Chapter 23: Are the stars much closer than believed?

The most indigestible aspect of the heliocentric theory is, undoubtedly, its implications for the extravagant sizes and remoteness of the stars. In any event, the idea that some of the visible stars in our skies would be located several thousands of light years away is simply ludicrous. Let's pause for a moment to consider what exactly the distance known as "1 LIGHT YEAR" implies - and how it translates in units of kilometers:

1 AU (average Earth-Sun distance) = 149 597 870.7 km (or roughly 149.6 Mkm)

1 LIGHT YEAR = 63241.1 AU = 9 460 730 472 580.8 km (or roughly 9.46 TRILLION kilometers!)

Ever since the Copernican theory came along, the apparent angular diameter of the stars as perceived from Earth by the human eye has been one of the most hotly debated issues of astronomy. Since the theory implied that the stars were hugely more distant than previously believed, it became imperative for the Copernican advocates to find some justification for the apparent size of the distant stars. This, because the stars in our skies (especially the largest or closest “first-magnitude stars”) appear to our naked eye to be far too large, if they were to be as formidably distant as currently claimed.

Let me use a real photograph of our night skies to illustrate the issue at hand. Note how the apparent diameter of the star Sirius seems to be roughly the same size, or even perhaps a tad larger, than that of Jupiter - as viewed from Earth by a naked-eye observer:

That’s right: if we were to trust our own eyes (something we may all probably need to learn anew!), we would have to conclude that Sirius is about 8834 times larger than the Sun. That is, of course, assuming that Sirius is truly as distant as currently claimed - i.e. 8.6 light years (or 543865 times further away than the Sun). Yes, that's more than HALF A MILLION times more distant than our Sun (which subtends only about 0.5° in our sky)!

Our Moon also subtends about 0.5° in our sky. Now, take a good look at the above photograph - and compare the visible sizes of the Moon and Sirius. Does Sirius appear to be several million times smaller than the Moon - the angular diameter of which is similar to our Sun? Of course not.

Moreover, we would have to accept that the most of the largest stars in our skies are hundreds of times larger than the Sun. As it is, this is precisely what Tycho Brahe held as the most unacceptable notion put forth by the Copernicans: the sheer absurdity of the gigantic star sizes and distances their novel model implied. Over the last centuries, volumes of science literature have sought to explain the apparent optical aberration of the observed star sizes. Ironically, it was that epochal technological advancement - the telescope - that provided the Copernicans with some "optical justification” (or, if you will, another sort of 'aberration of light excuse') for the pesky problem, courtesy of Astronomer Royal George Airy (yes, the same guy who disproved James Bradley's "aberration of starlight"!...)

Today, young astronomers are taught that the observed dimensions of the points of light emanating from the stars are totally spurious because they are artificially enlarged as they traverse Earth’s atmosphere. A phenomenon known as 'diffraction' would cause the angular diameter of the stars to appear much, much larger than they are in reality. Here’s a quote from Wikipedia describing “the Airy disk” diffraction phenomenon:

"AIRY DISK : The resolution of optical devices is limited by diffraction. So even the most perfect lens can’t quite generate a point image at its focus, but instead there is a bright central pattern now called the Airy disk, surrounded by concentric rings comprising an Airy pattern. The size of the Airy disk depends on the light wavelength and the size of the aperture. John Herschel had previously described the phenomenon, but Airy was the first to explain it theoretically. This was a key argument in refuting one of the last remaining arguments for absolute geocentrism: the giant star argument. Tycho Brahe and Giovanni Battista Riccioli pointed out that the lack of stellar parallax detectable at the time entailed that stars were a huge distance away. But the naked eye and the early telescopes with small apertures seemed to show that stars were disks of a certain size. This would imply that the stars were many times larger than our sun (they were not aware of supergiant or hypergiant stars, but some were calculated to be even larger than the size of the whole universe estimated at the time). However, the disk appearances of the stars were spurious: they were not actually seeing stellar images, but Airy disks. With modern telescopes, even with those having the largest magnification, the images of almost all stars correctly appear as mere points of light.”

