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.





-----------------------------------------------------------

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
-------------------------------------


Figure 3: Equator; minus ~52 km
-------------------------------------

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
-------------------------------------



Figure 5: 30 degrees south; minus ~1235 km
-------------------------------------



Figure 6: 45 degrees south; minus ~2127 km
-------------------------------------



Figure 7: 60 degrees south; minus ~3363 km
-------------------------------------

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.

I have displayed the time differences of the sun with the Mercator map from Timeanddate.

While the sun crosses the finish line of the 24-hour race to within two seconds at Christmas, the winner's trophy goes to November 3rd.
Team February crosses the finish line half an hour behind the winning time.

As a supplement to the three previous graphics:
The duplicated equation of time should make it a little clearer.
If the rotation of a globe earth would be slowed down like this, the mass inertia would show it clearly when the season of overturning objects has come again...

The analemma is so precise that time differences in the following year are only in the range of a few seconds, whereby the leap years also contribute their part.
Moreover, the amplitudes are not symmetrical.
Our creator liked it that way.

Fortunately, this beautiful piece has survived modern times.
A mobile sundial!

Note the equation of time in the lid.
In the past, knowing this was completely normal...

That is a beautiful instrument - any idea of it's age?

Sun dials have been around for many centuries and naturally these were used to track the analemma or the mid day- that point where the suns shadow is shortest cast by the gnomon.

The equation of time is the attempt to reconcile the heliocentric model with reality. It "tracks" the real solar position against the imaginary or "apparent" solar position i.e.  the suns deviation from where it should be according to the heliocentric model.

As you say it's wrong to ascribe this phenomenon to changes in earths velocity .

How do they get away with this?

@TyrannicalSawdustRex

The sundial dates from the early 1920s.
At least that is how it is described here:
https://www.gilai.com/product_852/Sunwatch-Combination-Sundial-and-Compass-by-Ansonia

I don't see the equation of time as just an attempt to justify something. It is crystal clear proof that the sun simply has its own orbit and changes its speed as it does so.
Precisely calculable and repeating itself every year.
Observable daily because the time at which the sun is exactly in the south changes, just as Timeanddate states at true noon.

Of course, the equation of time does not fit into the heliocentric world view.
It would make the fairy tale of the rotating earth even less credible.
But it is also proof of how little we know about our Earth today because true knowledge is no longer taught.
Everyone is only given as much insight as is necessary for their particular activity.
As I already wrote using the example of navigation on the world's oceans.

A spherical earth rotating 360 degrees in 24 hours would swap day and night in half a year, which is why the sidereal day was invented, which is four minutes shorter and thus a 361 degree rotation in exactly 24 hours is supposed to iron out this fiasco. But even with this model calculation, the “earth's rotation” would have to be variable.
That is bullshit. The earth is motionless.

This half hour between the greatest time differences amounts to almost eight degrees at the zenith of the sun above the earth.
The sun is then almost exactly at 15 degrees south latitude. That makes a difference of 525 nautical miles.
Unfortunately, today we navigate electronically; I would be very surprised if a captain still navigated in the traditional way...

For the manual calculation, even air pressure and humidity were taken into account due to refraction and the height of the sextant above sea level, as these influence the angle to the horizon and thus also the angle to the stars.
And yet the sailors believe they are sailing around on a sphere because they have been told so...

Of course, it could also be that the captains know and, like pilots, have to sign a non-disclosure agreement...

How can they get away with it?
They get away with it because they have suppressed independent thought from the flock of sheep out there.
People are being systematically dumbed down.
Chemtrails, fluoride, radiation, propaganda etc. etc. etc...
The few who still dare to have a different opinion are ridiculed or even persecuted.
In Germany in particular, the air has become very thin for dissenters.
The regime has even put doctors who issued their patients with a certificate exempting them from wearing a mask during the Chinese flu on trial and sentenced them to prison.
Punish one - educate thousands!
That's how you get away with it...

The equation of time is a heliocentric attempt trying and failing to explain why the sun isn't where it should be according to it's easily observable and measurable constant angular velocity of 15 degrees per hour.

The sun orbits at that constant angular velocity around the pole during it's journey to and fro between the tropics .

When the analemma is photographed over the course of one year this is done from the same spot with a tripod mounted camera . This is actually a sundial with a camera.

This sundial/camera will tilt as the passage of the sun affects the pressure on the continental land masses which float on the aesthenosphere , to use the scientific name , the waters beneath in my opinion.

That curve shown in the equation of time is the actual amount of yearly deviation of the land from plain level at the latitude of the observations from which these are taken .

We won't notice these slow minute variations but they are there.

The diurnal isostatic rebound is the main cause of tides , the daily atmospheric pressure changes caused by the suns passage above. This also leads to small tides in the southern regions compared to northern latitudes.

The yearly isostatic changes are caused by the suns passage between the tropics as recorded by sundials/cameras and represented in the deliberately mis-named "equation of time".

There are other longer term isostatic changes known to science.

All this is easy to research and was taught in earth science university courses.

Of course astronomers ignore these effects during their observations - science is controlled through compartmentalisation and the peer review
system.

Hope you can understand these arguments.

Our world is flat and stationary and lies beneath the rotating celestial dome. The dome rotates in 23hrs 56 mins, the sun travels around the plain in 24hrs with constant angular velocity.

I have been familiar with the immovable flat earth for quite a while now and am also a member of various German-speaking groups on the subject.
During this time I've gotten to know some very funny birds and I know when it's time to stop talking about something because it's a waste of time...
Thank you for your understanding.

We learn through dialogue and it's good for you to have friends with similar views , sorry if you feel aggrieved.

I have thought about the problem of analemma and have thoughts on how to remove the effects of earths isostatic movements .

Marine magnetic compasses are removed from ocean swells by floating these in a liquid contained within a gimballed basin - water always remains level.

Photographing the analemma from a gimballed station floating freely in an inland lake or pond, some such body of water since these are not affected by tidal or isostatic movement, may give a  different picture of the analemma as a result . Maybe even remove the need for helio math modelling involving imaginary positions, straighten out the analemma.

All land based observations of celestial objects over lengths of time will include the effects of isostasy unless these are removed by some method. The timeanddate website observations are included in this.

In my view observations made with this method will give us a truer view of this realm we live in.

Might try and fit a free floating sundial into my garden pond and pray for sunny days.

We are all searching for the truth and good luck in your endeavours.