Sizing and Placing Nemisis

In a prior posting, we “put some bounds” on the Nemisis thesis (that there is a small dark ‘companion star’ to the sun). In this posting, we will be looking at bounding the question of “does precession of the equinoxes mean we orbit Nemisis?”. So first we looked at “how complicated is this problem and what else is going on?”. Now we’re looking at “Ignoring all that, if there WERE a Nemisis, how big and how far?”. Then “Is that reasonable to be unfound?”

Prior posting:

One part of the “Dark Passenger” idea is that the object is dark. It needs to be dark so that we don’t have an obvious large bright star just a tiny bit of a light year away. Kind of hard to not see that…

So looking at the Brown Dwarf wiki, we find they are bounded by 80 Jupiter Masses ( Mj) at the upper end, and an ill defined lower bound, but somewhat near 10 Mj. As the “orbital calculator” I found online uses Solar Masses (Ms) we need to convert those. Mj is about 0.0009546 Ms, so those become LB: 0.009546 Ms and UB: 0.076368 Ms.

At this orbital calculator:

I made the simplifying assumption that if we are ‘swinging’ in an orbit with the object, that both will have the same period. (Something of a tautology for a 2 body system, but in fact, as we have an N-body neighborhood, it’s really a bit more complicated. But I think most of that ‘ends up in the noise’ of 4th to 20th digits of precision and can be ignored for a ‘first cut’). Realistically, we ought to be using a 2 body mutually orbiting formula. Then again, at 1/100ths place relative mass, it isnt’ really all THAT wrong to assume the sun in the center).

OK, plug in the Ms numbers, make the AU distance some random thing, then look at the orbital period and “fiddle with” the AU distance until you get about 24,000 to 25,000 year period. That’s about how far away an object can be and still be causing us to orbit with it, with that period, and be small enough to not be bright in our field of view while still being big enough for us to notice a bit of a tug.

The results?

Lower Bound: 24,717 year orbit. 180 Astronomical Units. 0.009546 Solar Masses
Upper Bound: 24,204 year orbit. 355 Astronomical Units. 0.076368 Solar Masses

Just for fun, I put in a 1/10 solar mass. Yes, it ought to be glowing. But say someone didn’t measure EVERY star and just thought it was further away? Where would it have to be?

1/10 Solar: 25,298 year orbit. 400 AU. 0.1 Solar Masses

Not surprisingly, not that far off from a 1/10 x 3/4 upper bound to a Brown Dwarf. Surprisingly, very close.

OK, so it doesn’t move much further out as you bump the mass. How about a 1/4 solar mass?

1/4 Solar: 25,797 year orbit. 550 AU. 0.25 Solar Masses

At that point we’ve pretty much bounded it.

A 1/4 Solar Mass object is going to be glowing fairly strongly. “We’d notice”. Even a 1/10 Solar Mass object we would most likely have seen by now. (It’s kind of hard to not notice a star, even a dim one, at 400 AU).

How Far Is That?

The Kuiper Belt runs out to about 55 AU (Neptune is at 30 AU). So about 3 to 10 times the Kuiper Belt. Since we are finding planet sized things in the Kuiper Belt, and they are pretty dark, that implies we could see a “dark star” too, though with difficulty and most likely only in infrared.

The Oort Cloud picks up somewhere beyond that and runs out to about 50,000 AU (or nearly a light year, per the wiki). As we saw in the prior posting, the Hill Sphere of the sun is what matters for who orbits whom, and it runs out to about a light year for small objects.

So this places any such “dark star” as clearly INSIDE the Oort Cloud. And at about 1% of the distance to the outer edge (or 99% of the way IN from the outer edge). This ought to do a heck of a lot of perturbation of both the Kuiper Belt and the Oort cloud. Again, “I think we’d notice”. For this to work, we need a pretty good sized “gap” between Kuiper Belt Objects and the inner edge of the Oort Cloud. Then again, per the wiki, the Oort Cloud is: “is a hypothesized spherical cloud of comets”. So there really isn’t any problem hypothesizing it to be whatever we need it to be.

Or just outside all of this stuff in the Kuiper Belt (about 3 x or near the far edge of the calendar on my screen):

Outer Solar System and Kuiper Belt

Outer Solar System and Kuiper Belt

Original Image

The green bits are KBOs.

