Johannes Kepler famously stated that
“Mars is the key to understanding the solar system.”
Kepler, of course, notoriously obsessed about Mars for five harrowing years and, in his correspondence with fellow scientists, referred to his relentless pursuit as “his personal war on Mars”. We now know that (presumably out of sheer exhaustion) Kepler eventually resorted to the shameless fudging and manipulation of Tycho’s data published in his Astronomia Nova, a book still regarded as the “Bible of the Copernican Revolution”. This shocking discovery by Prof. Donahue, the American translator of Kepler’s epochal treatise, was made in 1988. Now, if Kepler had to cheat to make his heliocentric model work, what does this tell us about the overall credibility of the Keplerian and Copernican theories?
It will remain a mystery why Kepler, Tycho’s “math assistant”, eventually dismissed his own master’s cosmic model in favor of the Copernican – and this in spite of having plotted (at some point of his strenuous war on Mars) a working diagram of Mars’s geocentric motions, titled De Motibus Stellae Martis. History books only tell us that Kepler, upon Tycho’s untimely death (at age 55), seized the bulk of his master’s laboriously-collected observational tables and annotations, only to set about flipping Tycho’s model on its head. Professor Donahue’s detailed descriptions of how Kepler fudged his all-important Mars computations (moulding them so as to make them “fit” with the core tenets of his thesis) make for a most compelling read:
This short article succinctly sums up Kepler’s falsification of his much-heralded master work, Astronomia Nova.
“Done in 1609, Kepler’s fakery is one of the earliest known examples of the use of false data by a giant of modern science. Donahue, a science historian, turned up the falsified data while translating Kepler’s master work, Astronomia Nova, or The New Astronomy, into English.”
— Pioneer Astronomer Faked Orbit Theory, Scholar Says by New York Times (January 23, 1990)
Kepler’s manipulative antics may well go down in history as the triumph of mathematical abstraction over the empirical method. In his urge to make the complex & bewildering behavior of Mars agree with the fledgling Copernican theory, Johannes Kepler not only misused and twisted — but outright subverted Tycho Brahe’s most exacting observational data acquired throughout his lifetime.
Mars’s two Empiric Sidereal Intervals (ESIs)
Let us presently take a look at what the Maya knew about Mars. The ancient Maya astronomers were clearly aware of the peculiar sidereal period(s) of Mars — as viewed from Earth. As they kept count of the amount of days needed for Mars to realign again with a given reference star, they saw that Mars had in fact two sidereal periods: a more frequent, lengthier one of about 707 days — the “Long ESI” — and an odd, shorter one of about 543 (± 6.79) days — the “Short ESI”.
It is the “Short ESI” (of ca. 543 days – or ca. 1.5 solar years) that is of primary interest to us. As will be comprehensively demonstrated in Chapter 7, the Copernican model cannot possibly account for this odd / shorter sidereal interval of Mars.
“We discuss here a kind of period that we call the empiric sidereal interval (ESI), which we define as the number of days elapsed between consecutive passages of Mars through a given celestial longitude while in prograde motion. At first glance, one would imagine that the ESI would fluctuate widely about some mean because of the intervening retrograde loop, which in the case of Mars occupies 75 days on average between first stationary (cessation of) and second stationary (resumption of normal W-to-E motion). However, a closer look at modern astronomical ephemerides reveals that for a practical observer there are really two ESIs, a lengthier one that includes the retrograde loop (the long ESI) and a shorter one that does not (the short ESI).”
— Ancient Maya documents concerning the movements of Mars by Harvey M. Bricker, Anthony F. Aveni and Victoria R. Bricker in Proc Natl Acad Sci U S A. (February 2001)
The above-linked paper (a highly-recommended read) describes in great detail the Maya astronomers’ exacting knowledge of Mars’s sidereal periods — although it ultimately fails to address the profound implications raised by the existence of these two ESI’s of Mars.
The binary nature of the TYCHOS system with Mars’s peculiar, epitrochoidal orbital motion around the Sun, geometrically explains why Mars can realign with a given star within as little as 543 (± 7) days, or about 1.5 years. In Maya astronomy, this ca. 543-day period is called the Short ESI (Empiric Sidereal Interval) whereas Mars’s “habitual”, longer sidereal period of ca. 707.5 days is called the Long ESI. So why is the currently-accepted value of Mars’s sidereal period “686.9 days” as computed by Kepler?
