Chapter 2 — About binary / double star systems

Chapter 2: About binary star systems

Fig. 2.1 A 'classic' binary star system. (Image source: The SAO Encyclopedia of Astronomy (opens in a new tab))

2.1 Is our Sun a single star?

If you were to tell a child that practically all the stars we can see in the sky with our naked eyes have a binary companion, the child’s reply might be something like: “So, if the stars are suns like our own Sun, just farther away, why doesn’t the Sun also have a companion, dad?” Your best answer would probably be: “That’s what the astronomers say, honey, and they should know. They tell us the Sun is a single star.” It might occur to the child that our Sun must be the loneliest star in the universe. Incredulous, the inquiring child might then protest: “Dad, it’s not fair! If all the stars in the sky have a partner, then our Sun should have one too!” You could then attempt to ‘save face’ by reminding the child that you didn’t say “all the stars”, but “practically all the stars”.

Yet, it is a matter of historical record that for centuries the Copernicans rejected the very notion of binary stars:

"In a Copernican view, the idea of stellar systems containing two or more associated stars seemed a priori excluded by heliocentrism; all stars in the universe are suns like our own, all being equal in size and resting at the centre of other possible star systems. Given these premises, there cannot be a system with more than one star." "The Early Search for Stellar Parallax: Galileo, Castelli and Ramponi" (opens in a new tab) by Harald Siebert (2005).

Of course, this early Copernican axiom has since been categorically contradicted, as the vast majority of our visible stars have turned out to be double (or multiple) systems in which, more often than not, two central ‘stars’ revolve around a common barycenter. Wikipedia’s entry on double stars lists three main categories of double stars:

    1. Visual binaries: two or more gravitationally bound stars that are separately visible with a telescope.
    1. Non-visual binaries: stars whose binary configuration was deduced by indirect means, such as occultation (eclipsing binaries), spectroscopy (spectroscopic binaries), or anomalies in proper motion (astrometric binaries).
    1. Optical doubles: unrelated stars that only appear close together through chance alignment with Earth.

(Note that the third category above—unrelated stars which happen to be aligned along our earthly line of sight—is of no concern to us here.)

What we shall see is that, when considering the most recent discoveries of observational astronomy, a reasonable case could certainly be made that 100% of the stars in our skies are, in fact, binary (or multiple) star systems. If this is so, all the apparently single points in the firmament that we think of as individual stars have a smaller companion, almost always undetectable to the naked eye. The two stars in the system revolve around each other in intersecting orbits, and also around a common barycentre (or ‘centre of mass’, for lack of a better word), completing a revolution in variable time periods, ranging from a few hours, days, weeks, months or—more rarely—a few dozen years. Here are a few examples of binary star periods:

  • The binary system MIZAR A (composed of Mizar Aa & Mizar Ab) circle each other in only about 20.5 days.

  • The binary system MIZAR B (composed of Mizar Ba & Mizar Bb) circle each other in just about 6 months.

  • The binary system Polaris (composed of Polaris Aa & Polaris Ab) circle each other in ~29.6 years.

  • The binary system Alpha Centauri (composed of Alpha Cen A & Alpha Cen B) circle each other in ~79.7 years.

Amazingly, some binary systems have recently been observed to revolve around each other in only a few minutes:

"After a decade of mystery, astronomers have now shown that a pair of white dwarf stars spin around each other in just 5.4 minutes, making them the fastest-orbiting and tightest binary star system ever found, the researchers claim." Fastest Orbiting Stars Circle Each Other in Mere Minutes (opens in a new tab)

Our Sun, in stark contrast, is currently believed to complete one orbit in about 240 million years!

In other words, Copernican astronomers are asking us to believe that the Sun has no ‘local orbit’ (as I shall call it), unlike practically all other stars. This would of course imply that our Sun is potentially an exception to the rule and a quite formidable cosmic and statistical curiosity. To be sure, what we know today is that the vast majority of our visible stars are, in fact, part of binary/multiple systems. Unfortunately, a number of modern astronomy textbooks still state that no more than 50% of the stars are binary systems, neglecting to report the mounting evidence that over 90% of the known stars have companions.