Now, one bit of “finesse”. As you get to about the size of Brown Dwarfs, mass rises but radius holds more or less constant. We reach a realm where added “stuff” gets crushed by gravity enough to not add much radius but rather to increase density. So a “just smaller than brown dwarf” object, that did NOT glow in the Infrared, might well be “out there” and not visible easily. After all, something the size of Jupiter but several times more massive could still be pretty small in the visual field and it would be dark, even in the infrared (assuming it didn’t generate it’s own heat as Jupiter does…)

So how small and far a dark object can we see in the night sky “out there”?

2000 CR105 and Sedna

(148209) 2000 CR105,[…]is currently about the seventh most distant known object in the solar system. Considered a detached object, it circles the sun in a highly eccentric orbit every 3240 years at an average distance of 219 astronomical units (AU).

2000 CR105 has a diameter of around 253 km. This small size will probably prevent it from ever qualifying as a dwarf planet.

2000 CR105 and Sedna differ from other scattered disc objects in that at their perihelion distances, they are not within the gravitational influence of the planet Neptune. It is something of a mystery how these objects came to be in their current far-flung orbits. Several hypotheses have been put forward:
They were pulled from their original positions by a passing star.
They were pulled from their original positions by a very distant and as-yet-undiscovered (albeit unlikely) giant planet.
They were pulled from their original positions by an as-yet-undiscovered companion star orbiting the Sun. (See: Nemesis (star).)
They were captured from another planetary system during a close encounter early in the Sun’s history. According to Kenyon and Bromley, there is a 15% probability that a star like the Sun had an early close encounter, and a 1% probability that outer planetary exchanges would have happened. 2000 CR105 is 2–3 times more likely to be a captured planetary object than Sedna.

So here we have an object that is vastly smaller than Jupiter (at 71,492 km radius) and much further away, yet we can see it. The orbit ranges from 44 AU to 394 AU, so it’s “in the neighborhood” of any “Dark Passenger” that would be in the inner 1% of the Oort Cloud. It would need to be in some sort of “resonance” orbit to avoid being tossed out of the system (or into the inner parts). Dividing 25,787 (one of the estimates of the precession interval) by the orbital period of 3240.91 gives 7.949927644 which looks to me to be inside the error band of an 8:1 orbital resonance. OK, that argues for a “possible”.

Puts Sedna at 76 AU closest and 960 AU furthest orbit distances. With an 11,809 year orbital period (which, at 2.1818 is close to a 2:1 resonance so it could still “work”, but things are getting more complicated). At about 1500 km in diameter, it’s pretty small compared to a “Brown Dwarf”, yet we found it. So we are able to find things of about the aparent magnetude of our “Dark Passenger” (assuming that something of similar brightness, but 100 times greater diameter, and 100 times further away, would have about the same brightness; which ignores the inverse square light loss, but we’re ignoring so much already ;-)

OK, at this point it’s looking to me like any Brown Dwarf would have been spotted as they are certainly large enough and glow enough in the infra red that we ought to have noticed them at the inner edge of the Oort Cloud location. At the same time, an object just smaller than a Brown Dwarf might go un-noticed as we’ve not scanned the whole sky in fine enough detail and, frankly, once you are at “Jupiter diameter” but 1000 AU away, it will be very hard to see as it’s pretty dark out there. You are looking for a planet illuminated by “starlight” as the sun is just another star (albeit a bright one) in the sky at that distance. Darned Hard.

But I’d not call such an object a “Dark Star”, more of a “Big Cold Planet”.

In the Sedna wiki it also states:

It has been suggested that Sedna’s orbit is the result of influence by a large binary companion to the Sun, thousands of AU distant. One such hypothetical companion is Nemesis, a dim companion to the Sun which has been proposed to be responsible for the supposed periodicity of mass extinctions on Earth from cometary impacts, the lunar impact record, and the common orbital elements of a number of long period comets. However, to date, no direct evidence of Nemesis has been found. John J. Matese and Daniel P. Whitmire, longtime proponents of the possibility of a wide binary companion to the Sun, have suggested that an object of five times the mass of Jupiter lying at roughly 7850 AU from the Sun could produce a body in Sedna’s orbit

But as we’ve seen, for Nemesis to also account for the Precession, it would need to be so close we’d likely have seen it as “it glows”. So we’ve ended up at the “Dark Passenger” planet as the only thing likely. And that is the same thing suggested at the end of that wiki article. A 5 Mj giant planet at 7850 AU. But does that “work” in our orbital calculator?

