Chapter 5 — Mars, the “key” that Kepler never found

Chapter 5: Mars, the “key” that Kepler never found

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 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 soundness and 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 at will, so as to make them “fit” with the core tenets of his thesis) make for a most compelling read:

"Kepler’s Fabricated Figures – Covering up the Mess in the New Astronomy" - by W. H. Donahue -Journal for the History of Astronomy (1988) (opens in a new tab)

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) (opens in a new tab)

As I see it, Kepler’s manipulative antics are destined to go down in history as the triumph of mathematical abstraction over empirical observation. In his urge to make the befuddling behavior of Mars agree with the heliocentric Copernican theory, Johannes Kepler not only misused and twisted - but outright subverted Tycho Brahe’s most precious and exacting observational data acquired throughout his lifetime. In any event, there can be no doubt that Tycho's priority and main concern was that of understanding the motions of Mars. The fact that he entrusted this crucial task to his young, ambitious and petulant assistant (Johannes Kepler) may well have been the greatest mistake of his life. Anyhow, it is a documented fact that Tycho Brahe had identified some curious systematical, additional inequality in the planetary motions, "not known to Ptolemy or Copernicus":

"Tycho also realized that Copernican predictions for all the planets differed systematically from the observations and wondered whether an additional inequality, not known to Ptolemy or Copernicus, might affect their motions. Or perhaps planetary theories should be referred to the true rather than mean Sun, as Ptolemy had done, and the other inequality could be solved by modifying the solar eccentricity. Given the similarity of Mars’s orbit to the Sun’s, Tycho suspected that the red planet might provide a key for reworking all the planetary theories."


Let us presently take a look at what the Maya knew about Mars. The ancient Maya astronomers were clearly aware of the VARIABLE 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 546 days - the “Short ESI”.

It is the “Short ESI” (of ca. 546 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 (February 2001) (opens in a new tab)

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 546 days, or about 1.5 years. In Maya astronomy, this ca. 546-day period is called the Short ESI (Empiric Sidereal Interval) whereas Mars’s “habitual”, longer sidereal period of ca. 707 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 days (on average) — but the eighth time around, Mars will realign with that same star in only about 546 days. That is, over a ca. 15-year time span, Mars exhibits seven Long ESIs (of ca. 707 days) + one Short ESI (of ca. 546 days)!

MARS sidereal period ESI sequence:
707 / 707 / 707 / 707 / 707/ 707/ 707 / 546
Total: 5495 days – or ca. 15 years.

Now, since 5495 / 8 ≈ 686.9 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, Kepler's 686.9-day Mars period is not something that can ever be observed from Earth! The (currently-accepted) Keplerian 686.9-day value of Mars’s sidereal period was just mathematically extrapolated on the assumption that Earth revolves around the Sun once a year.

Yet Mars does indeed, in reality (i.e. as can be directly observed), alternate its sidereal periods - over a 15-year cycle - as of the above ESI sequence!

You may now justly 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 and 546 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 further expound upon.

Please note that, in reality, Mars does indeed have a 686.9-day period (or ca. 687d): that’s the period needed for Mars to revolve once around the Sun. Ergo, it is not Mars’s “mean sidereal period” as viewed from Earth. 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 days (about 23 days less than two solar years of 730.5 days. More precisely, Mars returns facing the same star 23.3 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:

48.7 days + 23.3 days = 72 days
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. 72 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:

707.2 + 72 = 779.2

Thus, in 16 solar years MARS completes 7.5 synodic periods.

779.2 X 7.5 = 5844 days = 16 solar years.

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:

45 min. X 32 = 1440 min.
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 the observed orbital behavior of Sirius A and Sirius B - the very brightest star system in our skies.

The 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:“Preposterous! Sooner or later, Mars and the Sun must collide!”. Today, their pooh-poohing ways may perhaps be excused for back in those days, no one was aware of the very existence of binary systems (the ubiquity of which was only realized long after the invention of the telescope). In hindsight, one may graciously say that Tycho Brahe was ridiculed out of academia's pre-telescopic ignorance.

As you can see, the above orbital configuration is wholly consistent with the models of Tycho Brahe and Pathani Samanta, albeit with a little - yet crucial - addition: the (clockwise) orbital motion of Earth - which is my main personal contribution to Tycho Brahe's near-flawless geoheliocentric model. For now though, let us focus our attention on Mars - and its peculiar motion around the Sun and Earth.

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) (opens in a new tab)

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) (opens in a new tab)

Of course, in the TYCHOS model, one may easily perceive 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

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 called Mars a “star”. His little-known diagram, 'De Motibus Stellae Martis' (“Of the Motion of the Star Mars”) traced the motions of Mars between 1580 and 1596 (a 16-year period). It was obviously based on and computed around his master’s (Tycho Brahe) exacting observations, yet he ultimately discarded it. Below, we compare this same 16-year period (as traced in the TYCHOSIUM 3D simulator) with Kepler's diagram. As you can see, it looks like Kepler had at one time really been on to something!

Presumably, Kepler was simply unable to conceive how and why Mars (or any celestial body) would possibly trace such oddly 'looping' trajectories. 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 spirographic orbital patterns are nothing but natural geometric manifestations of an object revolving around another revolving object.


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 compelling case that all of the bodies in our cosmos are stars at different stages of their evolution and that planets & moons are - quite simply - very old, "cooled-down" 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) (opens in a new tab)

Under this hypothesis, the older star of our binary Solar System would be Mars - as it orbits a much larger, younger and hotter star (the Sun). Interestingly, it is also suggested (opens in a new tab) that our Earth-Moon system may be an ancient, former binary star system which, as the two 'shed their skin' - eventually ended up as a planet and a satellite. To wit, the notion that Earth may be a former star shouldn't sound too outlandish: after all, the fiery magma trapped in Earth's core (which occasionally spurts out of our earthly volcanoes) may well be viewed as an indication that we are, in fact, living on the surface of an old, "cooled-down" star. In turn, our barren and volcano-less lunar satellite, the Moon, would thus be - under this compelling theory - a still older and cooler star.

