Chapter 11: Earth’s PVP orbit (Polaris-Vega-Polaris)
We shall now proceed to see how the TYCHOS model accounts for the all-important “Precession of the Equinoxes” - or, as modern astronomers would call it, the "General Precession". Here's how this name change is explained at the Wikipedia entry for "Axial precession":
"With improvements in the ability to calculate the gravitational force between planets during the first half of the nineteenth century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession, as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession, instead of precession of the equinoxes."
If, as demonstrated by several modern-day independent studies, Earth does NOT wobble around its polar axis, it follows that we need to explain how and why our Pole stars keep changing over time. We know that the (binary) star system Thuban, for instance, was our “North star” roughly 4600 years ago. In our current epoch, the (binary) triple star system Polaris is our “North star”. In about 11700 years from now - around the year 13720AD - the (binary) star system Vega will become our “North star”. This is generally agreed upon by most of our world's astronomers.
Here is a classic / conventional illustration plotting the circular motion responsible for our “North Stars” to change over time. Please note that, if viewed from an imaginary spaceship hovering above our North Pole, this circular motion proceeds in a clockwise direction:
Above — from Professor Mahoney’s Astronomy Website by Robert Mahoney (2016)
Now, if Earth doesn’t wobble around its polar axis (as currently believed), could it instead be physically moving clockwise (as seen from our North stars) below the circular path which extends from Polaris to Vega, and back again to Polaris? Surely, this wouldn’t be too much of a fanciful proposition; after all, we now know that every single celestial body in our skies move around 'local' orbits of their own. In any event, to believe that Earth would be the ONE-AND-ONLY orbitless, non-rotating and immobile body in the entire universe is just silly - yet, this is what most 'biblical' geocentrists (and flat earthers) propose...
Let us put this proposition to the test and see if we can find out at what speed the Earth would travel as it completes this 360° journey - around a circle which I have called the PVP orbit (Polaris-Vega-Polaris). To do so, we will first need to estimate its approximate diameter. My next set of graphics should hopefully illustrate in a comprehensible manner the methodology behind my appraisal of the PVP orbit's diameter.
Perusing 'earthbound' digital simulators such as the Neave Planetarium, we can see that the Sun (as it moves around our 360° celestial sphere) covers a distance subtending 2h56min of RA (Right Ascension) in 44 days - or 1056 hours.
In this other conceptual graphic, I show how the Sun would 'visually' employ ca. 44 days to cover the distance between Polaris and Vega (as viewed under an imaginary circumpolar orbit of the Sun). I do realize that my conceptual graphics can be somewhat challenging to envisage - but they are the best I can do to help the reader 'visualize' the train of thoughts that led me to formulate the TYCHOS model's PVP orbit.
We may therefore perform a simple calculation to estimate the diameter of our PVP orbit. Assuming the Sun travels at 107226 km/h, in 1056 hours the Sun would cover the distance of:
107226 km/h X 1056h = 113 230 656 km (the diameter of our PVP orbit)
Hence, the circumference of Earth’s orbit will be:
113 230 656 km X π = 355 724 597 km (the circumference of our PVP orbit)
In this last diagram, I illustrate in further detail how all of this would be consistent with empirical observations:
- Polaris is currently observed to be at 89° of declination (i.e. almost exactly above our North Pole).
- Vega is currently observed to be at 39° of declination (i.e. about 50° 'away' from Polaris).
- In about 11700 years, Vega will become our North star (although only at 86° above our North pole - as officially predicted).
In about 11700 years Earth's axis will then be tilted (as officially predicted) by 22.9° - as opposed to the current 23.4° - for a total axial rotation (in relation to our 180° Northern celestial hemisphere) of 46.3°. This 3.7° difference (between 50° and 46.3°) can be accounted for by Earth's 113.2 Mkm displacement along its PVP orbit. This, because in the TYCHOS (as we shall see later on) the Earth-Vega distance is estimated to be ≈37AU. The PVP orbit's diameter of 113.2 Mkm (or 0.757AU) amounts to ca. 2.05% of 37AU - and that aforementioned 3.7° difference amounts to ca. 2.05% of 180°.