“In fact, the majority of stars happens to be part of a binary or multiple system, and consequently binary star research covers most areas of stellar astronomy.” Binary stars and the VLTI: research prospects (opens in a new tab) by Andrea Richichi and Christopher Leinert (2000)

It is important to point out that Tycho Brahe was unaware of the existence of binary systems. The first binary system (Mizar A and B) was discovered in 1650 by Giovanni Riccioli, half a century after Brahe’s death, and only following the invention of the telescope. However, it wasn’t until more than a century later that William Herschel formally announced his discovery of what he described as ‘binary sidereal systems’:

“In 1797, Herschel measured many of the systems again, and discovered changes in their relative positions that could not be attributed to the parallax caused by the Earth's orbit. He waited until 1802 to announce the hypothesis that the two stars might be "binary sidereal systems" orbiting under mutual gravitational attraction, a hypothesis he confirmed in 1803 in his Account of the Changes that have happened, during the last Twenty-five Years, in the relative Situation of Double-stars; with an Investigation of the Cause to which they are owing. In all, Herschel discovered over 800 confirmed double or multiple star systems, almost all of them physical rather than optical pairs. His theoretical and observational work provided the foundation for modern binary star astronomy." William Herschel - Wikipedia (opens in a new tab)

*Fig. 2.12 is a chart of Herschel’s 805 certified double star systems. One can only wonder why Herschel’s paradigm-shifting discoveries didn’t trigger a revolution within the field of astronomy and why no one to this day has seriously reconsidered the Tychonic model, with its intersecting orbits of the Sun and Mars clearly suggestive of a binary configuration.
Fig. 2.2 Image source: William Herschel's double star discoveries (opens in a new tab)

In any event, one cannot blame Brahe for failing to notice and identify, within his own Tychonic model, the obvious binary nature of the orbital interactions of Mars and the Sun: in his time, no binary star systems had yet been discovered. He was thus unable—understandably so—to reach the logical conclusion that the Sun and Mars must make up a binary system, like the vast majority (or perhaps all) of the stars in our skies.

It was precisely this ‘bizarre’ feature of Brahe’s proposed model (the intersecting orbits of Mars and the Sun) that triggered the scoffing and derision of his peers: “Sooner or later, the Sun and Mars must smash into each other”, they jeered. This is a good example of how the regrettable group-think mentality pervading the so-called scientific community responds to new ideas that challenge long-held beliefs. I would strongly recommend reading Howard Margolis’ impeccable demonstration that the perception that the Sun and Mars would necessarily collide in a system like the Tychonic was never more than a crafty illusion—albeit one that befuddled the entire scientific community. It makes for an exemplary case study of how even the sharpest human minds can be fooled for centuries on end by relatively simple tricks of geometry.

"Tycho’s Illusion: How it lasted 400 Years, and What that implies about Human Cognition" - by Howard Margolis (1998) (opens in a new tab)

Figure 2.3 depicts a classic binary star scheme taken from the website of the University of Oregon. The site tells us that the vast majority of the stars in the Milky Way are binary systems.

Fig. 2.3 A schematic of a basic binary star system. (Image source: University of Oregon)

“In fact, 85% of the stars in the Milky Way galaxy are not single stars, like the Sun, but multiple star systems, binaries or triplets.” Source: "Binary Stars" by Jim Schombert - for University of Oregon (2018)

Today, the numbers of known binary star systems are in the range of several hundreds of thousands, as we can read in this Russian academic paper by Malkov, Karchevsky, Kaygorodov, Kovaleva and Skvortsov (October 2018):

"Binary Star Database (BDB): New Developments and Applications. The Identification List of Binaries (ILB) is a star catalogue constructed to facilitate crossreferencing between different catalogues of binary stars. [...] ILB currently contains about 520,000 entries: 120,000 systems, 140,000 pairs and 260,000 components."Binary Star Database: New Developments and Applications" (opens in a new tab)

Clearly, binary systems are anything but rare, as believed only a century ago. For instance, we know today that the 20 stars closest to Earth are, in all probability, ‘locked’ in binary systems. Now, a most significant aspect to consider is that many of those 20 stars were discovered to be binary/multiple systems as recently as this last half-decade (2015-2020), showing how difficult it can be to detect stellar companions, let alone determine what sort of orbital relationship they have with their host star. This naturally raises the question: How many other distant stars held to be single stars are, in reality, double stars?