Well, here are the (observable) facts: Mars will typically realign with a given reference star on seven successive occasions in successive intervals of circa 707.5 days (on average) — but the eighth time around, Mars will realign with that same star in only about 543 (± 7) days. That is, over a ca. 15-year time span, Mars exhibits seven Long ESIs (of ca. 707.5 days) + one Short ESI (of ca. 543 days)!
Now, since 5495.5 / 8 = 686.9375 days, we can see how Kepler must have just “averaged out” these eight observable Mars periods in order to get his estimated sidereal period of Mars. As it is, we are told that this supposed 686.9-day period (said to represent one Martian year) is not something that can be observed from Earth. The (currently-claimed) Keplerian 686.9-day value of Mars’s sidereal period was just mathematically extrapolated on the assumption that Earth revolves around the Sun.
Yet Mars does indeed, in reality (and as can be directly observed), alternate its sidereal periods as of the above ESI sequence!
You may now rightly ask yourself, “How is this even possible? How can Mars realign with the same star — as seen from Earth — in two wholly different time periods (707.5 and 543 days)?” This is indeed a very good question. The short answer is: in the Copernican model, it simply can’t. In the TYCHOS model, it can and will naturally do so — for demonstrable, geometric reasons which I will now expound.
Please note that, in the TYCHOS, Mars does indeed have a 686.9-day period (or ca. 687d) — but that’s the period needed for Mars to revolve once around the Sun. Ergo, it is not Mars’s “true mean sidereal period” as Kepler had it. It is the period for Mars to return to its degree position relative to the Sun, as I have illustrated below.
Why is Mars behaving in this way? It will become clear as we take a look at the synodic period of Mars.
About the synodic period of Mars
We just saw that Mars’s “habitual” sidereal period (the Long ESI) lasts for around 707.5 days (about 23 days less than two solar years of 730.5 days. More precisely, Mars returns facing the same star 22.8 days earlier than the Sun does, in a two-year period). The average synodic period of Mars is 779.2 days; this is the time period needed for Mars to line up again with the Sun as viewed from Earth. We see that this is 48.7 days more than two solar years (730.5 + 48.7 = 779.2). Now, we also see that:
i.e. the average duration of the “retrograde periods” of Mars
This leads us to a most remarkable realization: since the two binary companions, Sun and Mars, are locked in a 2:1 orbital ratio, one might think that the two of them will “meet up” every 730.5 days (i.e. 2 solar years) ; but due to Mars retrograding biyearly by ca. 71.5 days (on average), Mars will “slip out of phase” with our timekeeper, the Sun — hence, with our earthly calendar. Therefore, Sun and Mars will conjunct (as viewed from Earth) only every 779.2 days
Thus, in 16 solar years MARS completes 7.5 synodic periods.
In 16 years, Mars and the Sun do in fact conjunct with Earth — although on opposed sides of our planet. Mars will need another 7.5 synodic cycles, for a total of 32 years (i.e. 2 X 16 or 15 + 17) to complete one of its 32-year cycles. Since Mars processes biyearly (vis-à-vis the Sun) by ca. 45 min. of Right Ascension (on average), in 32 solar years it will process by about:
a full 360° procession around its “host”, the Sun.
Next, we will see how the respective orbital paths of Sun & Mars, as concluded by Tycho Brahe, can and do indeed intersect in typical binary fashion — much like Sirius A and Sirius B.
The synchronized 2:1 binary dance of Sun and Mars
As mentioned earlier, Tycho Brahe’s boldest contention was, undoubtedly, that the orbits of Mars and the Sun intersect. Back then, Tycho’s opponents would jeer: “Absurd! Preposterous! Sooner or later, Mars and the Sun must collide!” Today, their ways may perhaps be excused for back in those days, no one was aware of the very existence of binary systems.
As you can see, the above orbital configuration is perfectly consistent with the models of Tycho Brahe and Pathani Samanta (as illustrated in Chapter 2) albeit with a little — yet crucial — addition: the clockwise orbit of Earth. For now, let us focus our attention on Mars and its peculiar motion around the Sun and Earth.
Seeing Mars’s path is essential viewing for the reader. It shows you the first version of what eventually became the TYCHOS Planetarium, a joint effort between my invaluable research assistant & computer programmer Patrik Holmqvist and yours truly. Naturally, our initial objective was to animate and digitally simulate the motions of Mars — under the TYCHOS model’s paradigm — so as to verify its sustainability. On my side, I provided the observational data (borrowed from official, undisputed astronomy tables — yet interpreted from a “Tychonic perspective”) while Patrik, on his side, translated it all into computer language.