As will be extensively tested and cross-verified throughout this book, the duration of Earth's "Great Year" (as of the TYCHOS model) is 25344 solar years. This is about 1.68% shorter than the current 'official' estimate of 25771 solar years - for motives that will be clarified in Chapter 12.
There are 8766 hours in 365.25 days. Therefore, 25344 years will add up to:
25344 X 8766 hours = 222 165 504 hours
Now that we know how many hours that Earth will need to cover the distance of 355 724 597 km (the PVP orbit’s circumference), we may compute Earth’s orbital speed:
355 724 597 km / 222 165 504 hours = 1.601169 km/h or approximately 1 mph! (1 mph = 1.609344 km)
This is Earth’s proposed orbital speed in the TYCHOS model.
“By Jove! Could our dear old Mother Earth be tranquilly strolling around at window-shopping pace?”
My very first thoughts - soon after computing Earth’s languid speed around its PVP orbit - was the following: has life on Earth, perhaps, been facilitated by this sluggish, snail-paced motion of our planet? Could this exceptional tranquillity graced to Earth (for being “stuck” at the barycenter of the Sun-Mars binary system) be a key prerequisite for habitability (along with water, photosynthesis, etc) and biological life as we know it to blossom on any given planet? Moreover, isn’t this serene situation enjoyed by our planet rather reminiscent of a ship gently circling around the calm zone in the eye of a tropical cyclone - while the spinning storm rages around it, moving in the opposite direction of the ship?
For now though, I shall leave my poetic & philosophical musings aside and proceed to put this posited orbital speed of Earth to the test - in methodical fashion. As we proceed one step at the time, we shall see that Earth’s 1-mph-motion around its PVP orbit effectively resolves a number of extant puzzles, quandaries and still unresolved enigmas of astronomy - as readily admitted by most earnest and free-thinking astronomers.
We can now work with an empirically testable Sun-Earth velocity ratio. To be sure, that is not the same as stating (as current theory does) that “the Sun hurtles around the galaxy at 800000 km/h along with our system’s planets – while Earth revolves around the Sun at 107226 km/h”, all of this in the absence of any observational indications in support of such formidable, hypersonic speeds. One may well say that these outlandish velocities upheld by Copernican theorists have been an offense to human intelligence all along, since this would mean our entire Solar System travels across space by more than 7 billion kilometers each year. Yet, the stars in our Milky Way (which supposedly all revolve 'in unison' around the centre of our galaxy) all exhibit microscopic proper motions in all sorts of random directions - their only common (and much larger) motion being that annual ≈50 arc-second eastward drift known as the "General Precession". In the TYCHOS model, of course, this common ≈50 arc-second eastward drift of the entire firmament is simply caused by Earth's motion around its PVP orbit.
Those familiar with the infamous Michelson-Morley experiment, billed as "the most failed scientific experiment of all time", may begin to sense that the TYCHOS model might yet vindicate the same; the experiment’s objective was to try and measure Earth’s translational velocity across space (or through the “aether”). Of course, the expected speed of Earth was something in the region of 107000 km/h, yet nothing of the sort was found. Here is what we may read in astronomy literature:
Above — Extract from p.74, The Methodology of Scientific Research Programmes: Philosophical Papers Volume 1 (Book 1) by Imre Lakatos, Cambridge University Press (November 28, 1980)
As you can see, not only did Michelson conclude that Earth’s speed had to be quite small, but he even “thought of the possibility that the solar system as a whole might have moved in the opposite direction to the Earth”. In hindsight, both of those assertions would seem to be congruent with the TYCHOS model‘s proposed, snail-paced 1-mph motion of Earth, as it revolves in the opposite direction of our Solar System's 'family members'. In any event, the numerous successive interferometer experiments performed by other scientists all failed to detect speeds anywhere near the presumed orbital speed of Earth (107226 km/h - or ≈30 km/sec). The speeds detected were, oddly enough, dismissed as "null" by the scientific community of the time. However, none of the many interferometer experiments yielded "null" results; they generally agreed with each other to some extent, and would actually seem to support Earth's 'snail-paced' orbital speed - as will be thoroughly expounded further on.