Our 20 nearmost stars and their confirmed/suspected companions:

  1. Proxima Centauri A / Proxima Cen B / Proxima Cen C (companions B & C discovered in 2016 and 2020)
  2. Alpha Centauri A / Alpha Centauri B (companion B discovered long ago)
  3. Barnard’s Star A / Barnard’s star B (companion B discovered in 2018)
  4. Luhman A / Luhman B (companion B discovered long ago)
  5. WISE 0855−0714 A / WISE 0855−0714 B (companion B discovered in 2018)
  6. Wolf 359 A / Wolf 359 B / Wolf 359 C (companions B & C discovered in 2019)
  7. Lalande 21185 A / Lalande 21185 B (companion B discovered in 2017)
  8. Sirius A / Sirius B (companion B discovered long ago)
  9. Luyten 726-8 A / Luyten 726-8 B (companion B discovered long ago)
  10. Ross 154 (“flare star”, Wikipedia) (flare stars are suspected of being double stars)
  11. Ross 248 (“flare star”, Wikipedia) (flare stars are suspected of being double stars)
  12. Epsilon Eridani A / Epsilon Eridani B (companion B discovered long ago)
  13. Lacaille 935 (“has 3 known planets” - Wikipedia)
  14. Ross 128 A / Ross 128 B (companion B discovered in 2017)
  15. EZ Aquarii A / EZ Aquarii B / EZ Aquarii C (companions B & C discovered long ago)
  16. 61 Cygni A / 61 Cygni B (companion B discovered long ago)
  17. Procyon A / Procyon B (companion B discovered long ago)
  18. Struve A / Struve B (two more companions discovered in 2019)
  19. Groombridge A / Groombridge B (companion B discovered long ago)
  20. DX Cancri (“flare star” - Wikipedia) (flare stars are suspected of being double stars)

Source: "List of nearest stars" - Wikipedia (opens in a new tab)

As a matter of fact, the percentage of stars observed (or determined by spectrometry) to be locked in binary systems has been rapidly increasing in later years thanks to advanced spectrometers and so-called adaptive optics (based on the Shack-Hartmann principle). The latter technological advancement has spectacularly improved the ability to detect and reveal double stars formerly believed to be single stars. Of course, the difficulty resides in the fact that double stars are always relatively close to each other and/or that the ‘junior’ companion can sometimes be extremely small (such as the tiny Sirius B, which is only about 0.5% the size of Sirius A). The two images below illustrate how, in May 2013, the star HIC 59206 (previously thought to be singular) was revealed to be yet another binary system thanks to the use of adaptive optics technology (in this case, the two companion stars are fairly similar in size):

Fig. 2.4 ESO imagery of a binary star (HIC 59206) imaged without and with adaptive optics correction. Note distinct binary appearance with adaptive optics. - European Southern Observatory (May 13, 2003). For more information about Adaptive Optics: "Adaptive Optics" - Wikipedia (opens in a new tab).

To wit, if it eventually emerges that 100% of the stars in our skies are binary/multiple systems, the current Copernican heliocentric theory, which holds that our Sun is a companionless star, will have to be definitively abandoned, beyond appeal, for being a most improbable exception to the rule or, if you will, a one-of-a-kind cosmic anomaly, unless one accepts the truly astronomical odds of our own star (the Sun) being the one-and-only ‘bachelor’ in the entire universe—a most irrational and exceptionalistic notion, if there ever was one! In any case, the situation we have today is that virtually all of our nearmost stars are observed to have a binary companion, and more are being continuously discovered, with no end in sight.

In the 1980s, one of the world’s top experts in binary star systems, Wulff Heintz, announced at the end of his illustrious career that at least 85% of all the stars in our skies must be binary systems, leaving us to wonder whether the remaining 15% are really ‘bachelor’ stars (as our Sun is believed to be). Now, this announcement was made about 40 years ago; since then, thanks to technological advancements (e.g., adaptive optics, as mentioned above), we have seen an incessant flow of new reports of companions revolving around larger host stars that were formerly believed to be single stars. In later years, we have heard on the news, almost on a weekly basis, about the discovery of so-called ‘exoplanets’. Rarely though, if at all, is it suggested that some of these ‘exoplanets’ might be formerly unregistered companions of larger stars, possibly because of the growing ‘academic fear’ that all stars, without exception, may turn out to be binary/multiple systems. The scientific establishment is obviously keen to avoid such a conclusion: there could be no more horrifying prospect for ‘mainstream’ astronomers (for lack of a better term) than having to admit that stars are by definition binary/multiple systems, as this would spell the end of heliocentrism.