5 Mj is 0.004773 Ms. Plugging that in with 7850 AU gives an orbital period of 10,067,232 years. Ooops. Not going to work… Put it at 150 AU and you get 26591 as the orbital period.

So we seem to be at a conundrum. If you make the proposed object big enough to account for the “action” while far away, it’s rather large and ought to be visible (a Brown Dwarf or other object glowing in the visible or infrared). As you move it further away, it must get larger and even more self luminous. As you bring it closer (so smaller and not self luminous) you must be inside a range that has much smaller objects already discovered (it must be an object larger than those we have already found by a couple of orders of magnetude). To be both dark, and accounting for the orbit of Sedna, it must be way too far away to account for precession.

At this point, we’re back into the N-body problem. It’s always possible that the object has a very eccentric orbit, so only sometimes does it come close enough to cause precession effects and / or disturb KBOs or eccentrics like Sedna.

But for that to hold, we can’t have much “stuff” left in the Oort Cloud. Such an eccentric orbit would have a very large (multiple Jupiters) sized object scouring the Oort Cloud turf with a hill Sphere of giant proportions. It would have captured or disrupted anything out there some long time ago. Even then, for our present precession to be accounted for by it, it would presently have to be at about the calculated distances. We’re back in the “size / visibility” conundrum again, but only for “now” as “later” it could be “far far away” at 50,000 AU.

In the end, it all comes down to: What are the odds that an object roughly the diameter of Jupiter, but not glowing in the IR band much or at all, and with about 5 Jupiter Masses, could be on a very elipitical orbit (so Sedna could have it’s orbit work out as a resonance) and yet be near enough at the moment to account for our precession (or about 150 AU) and remain unobserved?

I’d make that “very low”, but clearly non-zero. At 2 x the Sedna distance but 100 times the Sedna diameter, it ought to be visible. But we might just not have looked in the right place, at the right time, with the right spectrum to have noticed it.

To go beyond this point will take more compute facilities and more time looking at more “odd cases” than I can manage to do. It requires solving an N-body problem for at least 2 large objects “in the area” with the proposed “Dark Passenger” along with the central solar system as a body and D.P. itself. That’s at least a 4 body problem even with simplifications like lumping everything inside the Kuiper Belt into one object. But my sense of it is that it’s highly unlikely to “work out”.

Though if we find one it would be “way cool” as it implies the Oort Cloud has been given a good scouring over the last few billion years. Perhaps that is where the 4+ Billion year ago “cometary bombardment” came from…

IMHO, much more likely would be some collection of other explanations. Some collection of objects in the inner Oort Cloud orbital area accounting for Sedna’s orbit. The combined gravitational vectors of all the OTHER Brown Dwarfs et. al. inside a 5 light year area of Sol creating a “local stars barycenter” about which the solar system orbits on a 25,000 year period (but with instabilities as various stars leave our local group). Then you can have your mass, but keep it dark enough and far enough away to be effectively invisible. Could we really see 10 Brown Dwarfs that were at the lower bound (so about 700 C) and a light year or so away? It would be very hard.

So far we’ve found only a couple, and they tend to be orbiting other things (that would make finding them easier) or somewhat brighter:

The rare object is only 12.7 light years from Earth, circling a primary star that itself was discovered only recently in the southern hemisphere constellation Pavo (the Peacock).

Only one other brown dwarf system has been found closer to Earth, and it’s only marginally closer.

The primary star is only one-tenth the mass of our sun. This is the first time astronomers have found a cool brown dwarf companion to such a low-mass star. Until now, none has been found orbiting stars less than half the mass of our sun.

The brown dwarf is 4.5 AU from the star, or four and one-half times farther from its star than Earth is from our sun. Astronomers estimate that the brown dwarf is between nine and 65 times as massive as Jupiter.

Brown dwarfs are neither planets nor stars. They are dozens of times more massive than our solar system’s largest planet, Jupiter, but too small to be self-powered by hydrogen fusion like stars.

Only about 30 similarly cool brown dwarfs have been found anywhere in the sky, and only about 10 have been discovered orbiting stars.

“Besides being extremely close to Earth and in orbit around a very low-mass star, this object is a ‘T dwarf ‘ – a very cool brown dwarf with a temperature of about 750 degrees Celsius (1,382 degrees Fahrenheit),” said Beth Biller, a graduate student at The University of Arizona.

