Chapter 11: Earth’s PVP orbit
11.1 Introduction
We shall now proceed to see how the TYCHOS model accounts for the Precession of the Equinoxes or, as modern astronomers like to call it, the General Precession. The name change is explained in 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. Currently, the triple star system Polaris acts as our north star, but we know that the binary star system Thuban was our north star roughly 4200 years ago, and that in about 11500 years from now (~13500 AD) the binary star system Vega will play the role as north star. This is generally agreed upon by astronomers of all stripes.
Figure 11.1 is a conventional plot of the circular motion responsible for the cyclical change in north stars. Note that, if viewed from an imaginary spaceship hovering above our north pole, the direction of the motion is clockwise.
Fig. 11.1 Today, our north star is Polaris. In about 11500 years from now, our north star will be Vega. (Image source: Oakton Edu (opens in a new tab))
Assuming that, contrary to Copernican dogma, Earth does not wobble around its polar axis, but moves clockwise in a local orbit under the pole stars, the same effect would be produced. It may at first seem highly unorthodox to assign a local orbit to Earth, but is it really? After all, every single celestial body in our skies is known to move in a local orbit of its own. Let us put this proposition to the test and see if we can determine at what speed the Earth would travel as it completes this circular journey, from Polaris to Vega and back again to Polaris (hence, PVP). To do so, we will first need to estimate the diameter of this local orbit.
11.2 The PVP orbit: Earth’s path below our north stars
The following figures illustrate the method used to estimate the diameter of the PVP orbit.
Fig. 11.2 The width of the Earth's 25344-year journey underneath our north stars subtends ca. 44°.
The diameter of the PVP orbit can be estimated with a simple calculation. Assuming the Sun travels at 107226 km/h and covers the distance between Polaris and Vega in 44 days (1056 hours), we would have:
107226 km/h x 1056 h = 113 230 656 km = the diameter of the PVP orbit
113 230 656 km x π = 355 724 597 km = the circumference of the PVP orbit
Fig. 11.3 How the diameter of Earth's PVP orbit was estimated
Figure 11.3 is a conceptual graphic showing how the Sun would ‘visually’ employ around 44 days to cover the distance between Polaris and Vega, as viewed under an imaginary circumpolar orbit of the Sun. Conceptual graphics can be somewhat challenging to translate in the mind, but they are the best I can do to ‘materialise’ the train of thoughts that led me to formulate the PVP orbit in the TYCHOS model.
Fig. 11.4 This illustration shows in greater detail how all this would be consistent with the geometry implied by the proposed PVP orbit, as well as with officially calculated (heliocentric) predictions.
→ 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° from Polaris).
→ In about 11500 years, Vega will be our north star (at 86° of declination).
In about 11500 years, Earth’s axis will, according to official predictions, be tilted by 22.9°, as opposed to the current 23.4°, for a total axial rotation of 46.3° in relation to the 180° northern celestial hemisphere. 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 is because, in the TYCHOS model, as we shall see later on, the Earth-Vega distance is estimated to be ~37 astronomical units (AU). The PVP orbit’s diameter of 113.2 Mkm (0.757 AU) amounts to approximately 2.05% of 37 AU. The 3.7° difference observed above amounts to approximately 2.05% of 180°.
11.3 Estimating the orbital speed of Earth
The time required for a complete Precession of the Equinoxes is often referred to as ‘the Great Year’. Copernican astronomers estimate the duration of the Great Year to be 25771 solar years. However, the TYCHOS model allows to correct this estimate to 25344 solar years (henceforth referred to as the TYCHOS Great Year, or TGY), a claim that will be extensively tested and cross-verified throughout this book. For reasons that will be clarified in Chapter 12, the TGY is about 1.68% shorter than the Copernican Great Year.
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
That’s right: in the TYCHOS model, Earth’s proposed orbital speed is approximately 1 mph! Could old Mother Earth really be strolling along at window-shopping pace, and not a breakneck speed, as the heliocentrists demand?
When I discovered Earth’s languid pace around the PVP orbit, my very first thought was that life on Earth may not only benefit from but actually require a very low orbital speed. 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 and biological life? It would seem that this serene situation enjoyed by our planet is almost like that of a ship gently circling around the calm zone in the eye of a tropical storm, with everything else spinning in the opposite direction.