Critics of the TYCHOS have objected that the model “violates Newton’s laws” and, ironically, that it is “stuck in the past, rehashing obsolete ideas”, though much of its argumentation is based on modern observations and advances in astronomy. Sir Isaac Newton died in 1726, several decades before Herschel’s formal identification of ‘binary sidereal systems’ in 1797, so he never had a fair chance to study them. Moreover, Newton’s laws have been seriously challenged by numerous physicists over the last three centuries, and many paradigm-shifting astronomical discoveries have been made, even in the 21st century. So, rather than continue appealing to ‘Newtonian authority’, I suggest readers leave Newton’s sacrosanct laws at the door for now and allow themselves to take an unprejudiced look at the undeniable evidence of our telescopes and the plain facts of geometry.

Having said that, I am sure Sir Isaac was an exceptionally gifted scientist. But keep in mind that none of his studies addressed the physics or celestial mechanics of binary star systems for the simple reason that little or nothing was known about them in his time. As for that other science icon, Albert Einstein, here’s what Tom Van Flandern had to say about his theories as applied to binary stars:

“If the general relativity method is correct, it ought to apply everywhere, not just in the solar system. But Van Flandern points to a conflict outside it: binary stars with highly unequal masses. Their orbits behave in ways that the Einstein formula did not predict. ‘Physicists know about it and shrug their shoulders,’ Van Flandern says. They say there must be ‘something peculiar about these stars, such as an oblateness, or tidal effects.’ Another possibility is that Einstein saw to it that he got the result needed to ‘explain’ Mercury’s orbit, but that it doesn’t apply elsewhere.” Tom Van Flandern articles (opens in a new tab)

In other words, Einstein’s famed formulae fail to predict the orbital motions of binary stars. Now, that is a rather serious problem, for if it eventually turns out that our universe is exclusively populated by binary star systems, it is back to the drawing board for the heliocentrists and for the devotees of the general theory of relativity.

2.2 About "variable stars" and "flare stars"

At the start of the 20th century, astronomers were debating whether so-called ‘variable stars’ (stars which change in brightness over regular time periods) were, quite simply, nothing but binary systems where the companion star periodically transited in front of its brighter binary partner, thus temporarily reducing its brightness. However, astronomers are still classifying many stars (those not yet officially recognized as binary stars) as ‘variable stars’ or ‘flare stars’. So what exactly are variable stars? This is what Wikipedia can tell us about them:

Variable stars (Wikipedia) "A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either: - Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks. - Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it. Many, possibly most, stars have at least some variation in luminosity.

I think we can all agree that the hypothesis of “stars that periodically swell and shrink” is rather outlandish. But let us move on:

Flare stars (Wikipedia) "A flare star is a variable star that becomes very much brighter unpredictably for a few minutes at a time. Most flare stars are dim red dwarfs, although less massive (lighter) brown dwarfs might also be able to flare. The more massive (heavier) RS Canum Venaticorum variables (RS CVn) are also known to flare, but scientists understand that a companion star in a binary system causes these flares.

Thus, in both cases (variable and flare stars) we see that the least speculative explanation is that these stars are, quite simply, binary star systems whose brightness periodically dips as one companion obscures the other. There is no need to classify them as anything else but binary stars.

Here are some relevant extracts from the book "Astronomy of to-day", by Cecil G. Dolmage:

“It was at one time considered that a variable star was in all probability a body, a portion of whose surface had been relatively darkened in some manner akin to that in which sun spots mar the face of the sun; and that when its axial rotation brought the less illuminated portions in turn towards us, we witnessed a consequent diminution in the star's general brightness. [...] The scale on which it varies in brightness is very great, for it changes from the second to the ninth magnitude. For the other leading type of variable star, Algol, of which mention has already been made, is the best instance. The shortness of the period in which the changes of brightness in such stars go their round, is the chief characteristic of this latter class. The period of Algol is a little under three days. This star when at its brightest is of about the second magnitude, and when least bright is reduced to below the third magnitude; from which it follows that its light, when at the minimum, is only about one-third of what it is when at the maximum."

"It seems definitely proved by means of the spectroscope that variables of this kind are merely binary stars, too close to be separated by the telescope, which, as a consequence of their orbits chancing to be edgewise towards us, eclipse each other in turn time after time.” [...] “Since the companion of Algol is often spoken of as a dark body, it were well here to point out that we have no evidence at all that it is entirely devoid of light. We have already found, in dealing with spectroscopic binaries, that when one of the component stars is below a certain magnitude its spectrum will not be seen; so one is left in the glorious uncertainty as to whether the body in question is absolutely dark, or darkish, or faint, or indeed only just out of range of the spectroscope."