“It is also likely the brightest known object of its temperature because it is so close,” Biller said. “And it’s a rare example of a brown dwarf companion within 10 astronomical units of its primary star.”
“What’s really exciting about this is that we found the brown dwarf around one of the 25 stellar systems nearest to the sun,” Close said. “Most of these nearby stars have been known for decades, and only just recently a handful of new objects have been found in our local neighborhood.”
Close helped develop the special adaptive optics camera, the NACO Simultaneous Differential Imager(SDI), that the team used to image the brown dwarf. The camera is used on ESO’s Very Large Telescope (VLT) in Chile. Another SDI camera is used at the 6.5-meter MMT Observatory on Mount Hopkins, Ariz.
The discovery of this brown dwarf suggests there may be more cool brown dwarfs in binary systems than single brown dwarfs floating free in the solar neighborhood, Close said. A “binary system” is where a brown dwarf revolves around a star or another brown dwarf.

Astronomers now have found five cool brown dwarfs in binary systems but only two single, isolated cool brown dwarfs within 20 light years of the sun, Close noted. They can expect to find more T dwarf companions in some newly found stellar systems within 33 light years of our solar system, he added.
The NACO Simultaneous Differential Imager(SDI) uses adaptive optics to remove the blurring effects of Earth’s atmosphere to produce extremely sharp images. The camera enhances the ability of the VLT to detect faint companions that would otherwise be lost in the glare of their primary stars.

So if we’re seeing these guys at 12 light years away, with stars or alone, it seems very unlikely that we’d miss one at under 1 light year. Possible, yes, as it’s easier to spot one thing where you are looking than to have looked everywhere. Since these are relatively new tools, the odds that we’ve done a full scan of the night sky is pretty slim. It will all come down to “how many wide scan instruments of this sort are in use and how much of the sky have they looked at?”. That is specialized information I don’t have.

Given all that, my conclusion has to remain:

It’s not highly likely, but it’s a distinct possible. We don’t know, and we can’t know until a long inventory of the sky is completed. Whatever it might be, it would need to be small diameter and dark, and that limits the placement in the sky to ‘fairly close’, and that reduces the odds that we’ve “missed it” and increases the odds that “it just isn’t there”. It would need to be at the inner edge of the Oort cloud and that implies a fairly empty Oort cloud.

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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13 Responses to Sizing and Placing Nemisis

  1. Soronel Haetir says:

    Something that occurs to me, having an object with an orbital period of 24k years is not going to be enough. At least not on its own. Any such object is not going to drag the entire solar system around with it on a per orbit basis. Some yes, but not all the way, probably not even half, maybe 1 radian per orbit and even that seems pretty optimistic. Maybe if the Sun were the gravitationally weaker partner, but that seems even more far fetched than an unseen object with the proposed properties.

  2. E.M.Smith says:

    @Soronel Haetir:

    Yeah, I “assumed that one away” as it was inconvenient ;-)

    The reality is more that it would make the sun wobble and rotate about a barycenter on a 24,000 year basis, but the planetary orbits would be more disrupted than “fixed in relation to the sun” with a similar 24,000 year movement.

    IMHO, it more or less “kills the deal” right there as the object needs to be more massive than the sun, and that mean it would be lit up way bright.

    But as I didn’t want to have to think about a N-body where N is over 20 for the big bits problem; I ‘assumed the solar system moves as a unit’. And while that is reasonable if Nemisis is 20 Sol masses and far far away, it breaks down if Nemisis is 1/100 solar mass and is at 120 AU (with Neptune at 40, it would disrupt Neptune like crazy…)

    But that does not mean the exercise is an empty one. It showed that Nemisis has to be inside that size and placement range where the assumption breaks down from the planets getting screwed up…

    Though it does leave open the need to calculate at exactly what point does the solar system “wobbles as a whole” with the orbits not too perturbed. Given Neptune at 40 AU, that’s 80 AU diameter. I think you need a significant multiple of that for the differential to be very small. If it’s 4 x you are at 360 AU. Barely in the “possible” range. (And I’m not sure 4 x is the right multiple. If it’s 8 or 10 x things are a non-starter, IMHO). But that needs a level of detail I can’t just do right now. Other irons in the fire and all…

    So someone else needs to pick up that bit and run with it.