George Airy - Wikipedia

In short, Airy claimed that we cannot trust our eyes when it comes to judging the angular diameters of the stars, since points of light are distorted / enlarged as they traverse Earth’s atmosphere. However, there’s an obvious problem with Airy’s theory: why then wouldn’t the points of light emanating from our planets (e.g. Venus or Jupiter) be similarly affected? Doesn’t the light emanating from our planets also traverse our atmosphere - much like that emitted by the stars? Of course it does. Tycho Brahe’s estimate of the angular diameter of Vega (a so-called “first-magnitude star”) was 120 arcseconds, or only about 16 times smaller than the angular diameter subtended by the Sun (1920 arcseconds). Now, many of you will probably scoff at Brahe's “generous” estimate of the perceived angular size of Vega, so here’s a comparative graphic I made to illustrate what this would look like:

Big dot = the Sun. Small dot = a 1st magnitude star such as Vega, visually 16 times smaller than the Sun, according to Tycho Brahe.

Indeed, the small dot is only 16 times smaller than the big dot (representing the Sun). All in all, it doesn’t look too different from what we can see in reality with our own eyes, does it? As you can see (with your own eyes), Tycho Brahe's contention (that 1st magnitude stars such as Vega are only 16X smaller than the sun) would seem quite reasonable after all. Now consider this: Vega (the second-brightest star in the northern celestial hemisphere, after Arcturus) is currently believed to be 25 light years away, i.e. 1 583 000 times (yes, more than 1.5 million times!) further away than our Sun. Yet, Vega’s diameter is estimated to be only about 2.3 times larger than that of the Sun. Now, if I enlarged the big dot in my above comparative graphic 2.3 times, then scaled it down 1.5 million times, would it possibly be visible from Earth with any sort of telescope? I trust that you will realize the absurdity of it all. But it gets worse.


HOW CAN WE SEE SO MANY STARS WITH OUR NAKED EYES?

1 AU (average Earth-Sun distance) = 149 597 870.7 km (or roughly 149.6 Mkm)

1 Light Year = 9 460 730 472 580.8 km (or roughly 63241 AU !)

It is a matter of historical record that Tycho Brahe rejected the idea of the implied Copernican star sizes and distances. This conviction may be phrased in a question such as, “why would Alpha Centauri (our nearmost star) be so enormously more distant than, say, Saturn?” To be sure, this still-unanswered question was precisely what most bothered Tycho Brahe about the heliocentric Copernican theory.

“In the absence of any observed stellar parallax, Tycho scoffed for example at the absurdity of the distance and the sizes of the fixed stars that the Copernican system required: Then the stars of the third magnitude which are one minute in diameter will necessarily be equal to the entire annual orb [of the earth], that is, they would comprise in their diameter 2284 semidiameters of the earth. They will be distant by about 7850000 of the same semidiameters. What will we say of the stars of first magnitude, of which some reach two, some almost three minutes of visible diameter? And what if, in addition, the eighth sphere were removed higher, so that the annual motion of the earth vanished entirely [and was no longer perceptible] from there? Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.”

Tycho Brahe’s Critique of Copernicus and the Copernican System by Ann Blair (1990) from Journal of the History of Ideas 51(3): 355-377.

Here is the inescapable question our world's astronomers should be confronted with: how can so many stars possibly be visible to our unaided eyes?

If we consider the distances currently claimed for one of our brighter stars, Deneb (a.k.a. Alpha Cygni), the whole affair becomes well and truly outlandish. Deneb is said to be a good 200 times larger than our Sun - but we are also told that it is a whopping 2600 LY away from our eyes - or about 164 426 800 AU!

Well, that's over 164 MILLION times(!) further away than the Sun - or if you prefer, 24 598 249 280 000 000 km...