Indeed, it is a little-known fact that most celestial bodies identified as ‘stars’ are invisible to the naked eye. None of the so-called red and brown dwarfs (reckoned to make up 86% of all stars in the universe) are visible without the aid of powerful telescopes, and most are so faint and dim as to be barely detectable, even by our world’s largest observatories. Brown dwarfs are not even officially classified as ‘stars’ because, as we are told, “they are not massive enough to sustain hydrogen fusion reactions”. In the TYCHOS, of course, this may well be the case of Mars―the Sun’s proposed binary companion. Mars exhibits the characteristic reddish/orange hue associated with old ‘dying stars’. The fact that Mars’ diameter is only about 0.5% that of the Sun’s is often adduced by critics of the TYCHOS model, but this is a dull objection since the exact same proportion is observed for the binary partners Sirius A and Sirius B. In fact, Alvan Clark’s discovery in 1862 of the midget Sirius B caused an uproar in the 19th century scientific community as it was totally unexpected under Newton’s ‘laws’ that a tiny body like Sirius B (reckoned to be slightly smaller than Earth) could possibly be gravitationally bound to such a huge body as Sirius A.

Incredibly enough, the pesky riddle was eventually ‘resolved’ (explained away) by astrophysicists, claiming, in the absence of any conceivable experimental verification and in what must be one of the most flagrant ad hoc postulations in the history of science, that the mass / density / gravitational attraction (call it what you will) of the tiny Sirius B must be about 400000 times larger than that of Earth! In other words, we are asked to believe that Sirius B’s atoms are somehow ‘packed’ 400 thousand times tighter than our earthly atoms. Ironically though, one of Sir Isaac’s most hallowed precepts was that the laws of physics are unvarying and homogeneous across the universe.

2.3 Most recent discoveries of stellar companions

As recently as 2016, it was announced that a companion of our nearmost star, Proxima Centauri, had been discovered: it is now known as ‘Proxima b’ and it apparently revolves around Proxima A in just 11.2 days. Then, in January 2020, yet another companion to our closest star was announced, ‘Proxima c’, estimated to revolve around Proxima A in 5.28 years. Additionally, a faint signal with a period of only 5.15 days was detected during a 2019 exoplanet search using radial velocity data. If a planet is confirmed to be the cause of this signal, it would be designated as ‘Proxima d’. Again, these quite recent discoveries go to show just how difficult it is, even for our most advanced 21st century instruments, to detect the companions of any given binary system, even when the star is as close as Proxima Centauri. Now, it should be noted that the Proxima ‘family’ (a, b, c, and possibly d) are themselves reckoned to be slowly revolving around the binary pair Alpha Centauri A and B, the two Centauri star ‘families’ thus constituing a so-called ‘double-double’ system (more about this later).

The trend expressed by these recent discoveries seems to support the idea that all stars have binary companions. It is therefore reasonable to conjecture that, sometime in the future, thanks to improved techniques and instruments, all the stars now believed to be companionless will turn out to be binary systems. To be sure, much observational work remains to be done in this particular field of astronomy:

"Most known double stars have not been studied adequately to determine whether they are optical doubles or doubles physically bound through gravitation into a multiple star system." - "Binary star" - Wikipedia (opens in a new tab)

As recently as 2018, it was announced that a companion of our second-nearmost star (or star system), namely Barnard’s star, had been confirmed. As it happens, the existence of Barnard’s companion was the object of a bitter and long-lasting controversy (which every astronomy historian will remember) between Peter Van de Kamp and Wulff Heintz. The former was convinced he had proven the existence of two companions (which he named B1 and B2) of Barnard’s star, but Heintz would have none of it. For decades, vigorous efforts were deployed to discredit Van de Kamp’s discovery, including laughable claims that it was just an artifact caused by the improper cleaning of his telescope lenses. Yet, as we shall see, Van de Kamp’s observational work was finally vindicated, posthumously, in 2018 (even though yet another study released in July 2021 again disputes his findings; astronomy, it seems, is a permanent ‘battleground’).

Fig. 2.5 Wulff Heintz and Peter Van de Kamp.