    After all, it’s “outside my assumptions” ;-)

  3. Jerry Franke says:

    Having read both parts of your analysis of the Nemisis thesis, I have to agree with your conclusions that it is unlikely that there is such an object in orbit around the sun.
    The observed cyclical precession, however, seems to contradict that conclusion. You leave open the unlikely possibility that we simply have not yet found the object.
    Since I agree with your conclusion and don’t dispute the observed precession, I am forced to propose that there is some other explanation for the precession. However, any other explanation would seem to violate known laws of orbital mechanics. Perhaps not!
    I direct our readers to the phenomenon seen in the Keeler Gap in the ‘A’ ring of Saturn’s ring system. The gap is 42 km wide and is swept clean by a small moon (Daphnis) that orbits at a slight incline to the plane of the ring system. At both edges of the gap are waves in the ‘A’ ring that are perpendicular to the plane of the ring system.
    I have not been able to find an explanation as to how Daphnis can create such a high frequency of uniformly spaced waves. I understand orbital mechanics enough to know that Daphnis’s orbital speed is very close to the orbital speed of the particles comprising the waves on either edge of gap but I cannot understand why it produces waves so far from its current position. Since the amplitude of the waves are perpendicular to the plane of the rings, it follows that the particles comprising the wave are in an orbit that is inclined to the ring plane.
    If one scales this phenomenon up to the scale of our galaxy, one could imagine our solar system being an element in such a wave.
    So far, I am assuming that the observed waves in the Keeler Gap and the postulated wave that we are in are comprised of elements that are in an orbit that is inclined to the ring plane and galactic plane, respectively. Using that assumption, the postulation doesn’t fit for a precession cycle of 25,000 years since our revolution around the galaxy takes 230 million years. Therefore, for my idea to work, the perturbing body (Daphnis/Star X) must be creating a wave train within the gravitationally bound particles/solar systems. Is that possible? It could explain the uniform spacing of the waves in the Keeler Gap. If our solar system was an element in such a wave, wouldn’t it manifest itself in a precession? Wierd science, yes, but that Keeler Gap is wierd. This whole idea may just be Jerry’s Reasoning Gap.

  4. Joel Heinrich says:

    How about a blob of dark matter and/or dark energy, as 95% of the “stuff” in our universe is supposed to be comprised of them. And yes, it would be invisible but still influence gravitationally.

    Sure, it sounds like a “I don’t know what it is, so let’s call it god (or dark energy)” (pun fully intended ;-) ) reasoning. But then, this is the whole reasoning behind the dark matter/energy.

  5. Hugo M says:

    I’m very grateful for you having brought up Hill spheres. That theory answers an very old question of mine. Regarding your planet ‘x’: Your limits would include a planet at n=10 corresponding to 307 AU when applying the Titius – Bode rule. I know that it’s validity is widely doubted. However, when John Tukey once explained the difference between exploratory and confirmatory data analysis, he said that we unfortunately did run out of planetary systems when trying to confirm the Titius-Bode series. That situation is beginning to change now:

    Since Hill radii are proportional to the semi-major axes, the orbital distances of successive planets with similar masses will tend to obey an approximate exponential law, much like the century-long debated and polemical Titius-Bode law in the Solar System. Indeed, Hayes & Tremaine (1998) have shown that any planetary system subject to some ’radius-exclusion’ law such as the Hill criterion is likely to have its planets distributed according to a geometric progression.Source:

    Figure 14 of this paper shows a fit of exponential laws to semi-major axes as a function of planet number for the inner Solar System, HD 40307, GJ 581, HD 69830 and HD 10180.

    Below is some lines of R code to plot the Titius-Bode Series:

    n = c(-1:11); # -1 as a plotting surrogate for -Inf
    xyplot( (0.4+0.3*2^n) ~ n,
             xlab   = "n",
             ylab   = "Solar Distance [AU]",
             main   = 'Titius-Bode Rule\n a = 0.4+0.3*2^n [AU]',
             scales = list(y=list(tick.number=10)),
             type   = c("g","p") );
  6. pascvaks says:

    Not to mess up anyone’s train of thought, or add unwarented speculation to the work, so if this sound’s too Batman and Robin (High School), please delete –

    the Kuiper Belt & Oort Cloud must have an effect on the Sun and inner solar system which would need to be eliminated as responsible for the presession question?

  7. Hugo M says:

    the Kuiper Belt & Oort Cloud must have an effect on the Sun and inner solar system which would need to be eliminated as responsible for the presession question?