For now though, I shall leave my poetic and philosophical musings aside and proceed to put this posited orbital speed of Earth to the test in systematic 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 long series of puzzles and enigmas that have been haunting not only astronomers but the entire scientific community for centuries.
We can now work with an empirically testable Sun-Earth velocity ratio. To be sure, this is very different from the heliocentrists’ claim 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 which in the dire absence of any observational or experimental evidence to support such formidable, hypersonic speeds. One may say that these outlandish velocities proposed by Copernican theorists have been an offense to human intelligence all along since they imply that our solar system travels across space by more than 7 billion kilometers each year. Yet, our surrounding stars, which allegedly all revolve in unison around the centre of our galaxy, only exhibit infinitesimal ‘proper motions’ in any direction from one year to the next. In fact, the only common motion of the stars is that constant annual ~50 arcsecond eastward drift known as the General Precession. In the TYCHOS model, of course, this ~50 arcsecond eastward drift of the entire firmament is simply an optical effect of 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”, will by now have realized that the results of that experiment are actually supportive of the TYCHOS model. The objective of the experiment was to measure Earth’s translational velocity across space (or through the ‘aether’), expected to be in the vicinity of 107000 km/h, yet nothing of the sort was found. Here is what we can read in the astronomy literature:
Fig. 11.5 Source: "The Methodology of Scientific Research Programmes" (Book 1) (opens in a new tab) by Imre Lakatos (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 assertions would seem to be congruent with the TYCHOS model’s proposed snail-paced motion of Earth, as it revolves in the opposite direction of the system’s other components. In any event, the long series of 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 detected speeds 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, as we shall see in Chapter 24, rather support the notion of an orbital speed of 1.6 km/h.
11.4 Estimating the annual constant of precession (ACP)
If we consider that 25344 years represents a full 360° equinoctial precession, we can easily determine how long it takes for Earth’s equinoctial axis to rotate by 1° in relation to the firmament. For the sake of curiosity, let us see if we can correlate the TGY with the observed synodic periods of Mars, Venus, Mercury and the Moon:
1 equinoctial precession = 25344 years (1 TGY)
→ 1° of precession = 25344 / 360 = 70.4 solar years = 25713.6 days
Mars’ synodic period = 779.2 days → 33 synodic periods of Mars (779.2 x 33) = 25713.6 days
Venus’ synodic period = 584.4 days → 44 synodic periods of Venus (584.4 x 44) = 25713.6 days
Mercury’s synodic period = 116.88 days → 220 synodic periods of Mercury (116.88 x 220) = 25713.6 days
The Moon’s synodic period = 29.22 days → 880 synodic periods of the Moon (29.22 x 880) = 25713.6 days
We can 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 in every century (100 years) they will process by:
100 / 70.4 = 1.42045° - or 5113.63" arcseconds
Earth’s annual ‘equinoctial procession rate’ = 5113.6363 / 100 = 51.136" arcseconds
I will henceforth refer to this all-important periodic value of 51.136″ as our ‘annual constant of precession’(ACP). Interestingly, back in the 16th century, when most astronomers estimated the annual precession to be about 50″ or less, Longomontanus and 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)." "Longomontanus on Mars: The Last Ptolemaic Mathematical Astronomer Creates a Theory" (opens in a new tab) by Richard Kremer (2015)
Further on in the book, we shall see how the ACP, derived from the Earth’s tranquil revolution around the PVP orbit, admirably accounts for the observed motions of our Solar System.
11.5 Mars’ closest passages to earth, in the middle of the PVP orbit
As we saw in Chapter 5, Mars can transit as close as 0.373 AU from Earth (as it did in 2003). However, as shown in Table 11.1, the mean figure of its closest passages is about 0.379 AU, or just about 56.6 Mkm (i.e. the radius of the PVP orbit).
Table 11.1
I’d like to state for the record that I only realized this astounding fact long after I had estimated the diameter of the PVP orbit (113.2 Mkm, or 2 x 56.6 Mkm). Needless to say, it lends considerable support to the proposed diameter of the PVP orbit—unless you are willing to chalk it all up to sheer coincidence.