Yet, Deneb is one of the brightest “naked-eye stars” in our skies!

“A blue-white supergiant, Deneb is also one of the most luminous stars. However, its exact distance (and hence luminosity) has been difficult to calculate; it is estimated to be somewhere between 55,000 and 196,000 times as luminous as the Sun.”

— from Wikipedia entry on “Deneb”

Huh? "Between 55,000 and 196,000 times as luminous as the Sun"?... With such a vast range of brightness (or luminosity) estimates, one may suspect that these estimates are no more than wild guesses. Besides, could these formidable luminosity estimates just be a way of "justifying" the immense stellar distances that the Copernican model requires? The above Wikipedia page for star Deneb goes on to say that,

“One 2008 calculation using the Hipparcos data [gathered by ESA’s Hipparcos satellite] puts the most likely distance at 1550 light-years, with an uncertainty of only around 10%.”

Yet, some modern planetariums have Deneb at a distance of 3227 light years, i.e. over twice as distant! Do the stellar distance estimations of our world’s astronomers ever agree with each other? Is star Deneb 1550, or 2600 - or 3227 light years away? Evidently, no one seems to know with any degree of precision! I, for one, grew up with the notion that astronomy was far more exacting than this. Virtually nothing adds up with these claimed star distances and luminosities - and the wildly conflicting estimates of the same. They are all, as TV-celebrity Carl Sagan liked to say, “extraordinary claims that require extraordinary evidence”. It should thus come as no surprise that - as we shall see further on - several independent astronomers have, in later years, vigorously questioned NASA and ESA (the European Space Agency) over their claimed star distances published in their official tables and catalogues.

At this point, you (the reader) will probably ask yourself: "Can the TYCHOS model provide any mathematical argument in support of the notion that the stars would be much closer than currently believed?" The answer to this question is in the affirmative. Let's now see how and why.

THE TYCHOS MODEL'S "42633-reduction FACTOR"

As we have seen, in the TYCHOS model, Earth only moves by 14036 km every year - or by 7018 km every 6 months.

Of course, star distances have always been measured / computed by astronomers under the assumption that Earth moves around the Sun. They assume that Earth's orbital diameter is 299 200 000 Mkm (or almost 300 million kilometers). Hence, they will 'take a picture' of a nearby star "X" (say, on June 21). Then, after six months (December 21) they 'take another picture' of star "X". They then look at how much star "X" has moved in relation to the 'fixed stars' (i.e. the much more distant background stars) and, with a simple trigonometry calculus, they estimate the distance from Earth of star "X".

Now, if Earth does NOT move laterally every six months by 299.2 million km - but only by 7018 km (as stipulated in the TYCHOS model) - it follows that the currently-accepted star distances are ALL inflated by a factor of:

299 200 000 ÷ 7018 ≈ 42633

This will be our proposed reduction factor for ALL of the stellar distances listed in the NASA and ESA catalogues.

This also means that, in the TYCHOS, the distance unit known as “1 Light Year” corresponds to less than 1.5 AU :

9 460 730 472 580.8 km (i.e. one “light year”) ÷ 42633 ≈ 1.4834 AU

Let's now put our TYCHOS reduction factor to the test - and see how close our closest star system (the Alpha Centauri binary pair) would be.

Alpha Centauri is said to be 4.37 LY away. In the TYCHOS, therefore, Alpha Centauri (our very closest star system) would be located about 6.5AU away from Earth :

4.37LY X 1.4834 ≈ 6.48 AU

This is quite interesting, for this TYCHOS-computed distance (6.48 AU) to Alpha Centauri would place our nearmost star at a distance somewhere 'between' Jupiter (4.2 AU) and Saturn (8.5 AU). Note however that the Alpha Centauri binary system is NOT located in the same plane as our solar system – but some 62° ‘below’ it.