The oddly-shaped “teardrop-loops” that Mars performs as it passes closest to Earth are, undeniably, a most difficult thing for the human mind to process. They are caused by the spirographic pattern of orbits in the shape of circles (and not ellipses or any other irregular shape) as they move in relation to one another. The “line” it draws is not circular but Mars is only ever moving in a circle, whose center is itself moving in a circle.
Once you overcome this cognitive hurdle, you will soon realize that it is nothing but a natural geometric consequence of a body revolving (in uniform circular motion) around another revolving body — the two of them remaining, at all times, “magnetically attached”. In fact, the Sun and Mars exhibit unequivocal evidence of being an interlocked binary pair.
In the TYCHOS model the Sun and Mars binary orbits are “interlocked” in a perfect 2:1 orbital resonance. However, this exact 2:1 Mars:Sun orbital ratio is not directly observable or noticeable from Earth, due to Mars’s peculiar epitrochoidal motion which causes it to return, every two solar years, at different celestial longitudes as illustrated below.
We may thus envision just why it has been nigh impossible, throughout the ages, for any observational astronomer to detect this harmonious 2:1 binary dance of the Sun and Mars — since Mars never returns to the same place within a 2-year period. Mars’s virtual “deferent” shown in the above graphic indicates Mars’s orbital offset (of ca. 22.2 Million km) in relation to the Sun’s orbit. The actual reason for this apparent offset of Mars’s circular orbit needs further study, yet it is fully consistent with observation — as I will now expand upon.
As it is, the motions of Mars posed the greatest difficulties to the astronomers of yore, Tycho included:
“We have seen that Tycho, like Ptolemy and Copernicus, assumed the solar orbit to be simply an excentric circle with uniform motion. But already in 1591, he might have perceived from the motion of Mars that this could not be sufficient, as he wrote to the Landgrave that ‘it is evident that there is another inequality, arising from the solar excentricity, which insinuates itself into the apparent motion of the planets, and is more perceptible in the case of Mars, because his orbit is much smaller than those of Jupiter and Saturn.’ ”
— p.346, Tycho Brahe: a picture of scientific life and work in the sixteenth century by John Louis Emil Dreyer (1890)
Mars has been the single most problematic body of observational astronomy, and the reasons for this should become clear as we go along. All over the literature, you may find statements hinting at the “uniqueness” of Mars’s cosmic behavior in comments like:
“Among the planets, Mars is a maverick, wandering off from the deferent-epicycle model more than most of the other planets.”
— The Ballet of the Planets: A Mathematician’s Musings on the Elegance of Planetary Motion by Donald Benson (2012)
Of course, in the TYCHOS model, one may easily imagine why Mars is a “maverick” of sorts — for the simple reason that it is the binary companion of the Sun. In hindsight, one of Kepler’s most famous quotes rings like a most appropriate omen, the irony of which I trust future astronomy historians will underline:
“By the study of the orbit of Mars, we must either arrive at the secrets of astronomy or forever remain in ignorance of them.”
— Johannes Kepler
Mars’s fluctuating oppositions
Whenever Mars finds itself at the opposite side of the Sun (“in opposition”), it is also as close at it gets to Earth in any given circa 2.13-year period (779.2 days on average). However, these closest passages fluctuate considerably : their range spans between 56.6 Mkm and 101 Mkm (on average) — a difference of 44.4 Mkm. This is due to the above-mentioned “offset” of 22.2 Mkm (which, of course, adds up to a total of 44.4 Mkm from side to side).
For instance, during Mars’s opposition of August 10, 1971, Mars came as close as 56.2 Mkm to Earth, whereas on February 25, 1980, Mars’s opposition occurred as far as 101.32 Mkm from Earth.
As you can more easily see in my below graphic, the cause of this discrepancy is simply Mars’s variable proximity from Earth each time it transits in opposition:
I call the green circle in the above graphic “Mars’s Opposition Ring”. The Mars oppositions regularly occur around this virtual ring, sometimes as close to Earth as 56.6 Mkm (on average) and sometimes as far as 101 Mkm (on average).
Note that, during the closest Mars oppositions, an earthly observer will see Mars retrograding for what will appear to be a shorter time than during the furthest oppositions. This, due to the different Earth-Mars distances, which can be demonstrated as follows:
Around March, 2012 (another Mars opposition period), Mars was much further away from Earth: 100.78 Mkm.