For those who are interested, a detailed account of Van de Kamp’s discovery of Barnard’s star companions is available in a 1969 Time magazine article (opens in a new tab). The epic feud between the two eminent astronomers and binary star experts, Heintz and Van de Kamp, truly deserves to be revisited. Below is an extract from the Wikipedia which briefly summarizes their protracted dispute. Warning: all Wikipedia entries involving historical controversies should be taken with a large grain of salt. As the old saying goes, one must read between the lines:

"The Barnard’s Star affair. In the spring of 1937, Van de Kamp left McCormick Observatory to take over as director of Swarthmore College’s Sproul Observatory. There he made astrometric measurements of Barnard’s Star and in the 1960s reported a periodic “wobble” in its motion, apparently due to planetary companions. Astronomer John L. Hershey found that this anomaly apparently occurred after each time the objective lens was removed, cleaned, and replaced. Hundreds more stars showed “wobbles” like Barnard’s Star’s when photographs before and after cleaning were compared - a virtual impossibility. Wulff Heintz, Van de Kamp’s successor at Swarthmore and an expert on double stars, questioned his findings and began publishing criticisms from 1976 onwards; the two are reported to have become estranged because of this. Van de Kamp never admitted that his claim was in error and continued to publish papers about a planetary system around Barnard’s Star into the 1980s, while modern radial velocity curves place a limit on the planets much smaller than claimed by Van de Kamp. **Recent evidence suggests that there is, indeed, a planet orbiting Barnard’s Star, albeit of much lower mass than Van de Kamp could have detected.

Indeed, it now turns out that Heintz was wrong and that Van de Kamp had been right all along. In November 2018, ESO (the ground-based European Southern Observatory) finally announced that the Barnard's star indeed has a companion:

"Super-Earth Orbiting Barnard’s Star Red Dots campaign uncovers compelling evidence of exoplanet around closest single star to Sun. A planet has been detected orbiting Barnard’s Star, a mere 6 light-years away. This breakthrough - announced in a paper published today in the journal Nature - is a result of the Red Dots and CARMENES projects, whose search for local rocky planets has already uncovered a new world orbiting our nearest neighbour, Proxima Centauri. The planet, designated Barnard’s Star b, now steps in as the second-closest known exoplanet to Earth. The gathered data indicate that the planet could be a super-Earth, having a mass at least 3.2 times that of the Earth, which orbits its host star in roughly 233 days. Barnard’s Star, the planet’s host star, is a red dwarf, a cool, low-mass star, which only dimly illuminates this newly-discovered world."Super-Earth Orbiting Barnard’s Star" - European Southern Observatory (2018) (opens in a new tab)

It is interesting to note that both ESA (in 2007) and NASA (in 2010) decided to discontinue their efforts to search for Barnard’s companion after having failed to detect it and, apparently, due to “lack of funding”. Here’s what we may read on Wikipedia about these curious circumstances:

"Null results for planetary companions continued throughout the 1980s and 1990s, including interferometric work with the Hubble Space Telescope in 1999. Gatewood was able to show in 1995 that planets with 10 MJ were impossible around Barnard's Star in a paper which helped refine the negative certainty regarding planetary objects in general. In 1999, the Hubble work further excluded planetary companions of 0.8 MJ with an orbital period of less than 1,000 days (Jupiter's orbital period is 4,332 days), while Kuerster determined in 2003 that within the habitable zone around Barnard's Star, planets are not possible with an "M sin i" value greater than 7.5 times the mass of the Earth (M🜨), or with a mass greater than 3.1 times the mass of Neptune (much lower than van de Kamp's smallest suggested value). (...) Even though this research greatly restricted the possible properties of planets around Barnard’s Star, it did not rule them out completely as terrestrial planets were always going to be difficult to detect. NASA’s Space Interferometry Mission, which was to begin searching for extrasolar Earth-like planets, was reported to have chosen Barnard’s Star as an early search target. This NASA mission was shut down in 2010. ESA’s similar Darwin interferometry mission had the same goal, but was stripped of funding in 2007. "Barnard's star" - Wikipedia (opens in a new tab)

So there you have it: both NASA’s and ESA’s efforts to search for the Barnard’s star companion(s) apparently failed and were shut down. One may legitimately wonder why. “Lack of funding” is not an entirely convincing explanation. Whatever their motivation is, one fact remains of which there can be little doubt: Van de Kamp’s solitary endeavors succeeded where NASA’s efforts had failed, in spite of their much touted, multimillion-dollar ‘space telescopes’ and immensely superior resources.

