Earthly Observer's Looping Frame of Reference

Hi Simon,

In chapter 21 of your book you write: “Since Earth also spins around its axis every 24 hours or so, it follows that the path traced by a man (standing still for a full year) will be a trochoid” with the following accompanying image:

I’m somewhat confused: how exactly does the Earthly observer’s frame of reference form a [prolate] trochoid (a loopty loop)?

I’ve read or heard you say that the motion of a light on a bicycle wheel creates a prolate trochoid, but to do so the light would have to be fixed outside the circle of the bicycle wheel which is physically impossible against a road surface.



In the first image above from your book, ‘Jim’ (the Earthly observer), who is standing at a fixed position on Earth as viewed from above the North pole, is not moving, yet in the duplicated Earth images he appears as if he is changing geographical positions from month to month (in March at or around London, in April at or around Moscow, etc.). I am sure his apparent geographical location is unimportant, so I am trying to understand how this looping frame of reference works.

I can imagine a prolate trochoid motion produced from a fixed point located outside a rotating circle and with the horizontal motion equal to the rotating circumference motion (as in the above gif), but in your yearly PVP Earthly motion example this is not so: the Earth is rotating sort of in place (about 365 times), and only moving, according to the binary geo-heliocentric model, a little more that once its diameter, as in the below image from your book:

I haven’t found any experimental demonstration of a rapidly rotating / very slowly moving circle with a fixed point of light that could help conceptualize your model.

Thanks for reading

Dear Greg,

you may wish to check out this trochoidal animation machine (by Lenore Horner):

You will see that a trochoid will indeed occur just as the TYCHOS model proposes.

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Dear Greg,

I wish to thank you for submitting your above question. I have now added a new graphic (see below) to Chapter 21 of my book which should definitively clarify this matter. See, the manifestation of a prolate trochoid (by a dot placed on a spinning ‘wheel’) primarily depends on these two factors:

  • The rotational speed of the ‘wheel’ (i.e. 1670km/h in the case of planet Earth)
  • The translational speed of the ‘wheel’ (i.e. 1.6km/h in the case of planet Earth)

Since Earth moves about 1000X slower than it rotates, a man standing at the ‘edge’ of the Earth (i.e. at the Equator) will indeed trace a prolate trochoid over a full year:

You can actually verify this for yourself at home in this simple manner:

Take a standard, 12-cm CD (compact disk) and draw a dot on its edge.

  • Place your CD at the left edge of a large sheet of paper or cardboard (with the dot placed like “Mar 21” as in my above graphic). Draw a dot on your paper - next to the dot on your CD.
  • Next, move the CD to the right by 1cm (i.e. the monthly distance covered by Earth) - and rotate it counter-clockwise by 30°(i.e. the amount that Earth’s orientation shifts between March 21 (at midnight) and April 21 (at midnight). Again, draw a dot on your sheet of paper next to the dot on your CD.
  • Repeat the above operation 12 times (or 15 times) - and you’ll see that a nice prolate trochoid will “magically” be traced on your sheet of paper.

Easy does it! :slight_smile:


Hi Simon,

Thanks for your answer; your helpful diagram is precisely what I was conceptualizing in my mind.

So what is this monthly 30 degree Earth orientation shift? How is Earth “shifting” by 30 degrees every month? Sorry, this is where I don’t get it.

Dear Greg,

Every solar day (24hours), the Earth rotates by more than 360° - or almost precisely 361° - as expounded and illustrated in Chapter 12 of my book. In fact, the Earth actually completes one full rotation around its axis in just 23h56min - i.e. 4 minutes (or 1°) less than 24 hours.

Here’s how you can verify this - with your own eyes :slight_smile: : go to the Tychosium 3D simulator , center the Earth in your screen and enlarge the view as much as you wish (by using your mousewheel). Next, select “1 second equals 1 DAY”. Now, click on the “step forward” button and you will see that, each day, the Earth ‘ticks counter-clockwise’ by a small amount. If you now select “1 second equals 1 MINUTE”, you will see that by clicking on the “step backward” button 4 times (i.e. 4 minutes), Earth will return to the (rotational) position it was the day before.

Hence, every 30 days or so, the Earth “ticks counter-clockwise” by about 30°.

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Here this is also explained, see question 6. And regarding this question, it doesn’t matter if we think it’s the Earth that moves around the Sun even though this is geometrically impossible as explained in Simons book, or if the Sun is orbiting Earth.


Hi Everybody,

I am also trying to wrap my head around this. I think there are several, different ways of gaining an understanding, and I think Simon’s example with a CD disc is excellent!