If we consider that 25344 years represents a full 360° equinoctial precession, we should now be curious to find out how long it takes for Earth’s equinoctial axis to rotate (in relation to the stars) by just 1°. Let's see how this supposition would pan out as we apply it to the observed synodic periods of Mars, Venus, Mercury and the Moon:
25344 / 360 = 70.4 solar years
We see that 70.4 solar years (or 25713.6 days) equals precisely:
33 synodic periods of Mars (779.2 days X 33 = 25713.6 days)
44 synodic periods of Venus (584.4 days X 44 = 25713.6 days)
220 synodic periods of Mercury (116.88 days X 220 = 25713.6 days)
880 synodic periods of the Moon (29.22 days X 880 = 25713.6 days)
We may now compute Earth’s annual “equinoctial procession rate” as of the TYCHOS system. If Earth’s equinoxes process by 1° every 70.4 years, then every century (100 years) they process by:
100 / 70.4 = 1.42045° - or 5113.63" arcseconds
Hence, our annual “precession rate of Earth’s equinoxes” is:
5113.6363 / 100 = 51.136 arcseconds
I will henceforth refer to this all-important value of 51.136"(periodic) as our ACP (Annual Constant of Precession).
Interestingly, back in the 16th century (when most astronomers estimated the annual precession to be about 50" or less), Longomontanus and Tycho Brahe used a fixed rate of 51 arcsecs/year for their precession calculi:
"Rather than using the Prutenic precession (variable rate) Longomontanus used Tycho’s precession (fixed rate of 51 arcsecs/year)."
In the following chapters, we shall see how this 51.136” value can, in a number of ways, correctly account for the observed motions of our Solar System - as Earth slowly revolves around its 25344-year “PVP” orbit at the tranquil speed of 1.6km/h (or 1mph).
MARS'S CLOSEST PASSAGES TO EARTH - IN THE VERY MIDDLE OF THE PVP ORBIT!
As we saw in Chapter 5, Mars can transit as close as 0.373 Mkm from Earth (as it did in 2003).
However, as shown in the below table, the AVERAGE figure of its closest passages is about 0.379AU.
CLOSEST MARS OPPOSITIONS (1924 – 2050):
0.372838 (Aug 23, 1924)
0.387873 (July 27, 1939)
0.378090 (Sept 7, 1956)
0.375684 (Aug 12, 1971)
0.393141 (Sept 22, 1988)
0.372709 (Aug 27, 2003)
0.384955 (July 31, 2018)
0.380399 (Sept 11, 2035)
0.374041 (Aug 15, 2050)
AVERAGE: 3.41973 / 9 ≈ 0.379 AU or almost exactly PVP orbit’s radius of 0.37845AU (or 56.615328 Mkm)!
I'd like to state for the record that I only realized this astounding fact long after I had tentatively estimated the diameter of the PVP orbit of 113.2 Mkm (i.e. 2 X 56.6 Mkm)! I trust you may imagine my delight when this was discovered - during one of my late night computing sessions. You may appreciate the utmost importance of this finding - as it would certainly support the proposed size of the PVP orbit's diameter. That is, unless you wish to chalk this up to some random, accidental coincidence...
We just saw that Mars can pass as close as 56.615328 Mkm from Earth. Let's now compare this distance with the mean Earth-Sun distance (i.e. 1 AU - or 149.5978707 Mkm):
149.5978707 Mkm / 56.615328 Mkm = 2.64235 (ergo, the mean Earth-Sun distance is 2.64235X larger than the closest Earth-Mars distance).
My estimation of the PVP orbit's diameter is 113.230656 Mkm. The Sun's orbital diameter is 299.1957414 Mkm.
299.1957414 Mkm / 113.230656 Mkm = 2.64235 (ergo, the Sun's orbital diameter is 2.64235X larger than Earth's PVP orbit).
We shall now look at a most remarkable 'relationship' between Earth's PVP orbit and the astronomical unit known as the "parsec".