    IF the matter in the Oort Cloud was evenly distributed among a sphere-like shape enclosing the solar system then there should be no net force inside that sphere. But the distribution of matter within the Oort cloud are unknown.

    The Kuiper belt objects on the other hand should influence inclined and far outreaching orbits like that of Pluto, i. e. pulling them gently towards to the ekliptic plane. But Pluto is also the most massive known object there.

  8. Nemesis (pronounced:Nhemeis)
    However, as for this: In Greek mythology, Nemesis (Greek, Νέμεσις), also called Rhamnousia/Rhamnusia (“the goddess of Rhamnous”) at her sanctuary at Rhamnous, north of Marathon, was the spirit of divine retribution against those who succumb to hubris (arrogance before the gods). The Greeks personified vengeful fate as a remorseless goddess; the goddess of revenge.The name Nemesis is related to the Greek word νέμειν [némein], meaning “to give what is due”, as in the word “economy”.[1] The Romans equated the Greek Nemesis with Invidia.[2]
    Returning to the point, we should ask: What is it a star. If an electrode (as EU guys say) then our Sun it is not as big as it is its what we see: its atmosphere. The core-electrode should be ( if we calculate it with the simple Law of the Octave):
    Sun´s Diameter:
    8477.30 km

  9. E.M.Smith says:

    @Jerry Franke:

    A very interesting idea! FWIW the spiral “arms” of the Milky Way are NOT made of star groupings that move directly forward through space as a feature. They are “compression waves” in the disk of stars.

    Like in a traffic jam where everyone speeds up, then comes to a slow spot and all ‘get close’ again, then as things speed up they spread out again, and repeat…

    So if we are “speeding up and slowing down”, what happens to a spinning top when you jerk it around? It precesses…

    So I’d be most inclined to think it’s an artifact of the “speed up / slow down” spiral arm motion. Oh, and there is an “up and down” component too, where we pop above the centerline of the galaxy and then the net gravity below us pulls us down to an overshoot the other way,,, until we get pulled back up…

    So with our “Top” spinning and being jerked up and down and back and forth, it may not take any individual star to cause us to precess. Just the collective gravity of the galaxy…

    Now if only I had the time to work out the angular momentum / rotation / precession changes from THOSE motions of the solar system ;-)

    (He hinted broadly for someone else to give it a crack ;-)

  10. David says:

    E,M,. thanks for this post and the preceding one. My understanding is slowly increasing in this area. I assume you read the entire BRI site, yet understand if you did not. If I am going over anything already posted then forgive the redundancy as all orbital mechanic processes are new to me so you may have addressed something relevant to my points below, and I did not connect how they were cogent.

    The most impressive “evidence” claim (IMV) made in the BRI site is that precession is only observed in relationship to objects outside the solar system, and is NOT observed on objects inside the solar system. If this is true it is fundamental and huge, accounting for the entire 50+˝p/y precession observable minus effects such as Nutation, Chandler wobble and other short-term polar motions would also appear to have a basis in local dynamics as the observation of precession then could only be the result of the solar system curving through local space. Your comment agreeing with my assessment here was as follows…“The one “niggling bit” that bothers me is their assertion that we use a non-precession set of coordinates for professional astronomers to find things inside the solar system, but a precessional one for things outside the solar system. I have no way to verify the veracity of that statement.
    To the extent it is true, that objects inside the solar system do not show the 24,000 year precessional cycle, then it simply must be that the solar system as a whole is rotating and / or orbiting something. But what?”

    Here is what I found in the BRI site in relationship to this. Studies (I do not know what studies he is referring to) show that changes in earth’s orientation relative to objects “inside” the SS (i.e. Sun, Moon, Venus, etc.) are negligible (less than an arc second or two p/y), whereas changes in earth orientation relative to objects “outside” the moving frame of the SS (fixed stars, quasars, etc.) are over 50˝p/y. In fact, rotation time equivalence studies and lunar studies show the earth hardly “precesses” at all relative to objects within the SS.