This might be another way of thinking?: In the TYCHOS the sun makes a full orbit around earth in 12 months. That’s 360/12= 30 degrees, or 1440/12= 120 minutes, per month. That’s about one degree, or 4 minutes per day. If we draw a straight line from the center of the sun to the center of the earth, this line will hit earth in the exact same longitudinal position the exact same time each day. But the latitudinal position will ofcourse vary from day to day, since the earth is tilted about 23.5 degrees compared to the sun’s orbital plane. So, for someone standing on earth at the exact same longitud and time each day, the sun will be at the same longitud compared to earth. But the sun will move 4 minutes per day Right Ascension (longitudinal position in the celestial sphere). In other words, earth is “following” the sun so to speak, as it orbits around earth.

This is my understanding anyway. I hope it might be of some help to somebody else trying to understand this concept :slight_smile: But please correct me if I have misunderstood something.

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Dear Timo,

Yes, you’ve got it right - but this particular issue is solely about celestial longitudes (RA / Right Ascension), so no need to complicate matters with celestial latitudes (DECL / Declination).

Quite simply, what astronomers have decided to call the “SOLAR day” (i.e. 24 hours) is 4 minutes longer than the “SIDEREAL day”(23h56min). The latter is the time that Earth employs to realign with a given star, whereas the former is the time that Earth employs to realign with the Sun. My below illustration (from Chapter 12 of my book) should clarify how the TYCHOS model neatly accounts for all this:


Therefore, in order to “follow the Sun” (as you rightly put it), Earth needs to “tick counter-clockwise” each day by about an extra 4 minutes - or 1° (after having rotated by 360° in 23h56m). Hence, every 30 days or so, the Earth “ticks counter-clockwise” by about 30°.

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You got it right Timo. The Earth has to rotate a little bit more than 360 degrees to line up with the Sun since it’s moving around us. And thanks to having built the Tychosium I get this thoroughly now. :slight_smile: And there’s another interesting phenomenon related to this. Even though our 24 hours represent precisely the time it takes for Earth to rotate about 361 degrees to line up with the Sun, the Sun will not be exactly at the place it was yesterday at noon. Most of the times it will be slightly behind or in front of that position. This phenomenon is called the analemma and until Simon took a good look at this, no reasonable explanation existed to why this occurs. But with the PVP orbit that Earth slowly moves in while the Sun orbits Earth, a simple and rational explanation to this phenomenon can be found. During the summer season, Earth will be moving slightly in the opposite direction that the Sun is moving around us in. And in the winter season it will be moving in the same direction in its PVP-orbit as the Sun. If you hold your right finger in front of you, moving it slowly to the right imagining it’s Earth, while at the same time having your left finger making a counter clockwise circle around “Earth”, you can see how this works. This is however only the basic cause of the analemma. The reason it is shaped as a disfigured eight has to do with “A mans yearly path” and is explained in detail here Chapter 21: A Man's Yearly Path, the Analemma - and the number 137


I stumbled onto this trochoidal pattern myself. Using CAD I drew a circle representing earths orbit and a small one representing the moons. The moon’s circle is divided with 28 ticks, of course earths circle would have 365. Put the moons circle center point on the larger diameter earth orbit. Day one, the moon is directly in line with a line going to the center point of eath’s orbit. Move (or copy in CAD) the small circle one tick mark/day, while at the same time changing moons position each time. So the earth moves 28 days around while the moon is moving in its circle around the earth. I know it is convoluted in words but the trochoidal patter begins to appear just like Simon’s graphic.

I was making a calendar for myself with the earth rotating around the sun, then I found Tychos model. The remarkable thing is this, you can use a scaled down orbit with metric, just drop the zeros and it works out. Except, you have to make earth larger or you would never be able to see it. But then I did the math and earth is moving (based on mainstream) ~201 earth diameters/day! And making a single rotation, talk about a knuckle ball! If you use that distance for your earth moon exercise above, the trochoidal pattern will never appear. It makes no sense to think that we are dragging along the moon while it is slowly moving each day around us, over 200 earth diameters every 24hrs! Absolutely nuts… I mean with the moon so close to us you would have to see some parallax if earth moved 200 diameters/day it seems to me.

If you use a bb as earth, a 20" beachball is approximately in proportion to the sun’s size. I was going to compare the distance earth moves every day and I got about sixty bb’s laid out and I said “screw this!”, it wasn’t worth the effort. But for the sun (beachball) to travel the same distance, you just roll the beachball one revolution!

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Indeed. We have a certain perspective on things, in this case that the heliocentric theory is reasonably correct since otherwise so many astronomers would be wrong and NASA would be peddling brazen lies.

But if we start to investigate the issue we find that it is possible to not only question, but disprove this theory using basic geometry.