2.4 Additional links to literature on binary systems

Here’s a selection of quotes about binary stars from various astronomy sources:

“There are many common misconceptions about binary star systems, one of the most common myths is that binary star systems are the cosmic oddity and that single star systems are the most prevalent, when, in fact, the opposite is true. 50 years ago binary stars were considered a rarity. Now, most of the stars in our galaxy are known to be paired with a companion or multiple partners.” "Binary Star Prevalence" (opens in a new tab) by the Binary Research institute

“Binary stars are two stars orbiting a common center of mass. More than four-fifths (80%) of the single points of light we observe in the night sky are actually two or more stars orbiting together. The most common of the multiple star systems are binary stars, systems of only two stars together. These pairs come in an array of configurations that help scientists to classify stars, and could have impacts on the development of life. Some people even think that the sun is part of a binary system.” "Binary Star Systems: Classification and Evolution" (2018) (opens in a new tab) by Staff

“Binary stars are of immense importance to astronomers as they allow the masses of stars to be determined. A binary system is simply one in which two stars orbit around a common centre of mass, that is they are gravitationally bound to each other. Actually most stars are in binary systems. Perhaps up to 85% of stars are in binary systems with some in triple or even higher-multiple systems.” "Binary Stars" - by CSIRO Australia Telescope National Facility(2017) (opens in a new tab)

The idea that the Sun is part of a binary system is not a new concept. Headed by Walter Cruttenden, the Binary Research Institute has been looking into this hypothesis for many years. Unfortunately, their reasoning process is stuck in the Copernican heliocentric paradigm; thus, their ongoing search for the Sun’s elusive binary companion has never considered Mars as a possible candidate. Their current, favored candidate for a binary companion of the Sun appears to be Sirius. However, Sirius is itself a binary system (Sirius A and B revolve around their common barycenter every 50.1 years). Nonetheless, Cruttenden and coworkers have done a sterling job demonstrating, in strictly methodical fashion, the untenability of the so-called lunisolar theory: Earth’s purported ‘wobble’ around its own axis (more on this in Chapter 10).

"A recent study of the phenomenon known as “Precession of the Equinox” has led researchers to question the extent of lunisolar causation and to propose an alternative solar system model that better fits observed data, and solves a number of current solar system anomalies." "Understanding Precession of the Equinox" (opens in a new tab) by Walter Cruttenden and Vince Dayes (2003)

Figure 2.6 shows a variety of complex patterns published in a fairly recent study concerned with the barycentric motions of stars. In the TYCHOS (as we shall see further on), the spirographic orbital paths of our planets bear some resemblance to the complex yet beautiful patterns some modern astronomers are observing in what they call “the barycentric motion of exoplanet host stars”:

Fig. 2.6 Image source: Page 6 of "The Barycentric Motion of Exoplanet Host Stars" (opens in a new tab) by M. A. C. Perryman and T. Schulze-Hartung (2010)

Only a century ago, astronomers believed that binary star systems were in the minority, mostly because red dwarfs (which make up 70% of all stars) had never been observed to have companions. In recent years, however, pairs of red dwarfs have been discovered to revolve around each other at very close distance, some in less than one Earth-day. This clearly constitutes a ‘game changer’ in the €eld of stellar statistics which may ultimately rule out the existence of single, companionless stars. In any event, it certainly lends support to the notion that all stars—without exception—are locked in binary systems.

Cool red dwarfs are the most common sort of star in our Milky Way galaxy. But astronomers said yesterday (January 10, 2022) that they’ve discovered what they called the tightest ultracool dwarf binary system ever observed. The two stars in this system both are extremely low in mass. And they’re so cool they emit their light mostly in the infrared–what we’d perceive as heat–and so are completely invisible to the human eye. What’s more, the stars are close together. They take less than an Earth-day to complete a single orbit around one another. (Source: "Ultracool dwarf binary stars break records", (opens in a new tab)

In light of the facts and considerations expounded in this chapter, the notion of the Sun and Mars being a binary pair should emerge (not least from a probabilistic perspective) as a perfectly sound and logical proposition. The child’s question posed at the beginning of this chapter is worthy of serious consideration: “If the stars are suns like our own Sun, just farther away, why doesn’t the Sun also have a companion?”