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) (opens in a new tab)

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.

79 / 16 = 4.9375

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 TYCHOSIUM 3D simulator, Mars is shown to revolve around a uniformly circular orbit - at constant, invariable speed. Hence, those “elliptical orbits” and “variable orbital speeds” (edicted by Kepler’s 'Laws of planetary motion') turn out to be no more than abstract mathematical constructs necessary to accomodate the heliocentric theory - yet entirely disconnected with physical reality. It bears reminding that, 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.

From a short, illustrated webpage "Kepler’s Discovery" (opens in a new tab) well worth reading in its entirety.

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:

Above: Mars Oppositions from 1956 to 2035 - from "Mars Oppositions" - by Hartmut Frommert (2008) (opens in a new tab)

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:

Difference between orbital diameters of Mars and the Sun: 456.8 Mkm – 299.2 Mkm = 157.6 Mkm

Diameter of the “opposition ring” of Mars (around which all Mars oppositions occur) = 157.6 Mkm

In fact, when Mars finds itself in opposition (as it is observed to reverse direction in the sky for 72 days on average), it can transit as close to Earth as 56.6 Mkm - and as far as 101 Mkm: 56.6 + 101 = 157.6 Mkm


As Mars transits in so-called opposition (i.e. when Mars and the Sun find themselves on opposite sides of the Earth), its usual West-to-East motion will appear to reverse direction (a.k.a. to 'retrograde') and to proceed East-to-West against the starry background for a (variable) number of weeks. My below graphic shows how the famed astro-photographer Tunc Tezel expertly captured the Mars retrogrades of 2003 and 2012 - and how these two periods are traced in the TYCHOSIUM 3D simulator (opens in a new tab)

Note that, in 2003, Mars passed almost twice closer to Earth (0.373AU - or 55.8 Mkm) than it did in 2012 (0.674AU - or 100.8 Mkm). Also, note that in 2003, Mars was observed to retrograde against the starry background by about 40min of RA (over 61 days) - whereas, in 2012, it retrograded by as many as 72min of RA (over 83 days) - as highlighted in my next diagram:

In other words, Mars reversed course for a shorter time AND distance in 2003 than it did in 2012. This is most remarkable because, under the Copernican model, it should be precisely the other way around! Remember: the Copernican theory contends that Mars appears to retrograde whenever Earth (on its 'inside lane') overtakes Mars (on its 'outside lane') and that it is just a matter of changing perspectives (i.e. of parallax) thereby causing a mere optical illusion of Mars back-tracking in the sky against the starry background. If this were the case though, the CLOSER Earth would be to Mars during such an overtaking maneuver, the LARGER the retrograde effect would be. Instead, the exact opposite is empirically observed!

The next graphic provides a closer comparative view of the two retrogrades of Mars in 2003 and 2012 - as illustrated above:

Hence, Mars's observed retrograde motions falsify (beyond appeal) the entire Copernican theory all by themselves. The heliocentric model's explanation for the retrograde motions of our planets is inadmissible and must be discarded - since it violates the most basic laws of spatial perspective. Let me further demonstrate this with my below representation of a real-world optical situation with which anyone can easily relate to:

In fact, there's an even simpler way to experience and verify this for yourself - without even the need to exit your living room:

  1. Raise your forefinger in front of your nose and stretch out your arm as far as you can (think of your forefinger as being Mars).

  2. Next, point your forefinger towards the books in that distant library at the far side of your living room.

  3. Now, rotate your neck from left to right as much as you can - while keeping your eyes focused on the books stacked in your library.

  4. Notice how many books will move from side to side in relation to your forefinger (which you'll have to keep immobile).

  5. Now, bring your forefinger 50% closer to your nose - and repeat your left to right neck rotation.

  6. Notice how a far larger amount of books (think of them as 'stars') will move from side to side in relation to your forefinger.

This basic law of perspective is as incontestable as it can get. Yet, incredibly enough, no Copernican astronomers have ever realized to this day that the observed retrogrades of Mars (as it transits closer or further from Earth) roundly falsify their theory about our planets' observed retrograde motions. As we shall see further on, the issue of Mars’s retrograde periods is not by any means the only aberration afflicting the tenets of the Copernican model; there are a number of far graver (and indeed insurmountable) problems with the heliocentric model we were all taught in school.

In conclusion, we may understand today why Kepler had to fudge with the flawless observational data provided by his master, Tycho Brahe. As the "staunch Copernican" that he was, he never had any chance to make any sense out of the complex motions of Mars, what with its unequal retrograde periods and seemingly fluctuating orbital speeds. Kepler's "war on Mars" was simply unwinnable, since the man was obstinately attached to the idea that the Sun had to be at the center of our Solar System. I will thus dare say that his devious and obdurate ways will go down in history as a text-book case of how scientific investigations should not be pursued; Kepler's ardent quest was fogged by that all-too-common defect of the human intellect: confirmation bias.

In the next chapter, we will take a good look at the most astounding similarities between the Sirius binary system and our own Solar System. Sirius, of course, is the very brightest (binary) star in our skies. I trust that the reader may imagine my pleasant surprise as I realized - in the early stages of my TYCHOS research - that the observed diameters of Sirius A and Sirius B are proportionally identical to our Sun and Mars...