And one of those proofs is this: The Moon lines up with the same stars at a certain time at night, despite that we’re supposed to have moved about 2.57 million kilometers in an orbit around the Sun since yesterday.

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Btw Patrik,
I want to commend you on the simulator. I was using it yesterday and I noticed how much detail you have put into the earth now with the tilt being very easy to see now (i don’t think it was originally as detailed as it is now) and all of the stars that are in place is really incredible!

I had a question too. This might be hard to word to make sense. In the simulator we can see that the sun travels through the zodiac in it’s yearly course. So from earth we see the constellations changing behind the sun, of course. Now if, the sun were at the center and we were moving around it, the constellations would be 180 deg rotated wouldn’t they? Flip-flopped so to speak.

It’s easier to see what I am saying when you have two diagrams beside each other, one with the earth in center the other with the sun in center.

Now if, the sun were at the center and we were moving around it, the constellations would be 180 deg rotated wouldn’t they? Flip-flopped so to speak.

Not so, dear Schoepffer. not so… :slight_smile:

The general orientation of the stars in the Tychosium simulator is (largely) equivalent to that of any heliocentric simulator - and is certainly not reversed by 180°, as shown in my below comparison :

However, the ‘problems’ arise when heliocentric astronomers wish to measure the parallax of any given star (e.g. Sirius, in the above example). Since they believe that the Earth revolves around the Sun, they presume that we move from “A” to “B” over a 6-month period - and that we would therefore be displaced laterally (in relation to the star) by a whopping 300 million kilometers. These 300 Mkm (or more precisely, 299.2 Mkm) will thus represent the trigonometric baseline upon which they will calculate the distance to Sirius (on the basis of the minuscule parallax that it exhibits). They will thus conclude that the star is several “light years” away. Sirius for instance, by far the very brightest star in our skies, is reckoned to be 8.7 light years away (or about 550 000 times further away than the Sun !!!). Now, since our Sun’s diameter only subtends a mere 0.5° in our sky, this means that Sirius ‘actual’ angular size would supposedly be: 0.5° / 550 000 = 0,0000009° ! Yet, this is what is officially claimed… Now, consider this:

“Humans can resolve with their naked eyes diameters of up to about 1 [arcminute] (approximately 0.017°)..” Angular diameter - Wikipedia

In the TYCHOS model, on the other hand, the Earth only moves by 7018km every 6 months. Since 7018km is 42633 times less than 299.2Mkm, the officially-claimed distances to the stars will be grossly inflated, by a factor of 42633. This would put Sirius, for instance, at a far more reasonable distance of 12.9AU (i.e. 12.9 times further away than the Sun) and an angular size of 0.0387°, which would also be more consistent with how we perceive Sirius with our naked eyes.

I knew it would be difficult to explain without an image.

The above screenshot from the Tychos shows the sun in Gemini from our vantage point on earth, where we are at the center.

Now, if instead we were orbiting the sun and it was we who were moving through the zodiac and we were in Gemini it would appear to us that the sun is in Sagittarius. So we would need to be on the opposite side of the sun or the zodiac would have to be rotated 180.

I could be completely wrong, but I think this indicates that we cannot be located where they say we are at, which of course is the premise of the Tychos.

Also, I believe I read in another post that you said if the earth orbited the sun the Northern Hemisphere would always be in winter? Clearly. The earth would have to wobble in it’s yearly orbit to do what Copernicans say that it does. And it would need to rotate counter to its orbital direction for half the year.

I realize that you know this but for anyone who might be reading this there is a very misleading diagram at NASA’s site What Causes The Seasons

These ridiculous cartoons that are all over the web show a tilted sphere that some how manages to “wobble” so that it’s orientation reverses itself. No, the axis would always face away from the sun. Try it at home. There are two motions the revolution about the axis and the orbit. An orrery has to add a “cam” gear or a third motion to re-create this diagram, if they even bother to do it all.

More illogical statements from the same site:

Many people believe that Earth is closer to the Sun in the summer and that is why it is hotter. And, likewise, they think Earth is farthest from the Sun in the winter.
Although this idea makes sense, it is incorrect.

in the Northern Hemisphere, we are having winter when Earth is closest to the Sun and summer when it is farthest away!

Really?? Isn’t the inverse also true then?

This sentence would be equally as accurate:

“In the Southern Hemisphere, we are having summer when the Earth is closest to the Sun and winter when it is farthest away!”

They go to great lengths to promote the charade because with the axis not remaining in it’s same orientation we would clearly not be aligned with the pole star the entire year, it would change by the month actually.

I’ve pointed this out to some of the smartest people I know and their minds just recoil. They go on a Google binge and it takes them about an hour to come back to me with the YouTube animations and this is what “we observe”. I think not. It’s what “we were taught”.