothing but the apparent degree of elevation above the horizontal when viewing an object. You need tables in the almanac to figure out where you are viewing from - and a good timepiece.

"A sun orbiting exactly in a 24-hour rhythm would cross this 180th degree of longitude every day of the year at exactly 0:00 UTC time." Your sentence.

Only if the the plain did not exhibit rhythmic motion and the sun did not travel across the tropics.

The earth moves rhythmically?
As if it were dancing a waltz?
WOW!

Nicely put.

https://websites.umich.edu/~gs265/isost.html

A scientific paper indicating the principles of isostasy and its effects on the landmasses. So surprising that mainstream science cannot see that the evidence presented by the solar analemma supports a local sun passing across plain.

Why must astronomers , in their observations , take no account of the floating land masses responding to the forces of density and buoyancy?

How ridiculously complicated has this globe model become?

I have now calculated the height of the sun once at 1 degree intervals and created a bar chart with these 90 individual values from the height.





On the left-hand side you can see that the height of the sun drops only slightly.
With a smaller angle, however, the optical height of the sun drops more and more.

If the sun appears to us at an angle of 5 degrees just above the horizon at sunrise and sunset, it is actually over 4000 km high.
If it moves a few degrees further, it sinks optically into the horizon.
From a certain point, its light no longer reaches us.







This also explains why the sun can illuminate the underside of the clouds, even though it is far above them.

Without the refraction and the time deviation of the sun during its rounds, the analemma would be a short line in the sky, which would also appear much higher.

So if the limit of sunlight is reached at 90° and the altitude of the sun is ~4050 km, the hypotenuse of this triangle would be around 7546 km.

√((6367×6367)+(4050×4050)) = 7545.938576479 km

This is how far sunlight can penetrate through the atmosphere.

We are all familiar with photos and videos taken from an airplane in which the sun and moon can only be seen just above the clouds.
This image is composed of two screenshots and comes from a video.



If you were near the zenith, you would of course see both of them high up in the sky.