From the Encyclopaedia Britannica:
"parsec, unit for expressing distances to stars and galaxies, used by professional astronomers. It represents the distance at which the radius of Earth’s orbit subtends an angle of one second of arc. Thus, a star at a distance of one parsec would have a parallax of one second, and the distance of an object in parsecs is the reciprocal of its parallax in seconds of arc." parsec - Encyclopaedia Britannica
Another dictionary describes the "parsec" unit (a well-known 'household term' to all astronomers and astrophysicists) as follows:
"A parsec is the distance from the Sun to an astronomical object which has a parallax angle of one arcsecond. (1 pc ≈ 206264.81 AU). A corollary is that 1 parsec is also the distance from which a disc with a diameter of 1 AU must be viewed for it to have an angular diameter of 1 arcsecond " parsec - sensagent dictionary
As we saw above, the radius of Earth's PVP orbit is 56.615328 Mkm. So let's perform the following thought experiment: we shall imagine a scenario in which Earth would travel in a straight line along its radius. In doing so, we shall use Earth's orbital speed, orbital radius and rate of precession - as proposed by the TYCHOS model.
In the TYCHOS:
Earth, moving at a speed of 1.601669km/h, will cover 14035.85km annually.
The radius of Earth's PVP orbit is estimated to be 56 615 328 km.
The (true) annual rate of precession is estimated to be 51.136" arcseconds (i.e. our ACP)
Hence, if Earth were to travel in a straight line along the RADIUS of its PVP orbit, it would employ about 4033.6 years to do so:
56 615 328 km / 14035.85km = 4033.62304384 years
In such a period, the stars would appear to ‘precess’ (according to the TYCHOS) by:
4033.62304384y X 51.136(periodic) arcseconds ≈ 206264.81” arcseconds
Wow - where did we just see this exact value? That's right: "1 parsec = 206264.81 AU !"
Let’s now multiply this value by 2Pi: 206264.81” X 2π = 1 296 000” arcseconds (i.e. a 360° circle: namely, our celestial sphere!)
You may now rightly wonder: "How can a value in units of arcseconds be 'commensurate with' (or even related to) a value in units of AU?" Well, this is when the Wikipedia entry for "Angular Diameter" can help us understand the optical issues involved:
"In astronomy, the sizes of celestial objects are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes. Since these angular diameters are typically small, it is common to present them in arcseconds (″). An arcsecond is 1/3600th of one degree (1°) and a radian is 180/π degrees. So one radian equals 3,600 × 180/π arcseconds, which is about 206,265 arcseconds (1 rad ≈ 206,264.806247"). These objects have an angular diameter of 1″:
- an object of diameter 725.27 km at a distance of 1 astronomical unit (AU)
- an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc)"
And, in fact, we see that: 206264.81 X 725.27km = 149 597 678.7 km – i.e. near-exactly 1 AU.
In any event, the fact that the stars would precess by 206264.81" arcseconds in a hypothetical scenario in which Earth were to travel the length of the radius of its PVP orbit (as proposed by the TYCHOS model) would certainly seem to merit further study. Unless, of course, you are inclined to dismiss it all as pure coincidence.
This concludes my account of how Earth's PVP orbit was determined - and consequently, how Earth's orbital speed of 1.6km/h was estimated.
Below are some basic Tychos data which you may wish to get familiar with - before continuing what should be a fascinating discovery journey.
Some SUN data (as of the TYCHOS model):
The Sun employs ca. 365.25 days to complete one revolution around its orbit.
As the Sun completes one revolution, Earth has moved by 14036 km (in the opposite direction) along its PVP orbit
The Sun completes 25344 revolutions around Earth in 25344 solar years (i.e. the "Great Year")
Circumference of Sun’s orbit: Ø 299 193 439 X π ≈ 939 943 910 km
The Sun's orbital speed: 107226 km/h
Daily distance covered by the Sun: 107226km/h X 24h ≈ 2 573 426 km
Annual distance covered by the Sun: 107226 km/h X 8766 h ≈ 939 943 910 km (i.e. the solar orbit's circumference)
Some EARTH data (as of the TYCHOS model):
Earth employs 25344 years to complete one revolution around its PVP orbit.
Circumference of Earth’s PVP orbit: Ø 113 230 656 X π ≈ 355 724 597 km
Earth's orbital speed: 1.601169 km/h (or 0.9949197 mph – i.e. roughly 1 mph)
Daily distance covered by Earth: 1.601169 km X 24 h ≈ 38.428 km
Annual distance covered by Earth: 1.601169 km/h X 8766 h ≈ 14036 km
In the next chapter, we shall see how the TYCHOS elegantly accounts for our solar vs sidereal days & years - and why the same cannot be said for the Copernican explanations for these fundamental solar periods.