We see that 100.78 / 55.76 ≈ 1.8074 (Ergo, Mars was about 1.8X further away in 2012 than it was in 2003).
Now, it can be verified on the NEAVE Planetarium that Mars was observed to retrograde by 40 min of RA (Right ascension) in 2003 and by 72 min. of RA in 2012. We see that 72 min. / 40 min. = 1.8. Hence, the age-old mystery of the variable durations of Mars’s retrograde motions is solved: it is simply a “time-space” illusion caused by the different Earth-Mars distances — from one opposition to another. This particular concept of “time-space” should be easily understood since the Sun is our temporal reference frame (our earthly “clock”). The apparent spatial motions of its binary companion, Mars, will fluctuate in accordance with Mars’s distance from Earth.
Most remarkably, it so happens that Kepler, during his five-year-long “war on Mars”, evidently spent some serious time considering a geocentric configuration of our system — and even named Mars a “star”. Below is his little-known diagram, De Motibus Stellae Martis (“Of the Motion of the Star Mars”). It was obviously based on and computed around his master’s (Tycho Brahe) exacting observations, yet he ultimately discarded it. Compare Kepler’s below diagram with my above “16-years of Mars” graphic; it looks like Kepler had at one time really been on to something!
Presumably, Kepler was simply unable to conceive how and why Mars could possibly trace such a peculiar trajectory. When it comes to envisioning the geometric dynamics of two magnetically-bound, mutually-orbiting objects (such as the Sun and Mars), the cognitive power of the human mind meets its limits. Modern motion graphics can help us overcome this mental hurdle and realize that these central “teardrop loops” are nothing but natural geometric manifestations of (binary) uniform circular motion.
Is Mars a planet or a star?
As we just saw, Kepler called Mars a star for unknown reasons. The reader may also have wondered why Mars (an object we have always considered as a planet) would revolve around our star, the Sun, while binary systems (such as Sirius A and Sirius B) are considered to be pairs of stars revolving around each other. Although it is beyond the scope of this treatise to determine just how stars and planets are formed, I nonetheless feel the need to state my support to a school of thought that, basically goes like this:
“Planets are nothing but very old stars which have cooled and solidified into rocky spheres.”
To be sure, this is not the current position of academia which considers stars and planets as wholly different, mutually exclusive entities. In their voluminous study Stellar Metamorphosis, Jeffrey Wolynski and Barrington Taylor make a most compelling case that planets are, quite simply, old stars:
“It is suggested that the rule of thumb of stellar age delineation is that old stars orbit younger ones, the younger ones being the more massive, hotter ones.”
— Stellar Metamorphosis by Jeffrey Wolynski & Barrington Taylor (2017)
In the TYCHOS, of course, the older star Mars orbits a younger, much larger and hotter star (the Sun). And yes, this would also suggest that our Earth is an ancient star. The fiery, hot magma occasionally spurting out of our volcanoes should be an indication to this fact.
The 79-Year cycle of Mars
“Long before Ptolemy, the Babylonians knew that the motion of Mars is repeated, very nearly, in a 79-year cycle – that is, oppositions of Mars occur at nearly the same longitude every 79 years.”
— Further pages from The Ballet of the Planets: A Mathematician’s Musings on the Elegance of Planetary Motion by Donald Benson (2012)
The intervals between two Mars oppositions closest to (or between two Mars oppositions furthest from) Earth (minimum 56.6 Mkm / maximum 101Mkm) will alternate between 15 and 17 years, due to the peculiar epitrochoidal path of Mars around the Sun and Earth. It is a cyclic 15y / 17y / 15y / 15y / 17y pattern that repeats every 79 years, in approximately five 16-year cycles.
This unique, alternating 15/17-year-pattern of the Mars cycles has never been satisfactorily explained until now. None of our other outer planets exhibit such an irregular pattern. Jupiter, for instance, invariably returns to the same place in our skies in about 12 solar years.
We thus envision the possibility that there is no need for Kepler’s notions of elliptical orbits, or for the idea of accelerating and decelerating planets, let alone an Einsteinian temporally warping time-space.