Undoubtedly, Tycho Brahe would be most satisfied with that, since his primary objection to the Copernican model was that the stars would have to be “absurdly large and distant” and that there would have to be a most unlikely enormous void between Saturn and our nearmost stars. In fact, Tycho Brahe’s expert opinion was that the stars were “located just beyond Saturn and of reasonable size”.

“It was one of Tycho Brahe’s principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn (then the most distant known planet) and the eighth sphere (the fixed stars).” — from the Wikipedia entry on “Parallax

In any event, should Alpha Centauri be located between Jupiter and Saturn, this would certainly help explain why we can see so many stars with our naked eyes and why first magnitude stars (such as Sirius or Vega) appear to be as large or only marginally smaller than, for instance, Jupiter.

Earlier on we saw that Vega, according to the expert judgment of Tycho Brahe, subtended 1/16th of the diameter of the Sun. Again, Tycho Brahe's main objection to the Copernican model was that the stars could not be so hugely distant - or else they would ALL have to be hugely larger than our sun. Brahe reckoned instead that the (true) respective diameters of the visible stars were more homogeneous, i.e. only somewhat larger or smaller than our Sun (as opposed to dozens or hundreds of times larger). One must admit that this sounds like sensible logic - for why the overwhelming majority of the stars in our 'cosmic neighborhood' be much, much larger than our Sun? From a purely statistical viewpoint, this simply doesn't make sense. But let's now take a comparative look at the estimated angular diameter of Vega - as proposed by Brahe, Galileo and our modern astronomers. Remember that Vega is reckoned today to be only 2.3X larger than the Sun (and not dozens or hundreds of times larger):

TYCHO BRAHE's estimate of VEGA's angular diameter: 120" arcseconds

GALILEO GALILEI's estimate of VEGA's angular diameter: 5" arcseconds

MODERN ASTRONOMERS' estimate of VEGA's angular diameter: 0.0029" arcseconds


We see that today, modern astronomers estimate the angular diameter of VEGA to be:

  • 1724X smaller than GALILEO's estimate

and

  • 41379X smaller than BRAHE's estimate (or very close to the TYCHOS' 42633 reduction factor).

Let's now do some simple maths and see if we may at least "rescue" the notion that VEGA is 2.3X larger than the sun - as currently estimated.

VEGA is claimed to be 25.04 light years away. In the TYCHOS model, 1 light year = 1.4834 AU (i.e. 42633X less than 1 light year).

Hence: Earth --> VEGA distance : 25.04 X 1.4834 = 37.144 AU.

Remember now that Tycho Brahe estimated VEGA's angular diameter to be about 16X smaller than our sun.

Well, if Vega is truly 37.144 times further away than the sun (and appears to be 16X smaller), this would indeed make Vega about 2.3X larger than the sun :

37.144/16 = 2.3215

In summary :

  • Tycho Brahe may have been right all along about the visible size of Vega (and the stars in general).

  • My proposed reduction factor of 42633 (for the currently estimated star distances) may well be correct - and seems to agree with Brahe's observations.

  • If the stars are 42633X closer than currently reckoned, their true diameters may not necessarily need to be 42633X smaller than current values.

In any event, further study is needed in the field of optical astronomy, a branch of human knowledge rife with controversy still today. To be sure, the long-debated question of the perceived star sizes and how they are affected by various phenomena (e.g. "Airy disk", diffraction, assorted optical aberrations, etc.) is far from being a settled matter.


IS OUR MOON SAYING GOOD-BYE TO MOTHER EARTH?

Modern astronomers will tell you that “the Moon recedes from Earth each year by (a little less than) 4 centimeters”. We shall now see how the Tychos model can account for - and dismantle - the rather alarming notion that our Moon would be slowly but surely "saying goodbye" to Earth!