    Most astronomers acknowledge this in practice by using a non-precessing tropical frame to locate objects “inside” the SS, whereas they require a precessing sidereal frame (or T[J2000]+PxY) to find objects “outside” the moving SS. For example, when they plot the position of planets or moons within the solar system they use a tropical frame, which by definition excludes precession (Footnote 2) thus no precession adjustment is required or even considered. However, when the position of a star needs to be found you first find the object at a point in time (say J2000) then add precession for each year that has passed since that point. Thus current ephemeris methods account for the two frames; precession is excluded when plotting objects within the solar system and included when plotting objects outside the solar system

    BRI states this through rotation time equivalence…
    365.24219878 x 86400s = 366.24219878 x 86164.0905382s = 31,556,925.97s
    This equation describes Earth’s complete 360° period of revolution of 31,556,925.97s relative to a fixed frame of reference, implying that the position of the vernal equinox remains fixed with respect to the orientation of Earth’s axis in space. The total number of rotations of Earth in such a complete orbit is expressed by the equations:
    1 ÷ (1- (86164.0905382 s ÷ 86400 s)) = 366.24219878
    86400 s ÷ 235.9094618 s = 366.24219878 No precession with respect to the SS frame.
    (I do not know if this means what he says it does.)

    BRI explains this in the “Evidence” tab discussing the Lunar Cycle, gives three links, and a sub heading, Missing Motion and the Lunar witness. (While my mathematically poorly educated mind can grasp the concept, I cannot validate the quality of the arguments here.) BRI gives further details on this under the Calculations tab, sub heading Precession Measurement Paradox.
    I understand that there are many forces of disparate strength affecting all such processes. However the fundamental current theory is the moon is thought to be the principal force acting upon the oblate earth. However, the moon is slowly receding from the earth (thereby theoretically producing less torque) whereas the precession rate is slowly speeding up (an indication of a greater force at work). While many of the historic changes in precession are due to better observations, the change in the rate of precession is real, dynamic and observed. The BRI site details this…In 1894, about the same time that the great astronomer Simon Newcomb gave us a precession formula with a constant of .000222 p/y (designed to predict changes in the precession rate), an Indian astronomer, Sri Yukteswar, explained that the moving equinox (precession) was a result of a moving solar system and he gave us a binary orbit periodicity of 24,000 years, with apoapsis at 500 A.D. Applying Kepler’s laws to Yukteswar’s orbit data (constrained by a 24,000 year orbit period and apoapsis at 500A.D.) to come up with a forced eccentricity and expected rate of change for the 100 year period between 1900 and 2000 of .000349˝p/y.

    If in 1894 someone had told the western world about Yukteshwar’s prediction vs. Newcomb’s they would have been ridiculed. Well we now have a 100 year observable and Yukteshwar’s prediction via Kepler’s .000349˝p/y rate of change applied to that 100 year period is almost exact to the actual observed, The actual rate of change for the precession observable (or change in angular velocity traveled by the solar system along its binary orbit path in the dynamic SS model – seen as parallax) was .000346”p/y. So it is a fact that Yukteshwar’s prediction was 41 times more accurate then Newcombs prediction of a .000222 linear and non dynamic change. The binary theory is predictive so if Yuketeshwar is correct the rate of precession should range from a low of about 50” p/y to a high of about 62” p/y.

    The BRI site says more about their projected solar mass and distance which you may find interesting under the “finding it” tab.

    Like you (only more so) I do not have the way and or time to evaluate either the range of Brown Dwarfs, or the details of the methods of observation which would enable me to reliable estimate what the chances are that we have missed a companion which fit’s the orbital requirements. I did notice a few things from your link in this regard. “Most of these nearby stars have been known for decades, and only just recently a handful of new objects have been found in our local neighborhood.” So they found the further ones first, for whatever reason. And this…“The discovery of this brown dwarf suggests there may be more cool brown dwarfs in binary systems than single brown dwarfs floating free in the solar neighborhood,
    Astronomers now have found five cool brown dwarfs in binary systems but only two single, isolated cool brown dwarfs within 20 light years of the sun,
    Evidence that T dwarfs in binary systems outnumber single, isolated T dwarfs in the solar neighborhood has ramifications for theories that predict single brown dwarfs will form more often than binary ones, Close said.”

    So they found further out ones first and they have indications that they are more likely to be binary then thought. Further reading showed that of the 1,700 or so brown dwarfs found there is a greater range of luminosity in various spectrum including both heat and x-ray then thought. Thanks as always for your time and interest.

    BTW, the solar system anuglar momentum chart in the BRI site was also interesting.