Let us examine the figures obtained so far to see if we can identify any possible correlations:
The mean Earth-Sun distance = 149.5978707 Mkm (1 AU)
Mars’ mean perigee distance = 56.615328 Mkm
Ratio between the mean Earth-Sun distance and the closest Earth-Mars distance: → 149.5978707 Mkm / 56.615328 Mkm = 2.6423
My estimation of the PVP orbit’s diameter = 113.230656 Mkm. The Sun’s orbital diameter = 299.193439 Mkm.
Ratio between the Sun’s orbital diameter and the PVP orbit: → 299.193439 Mkm / 113.230656 Mkm = 2.6423
So, if Mars regularly transits in the middle of the PVP orbit, what long-term implications would this have under the TYCHOS paradigm? Well, as Patrik Holmqvist and I proceeded to fine-tune the Tychosium simulator, we were obviously curious to see how Mars would ‘behave’ over a full Great Year of 25344 solar years. The result of this test is illustrated in Figure 11.6 which was put together by simply superimposing 4 screenshots from the Tychosium simulator, each one of them separated by 6336 years. All in all, the TYCHOS model reveals the breathtaking beauty and geometric harmony of our Solar System—in an even more spectacular manner than Johannes Kepler ever envisioned in his dreamy “Harmonices Mundi” treatise.
Fig. 11.6 The ‘central role’ of Mars in our Solar System – as it regularly transits in the middle of the PVP orbit.
11.6 The PVP orbit and the parsec
We shall now look at a most remarkable accord between Earth’s PVP orbit and the astronomical unit known as the ‘parsec’ (a household term among astronomers and astrophysicists). Here are two official definitions of the parsec:
"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 (opens in a new tab)
"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 (opens in a new tab)
At this point it would be interesting to perform a thought experiment using the orbital speed (1.6012 km/h), orbital radius (56.615328 Mkm) and ACP (51.136″) estimated with the help of the TYCHOS model. Let us imagine a scenario in which Earth travels in a straight line along its orbital radius:
Annual displacement of the Earth at 1.601169 km/h ≈ 14035.85 km
Time required to travel 56 615 328 km in a hypothetical straight line along the orbital radius:
→ 56 615 328 km / 14035.85 km = 4033.62304384 years
Amount of precession during 4033.62304384 years:
→ 4033.62304384 x 51.136 (periodic) arcseconds = 206264.81 arcseconds
→ 206264.81 arcseconds = 206264.81 AU = 1 parsec
→ 206264.81 x 2π = 1296000 arcseconds
→ 1296000 arcseconds = 360° circle = our celestial sphere
You may now rightly wonder how a value in units of arcseconds can be commensurate with or even related to a value in AU. 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 206265 arcseconds (1 rad ≈ 206264.806247"). 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)"
Source: "Angular Diameter" - Wikipedia (opens in a new tab)
In fact, if we multiply 725.27 km by 1296000 arcseconds (a full circle), we obtain 939 949 920 km, which is the Sun’s orbital circumference. Remarkably enough, we also see that 206264.81 x 725.27 km equals 149 597 678.7 km—near-exactly 1 AU. I am sure you will agree that the fact that the stars would precess by 206264.81 arcseconds in a hypothetical scenario which has the Earth travelling the length of the radius of its PVP orbit is quite significant and worthy of consideration.
This concludes my account of how Earth’s PVP orbit was determined and, as a result, how Earth’s orbital speed of approximately 1.6 km/h was estimated. Below are some basic values obtained with the TYCHOS model which you may wish to get familiar with before continuing on your journey of discovery.
TYCHOS DATA for the Sun:
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 "Tychos Great Year" - or "TGY")
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 ≈ 2 573 424 km
Annual distance covered by the Sun: 107226 km/h X 8766 h ≈ 939 943 910 km (i.e. the solar orbit's circumference)
TYCHOS DATA for the Earth:
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 model elegantly and accurately accounts for solar vs sidereal days and years, and why the same cannot be said for the heliocentric model.