In the TYCHOS model, the orbital speed of Mars is shown to be uniform and constant since it always returns at (near-)equidistant points of its “opposition ring”. Hence, those “elliptical orbits” and “accelerating / decelerating orbital speeds” (as promulgated by Kepler’s “Laws of planetary motion”) could well be illusory and may have to be revised, or possibly discarded altogether. Before Kepler’s laws came along, astronomers all over the world had been relentlessly pursuing the ideal concept of uniform circular motion. In fact so had Kepler himself before he started stretching and squeezing those recalcitrant Martian motions (observed by Tycho Brahe) in order to make them obey his ever-more-complex equations.
Here follows an extract from a Mars Opposition Catalogue, listing some past and future opposition dates of Mars (between September 1956 and September 2035) along with the respective Mars-Earth distances. As you can see, these distances vary from a minimum of ca. 56 Mkm to a maximum of ca. 101 Mkm. This full Mars opposition cycle resumes every 79 years — in the cyclic 15 y / 17 y / 15 y / 15 y / 17 y pattern mentioned earlier:
As you are reading, please make a note of this peculiar 79-year Mars cycle. We will soon look into the lesser-known 79-year cycle of the Sun, and demonstrate an even closer interrelated pattern between the Sun and Mars.
The Mars oppositions, with their average minimum distance from Earth of 56.6 Mkm and average maximum distance of 101 Mkm gives us the interesting size of our opposition ring: approximately 157.6 Mkm-wide.
As it happens, this value (157.6 Mkm) reflects the difference between the orbital diameters of Mars and the Sun!
Why is this significant? Consider the following:
Diameter of the “opposition ring” of Mars (around which all Mars oppositions occur) = 157.6 Mkm
This means that the difference in orbital diameters between the Sun and Mars is equivalent to the difference in Mars’s own oppositions.
Note also how, in the TYCHOS, the Mars oppositions occur in a neat and orderly manner, as Mars regularly returns to a place practically equidistant from the previous opposition point. This is in stark contrast with the Copernican model, according to which the various Mars oppositions would occur quite haphazardly around Mars’s orbit, at randomly-spaced celestial positions.
Here’s a Copernican chart of a number of Mars oppositions (1995-2014). According to the currently-accepted geometry of our Solar System, the Mars oppositions would occur (every 779.2 days on average) at apparently “random”, wildly unequal distances from each other.
As you can see, in the light of this, the Copernican model doesn’t appear to be so “elegant” after all.
Mars’s retrograde periods
My next graphic illustrates two such closest and furthest Mars oppositions (of August 2003 and March 2012) and their consequent retrograde periods during which we see Mars moving “backwards” for about 72 days (on average). The two said oppositions were documented by astro-photographer Tunc Tezel, who patiently snapped pictures of Mars at regular intervals for several months:
We see that, unlike our so-called outer planets (from Jupiter outwards), Mars traces a distinctive “teardrop-shaped” loop whenever it transits in opposition. We also see that Mars’s orbit is inclined just as would be expected in the TYCHOS model.
In the picture at top left (a Martian retrograde period which lasted from January 30th to April 21st, 2012), Mars is seen descending in our (Northern hemisphere) skies, much like the Sun does between July and September. Whereas in the bottom right picture (a Martian retrograde period which lasted from August 1st to October 3rd, 2003), Mars is seen ascending in our (Northern hemisphere) skies, much like the Sun does between February and March (always keep in mind that, whenever Mars transits in opposition, the Sun will be transiting at the opposite side of Earth).
Under Copernican theory, it is simply unfathomable why Mars (whose orbital inclination vis-à-vis Earth’s orbit is said to be only 1.85°) would possibly trace such pronounced and steeply inclined “teardrop loops” — whenever Earth “overtakes Mars on its inner lane”. Those retrograde loops are thought to be illusory — caused by Earth’s superior orbital speed (with respect to Mars’s orbital speed).
However, a mere orbital speed differential fails to explain why Mars would perform such peculiar teardrop-shaped loops. We should expect Mars to just reverse and resume direction in a straight line or, at the most, to trace only a very slightly “z” or “s”-shaped pattern; this, because Mars’s orbital inclination in relation to Earth’s orbit is reckoned to be no more than 1.85° as indicated in this NASA Fact Sheet:
Mars Fact Sheet
by Dr. David R. Williams (NASA, December 23, 2016)
As we shall see, Mars’s retrograde periods are not by any means the biggest problem with the Copernican model. There are a number of far graver (and indeed insurmountable) problems with the cosmic model we were all taught in school. The next chapter should, in a science-minded world, definitively spell the end of the Copernican era of astronomical belief.