“The Moon is gradually receding from the Earth, at a rate of about 4 cm per year. This is caused by a transfer of Earth's rotational momentum to the Moon's orbital momentum as tidal friction slows the Earth's rotation.” "WHAT WILL BE THE FATE OF OUR MOON?" - Physlink.com

“Although the moon’s distance from earth varies each month because of its eccentric orbit, the moon’s mean distance from Earth is nonetheless increasing at the rate of about 3.8 centimeters (1.5 inches) per year. That’s about the rate that fingernails grow.” "WAYWARD MOON RECEDING FROM EARTH" - EarthSky.org

According to the TYCHOS - the Moon is not receding from Earth and is not going to vanish in space - and thankfully so! Copernican astronomers are, of course, unaware of the existence of the PVP orbit (i.e. the 25344-year circle around which the Earth-Moon system revolves). Hence, their computations related to the Moon’s apogee oscillations will always fail to account for this ‘extra revolution’ (i.e. the Great Year) of the Earth-Moon system. As they measure (against the background stars) this minute “4-cm annual recession” of the Moon, they will conclude that “our Moon is slowly drifting away from Earth”.

However, we know that the Moon-Earth distance is constantly oscillating back and forth (i.e. cyclically approaching and receding). As we saw in Chapter 13, the Moon oscillates back and forth by 42108km. So could this possibly be connected with what astronomers interpret as an annual "4-cm recession of the Moon"? Let's see if this might be the case:

Since the Moon's apsidal precession amounts to 42108km - and since the Earth-Moon system revolves around a circle in 25344 years, we may calculate by how much the Moon's apogee would 'drift' annually in relation to the stars (as the Earth-Moon system revolves 360° in 25344 years):

42108km ÷ 25344y = 1.66km

Now, astronomers are of course using the stars as a reference background against which they gauge our Moon's annual displacements. However, we just saw that the stars may well be 42633 times closer than currently believed. So let's divide the above figure by 42633 - and see what we obtain:

1.66km ÷ 42633 = 0.0000389km = 3.89cm (i.e. very much what astronomers claim to be "the Moon's annual farewell rate"!)

In other words, the Moon is (thankfully) not parting from us anytime soon. What astromomers are "seeing" is just the very slow, 25344-year secular precession of the Moon's apsides - given by the tranquil 1-mph-revolution of the Earth-Moon system around the PVP orbit.

At this point, I must ask the reader to ponder this 'philosophical' question: since astronomers can detect minuscule variations such as this "4 centimeters-per-year recession of the Moon", how could this possibly be reconciled with the idea that ALL of our celestial bodies (including Earth) would be flying around at supersonic speeds? Surely, SOME BODY must be moving much, much slower - if such a tiny "4cm-per-year" variation can be detected? Well, the TYCHOS submits what you may agree is a quite sensible answer to that question: Earth's orbital speed of only 1.6km/h.

We shall now see how some other well-known astronomical data (related to stellar motions) go to support my proposed “42633 reduction factor”.


ABOUT OUR RELATIVE SPEED VIS-A-VIS THE STARS

The velocity value of ≈20 km/s (or more precisely, 19.4 km/s) keeps popping up all over astronomy literature. As shown in the below-quoted papers, there appears to be some sort of general consensus regarding this velocity value, although its actual meaning is rather nebulous. “A 20 km/s speed in relation to what?”

Nonetheless, it appears this value is meant to represent the “perceived average relative speed” between our solar system and the stars (as computed under the tenets of the Copernican theory and its implied Earth > Stars distances).

“…The solar system itself has a velocity of 20km/s with respect to the local standard of rest of nearby stars…”

— p. 10, Cross-Calibration of Far UV Spectra of Solar System Objects and the Heliosphere edited by Eric Quémerais, Martin Snow and Roger-Maurice Bonnet

“…the mean motion of the Solar system at 20 km/sec relative to the average of nearby stars”.

The ABC’s of Distances by Edward L. Wright (2011)

“The average radial velocity of the stars is of the order of 20 km per second”.