  11. David says:

    Some additional details on the Solar System precessional observations are on pages 12 and 13 of this attached PDF

    Click to access BRI-Evidence.pdf

  12. David says:

    Page nine of a different BRI PDF states that the Perseids Meteor Shower shows that the Earth goes around the Sun 360 degrees in a tropical year, as further evidence of the lack of precession within the S.S. ( BRI relly needs to consolidate all this to one paper)

    Click to access ComparisonPaper.pdf

  13. E.M.Smith says:


    I read the BRI site on the “evidence” part, but not the “finding it” part. (It’s on me “do sometime” list…) Figured I do my own “where would it be?” first (as it’s a cleaner slate that way) then go back for a ‘compare and contrast’ later.

    Yes the “niggling bit” is what you said. I just bothers me that, if it is true, we’ve got every astronmer on the planet trained to use two tools for finding things in the sky that just screams that precession is from solar system rotation, not planetary, yet they would not notice that does not agree with the precession explanation. So why are they not speaking about it? … Are they all that dense? That’s “niggling”…

    That we are still finding brown dwarfs and that their spectral character is highly variable says we COULD have a very cold and dark brown dwarf neighbor. (In fact, it could even be from the beginning of time, so have had an extra 10 billion years compared to us to cool down to nothing…)

    That’s why I took the “How far?” approach not the “How to see it?”. If you have something you might not be able to see, “that’s an issue”…

    And, frankly, that’s the thing that keeps it in the “possible”.

    By sizing and placing, we find that to be even modestly far away, it must be big enough to glow. 1/4 to 1/2 solar masses is going to be a very bright visible star. (Unless as was suggested, dark matter floats around in lumps… could you have a very old “burned out” solar mass object made of nothing but Iron? No nuclear furnace available any more, yet not a black hole or glowing neutron star? I just don’t know. But typical objects in those sizes are seen as stars.) That means our “Dark Passenger” has to be smaller to be dark. (This is the assumption I’d attack, BTW, the question of “must it be small to be dark?” is being stated as an assumption and that is not really known. But running with it…)

    So as we get small enough to be a dark Brown Dwarf, the object has to be at the inner bound of the Oort Cloud. That means it’s Hill Sphere will have “done a number” on any proto Oort Cloud and left it much emptier than theory suggests (ninus said Dark Passenger) AND it ought to have a very significant impact on the orbits of things in the Kuiper Belt. It also ought to be fairly easy to see, even if dark.

    Again we reach the point where we can’t say yea or nay.

    We are spotting OTHER smaller dark objects at those general sorts of ranges. But it’s easy to “see where you look” and just as easy to “not see it as you didn’t look at it”; so unless we’ve done an inventory of the whole sky (AND not been so unlucky as to survey a block, then move on, just the the object changed into that now abandoned block… thus missing it …) we simply might have ‘missed it’.

    Then there are things like Sedna that have an orbit suggeting it is there (or something was once) while other objects like Pluto have orbits that (being non-disturbed as near as I can tell) argue there is no large object “not too far away”.

    Pluto goes out to abot 50 AU. If D.P. is at 150 AU, then Pluto would vary from being 100 AU from it to being 200 AU from it. “We’d notice”. Unless it was in a resonance orbit such that it didn’t ever actually get close… which I’m not so sure can happen (I think it would need an inclination that put it “on the other side” of the ecliptic when “near” and that rotated at 24000 years, but that’s just speculation).

    So that’s where I ended. Not finished, just ended for now.

    Wondering if there is an easyier way solve this question than doing all the orbital mechanics “stuff” on Pluto, Neptune, Sedna, et. al. to show if they can “do what they do” even with a D.P. at 150 ish AU…

    And while “Unlikely but possible” is unsatisfying, that’s what Iv’e got. That, and the observation that we’re talking distances and masses that can have “local star neighbor” collective gravitational forces “doing odd things” to us as well. Common barycenter orbits, perturbations as some star a billion years ago passed inside the Oort Cloud distance, and is now long gone. That whole “galactic arm” compressional feature. (Being attracted to the higher gravity of the more dense star field, then, when at closest approach, having velocity that sends us on through it, only to have the density now slowing us from the other side, until we … repeat) and wondering if “bobbing around” as a giant top is causing the wobbly bits… (Sadly, I’m not good at mental modeling angular momentum problems. It’s a bit non-intuitive. Add that I’m a bit lazy on doing AM math, and it’s just one of those things that I’m not that great at doing. (Love watching a gyroscope tumble then be stable, then tumble again; but how to explain when and why?…)

    At any rate, this is about as far as I can move this question without either a lot more work or some new insight. I’m hoping for new insight ;-)

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