— p. 113, The Motion of the Stars by J. S. Plaskett (1928) for Journal of the Royal Astronomical Society of Canada, Vol. 22, p.111

“The Sun’s peculiar velocity is 20 km/s at an angle of about 45 degrees from the galactic centre towards the constellation Hercules.”

Spiral Galaxies by Dmitri Pogosian (2018) for University of Alberta, Astronomy 122: Astronomy of Stars and Galaxies

“The Sun is moving towards Lambda Herculis at 20km/s. This speed is in a frame of rest if the other stars were all standing still.”

What is the speed of the Solar System? by Deborah Scherrer, Hao Tai and J. Todd Hoeksema (2017) for Stanford University Solar Center

“The speed of the Sun towards the solar apex is about 20 km/s. This speed is not to be confused with the orbital speed of the Sun around the Galactic center, which is about 220 km/s [or 800.000 km/h] and is included in the movement of the Local Standard of Rest.”

— Wikipeda entry on “Solar apex

Here we have a more detailed account as to exactly how a ca. 20 km/s motion between the Sun and the stars was determined.

Furthermore, here are some more recent quotes concerning this approximate 20 km/s velocity (or more precisely, 19.4 km/s).

“The point on the celestial sphere, in the constellation Hercules (at about RA 18h, Dec. +30°), toward which the Sun is moving with respect to the Local Standard of Rest, at a rate of about 19.4 km/s (about 4.09 AU/year). As the Sun slowly orbits the galactic center, nearby stars (as seen from Earth) appear to move away from the solar apex because of the Sun’s relative velocity.”

Solar Apex by David Darling (2017, daviddarling.info)

Solar apex: The point on the celestial sphere toward which the Sun is apparently moving relative to the Local Standard of Rest. Its position, in the constellation Hercules is approximately R.A. 18h, Dec. +30°, close to the star Vega. The velocity of this motion is estimated to be about 19.4 km/sec (about 4. AU/year). As a result of this motion, stars seem to be converging toward a point in the opposite direction, the solar antapex.”

Antapex: The direction in the sky away from which the Sun seems to be moving (at a speed of 19.4 km/s) relative to general field stars in the Galaxy.”

An Etymological Dictionary of Astronomy and Astrophysics by M. Heydari-Malayeri (dictionary.obspm.fr)

The last sources quoted above seem to agree on the more exacting figure of 19.4 km/s rather than the rounded 20 km/s value. Hence, in the interest of accuracy, we should probably use this value of 19.4 km/s that appears to be our modern-day, currently-accepted value. Before we get on, let us convert this value from km/s to km/h.

19.4 km/s X 3600 = 69840 km/h

Note that this velocity is essentially described as representing the motion of the Solar system relative to the stars.

Now, remember that in the TYCHOS, Earth’s orbital velocity is deemed to be 1.6 km/h. This would constitute, of course, our 'proper motion' in relation to the stars. Hence, if the stars are much closer to us than currently believed, their perceived velocity as viewed from Earth would be “inflated” by our previously-computed “42633 star-distance reduction factor”. So let us divide this velocity by our proposed reduction factor and see what we obtain:

69840 km/h / 42633 ≈ 1.638 km/h

Good heavens! This is very nearly 1.601169 km/h – i.e. Earth’s orbital speed as proposed by the TYCHOS model!

In other words, this “general velocity perceived to exist between the stars and our Solar System” (ca. 19.4 km/s) would seem to support both of the TYCHOS model’s "boldest" - and most fundamental assertions:

• Earth moves around space at the very tranquil speed of 1.6 km/h.

• The stars are about 42633 X closer than currently estimated.


In the next chapter, we will see how Earth's claimed translational velocity (i.e. its supposed orbital speed of ca. 30km/s - or 107226km/h - as of Copernican theory) has never been experimentally verified nor confirmed. This is a hard fact which no earnest astronomer can deny - but relativists will unfailingly roll their eyes and tell you that "Einstein has long explained why Earth's motion in space is impossible to measure!!!"...