67P/Churyumov-Gerasimenko. A Single Body That’s Been Stretched- Part 17.

ANUKET-TO-ANUBIS: MATCHES EMERGING FROM THE TERMINATOR.

(Original, unannotated photo is reproduced at the end of this post).

This post is twinned with Part 16, the second of a pair of posts on simple, obvious matches based on recent NAVCAM photos. In part 18 we’ll return to a fourth monolith that floated across the width of the crater known as Site A.

The header photo shows the Anuket region of the neck and Anubis region of the body which are both becoming more and more illuminated as 67P rounds the sun towards perihelion in August 2015. The gradual creep in illumination is towards the right of the frame and, as a result, matches are emerging as they slowly cross from the dark side to the light side of the terminator. There’s a significant large-scale match, running for a kilometre or more along the head rim and shear line.

The head rim appears to follow an obvious corresponding line on the body. The two lines look as if they would fit together without any swiveling around (rotation in any axis) to seat them. In other words, they are almost perfectly parallel. This chimes with the tenets of stretch theory as described thus far because this is the most tipped-up part of the head rim due to being in line with the comet’s rotation plane (Part 10). This in turn means that the head rim at this point lifted straight up and parallel to the body, like the lid of a box. The front of the lid remains parallel to the body of the box whereas the sides of the lid are sloped with respect to the box body. Indeed the side of the head has been shown in numerous photos to be sloping up at about 30°-35° and this has been commented on in many parts of this series with specific reference to the tip-up being in line with the rotation plane, especially in Parts 10 and 11.


The two red-dotted lines would also require almost no sideways, translational adjustments, just the obvious downward translation to close the lid, so to speak. This is the exact reverse scenario of the stretch and tip that has been posited for stretch theory as the head lifted from the body.

So this simple closing of the lid to marry the matches is not just explained in retrospect by stretch theory but fully expected in advance.

CHECKING THIS MATCH AGAINST CONTACT BINARY THEORY

If the head and body lobes were two comets that had drifted together to form a contact binary, they would have had to come together while sporting these two ridges that match perfectly in 3 rotational axes (6 degrees of rotational freedom) and 2 out of 3 translational axes (4 out of 6 degrees of translational freedom). That means the two lines in the header photo have affinity in 10 out of the possible 12 degrees of freedom. The chance of this happening is virtually nil.

Imagine hurling a skyscraper-sized monolith from the other side of the sun, only to find that it landed in New York City, perfectly upright, its footprint perfectly aligned with the grid system but somehow hovering one kilometre above its designated block in the grid. That illustrates the coincidences needed for two such far-flung bodies to unite in the deep recesses of the Kuiper belt and satisfy 10 of the 12 degrees of freedom in the process.

Furthermore, they would have to approach each other at less than 1m/sec while both orbiting at speeds of anywhere between 400m/sec (per Sedna’s aphelion velocity at 936 AU) and 6km/sec (Pluto’s perihelion velocity inside Neptune’s orbit). This requires an absolute velocity match to within 0.25% at the very least and an approach angle of no more than sin-1(1/400). That would be the angle whose sin is 1/400, which is 0.15 degrees. This slimmest of chances would in fact be their best chance to come together and would apply only at 900 AU, for a few hundred years every few thousand years. In other words, both bodies would have to be, essentially, in identical orbits to have any chance of coalescing.

If 67P really is a contact binary, then this virtually impossible close approach dynamic for the two lobes had to satisfied or they would have simply sailed right on past each other. This, along with the astonishing affinity between the lobes, once they were joined, is an indication of the exquisitely accurate formation flying that these two supposedly disparate Kuiper belt objects are capable of. Not to mention their capacity for some sort of action-at-a-distance shape telepathy.

CHECKING THIS MATCH AGAINST THE ASYMMETRICAL EROSION THEORY

With regard to the other alternative theory, asymmetrical erosion of a single body, why would the two edges of the eroded cavity exhibit such convoluted, small-scale matching features sitting one kilometre apart?

CLOSE-UP OF THE MAIN MATCH

There is a particularly good correlation in the lower-right section of the header photo match. It’s reproduced here, zoomed in and matched in finer detail. Zooming is required as well as scrolling up and down to compare the two lines. The dots are small so as not to obscure the matching features.
Red: head-to-body match.

Green: an apparent matching strata feature i.e. a feature that has a 3-dimensional depth and is therefore replicated at a lower stratum layer. See the last few paragraphs for more discussion on the 3-dimensional nature of the matching lines, which will shed more light on this phenomenon.

THE NECK PROTRUSIONS AND THE SIGNATURE OF THE ANUBIS SLAB

The Anubis missing slab was briefly mentioned once before and it deserves a post of its own. However, it’s intimately related to this post’s match, so it’s included in order to understand the 3D properties of the match.

As well as showing the head fitting to the body, the header photo exhibits a noticeable triangular protrusion on the head rim. The photo is reproduced below with the protrusion annotated. But there is more than one protrusion. There are two more, directly below the main one. They’re sticking out of the neck and similarly triangular in shape. There are a few more stunted ones below that.
Red- main match as described above.

Yellow- tips of the three most obvious triangular protrusions. The more stunted ones extend below these three (not annotated due to risk of obscuring them).

Bright green- body protrusions (see below)

Orange- probable body ‘protrusion’ that has completely drooped over flat.

Mauve- another 3-dimensional depth match. This sits just in front of both red lines. See final paragraph.

Viewed together, these triangular head and neck protrusions look as if they used to be pressed together like the layers in a wafer or perhaps a compressed concertina. When the neck stretched, they were pulled apart but in line with each other just like the folds of the opening concertina.

It would be tempting to match the head protrusions to that obvious right-hand protrusion on the body, marked with bright green dots. They would have been seated near to this point when compressed together but probably not right on it. This is because this body protrusion and those to the left of it mark the boundary of Anubis which bears all the hallmarks of being the site of another missing slab (see Part 9 for the mechanism of departure for slabs A and B). This would explain the wholly different morphology of this region and the different morphology is certainly the reason for it being delineated by ESA as a separate region and named ‘Anubis’.

The height of that body protrusion (about 50 metres) and the others to the left of it would correspond to the depth of the slab. It’s where the slab would have torn away from the body and so these protrusions are now drooping over under the force of gravity, just like large portions of the Site A rim are currently drooping outwards where missing slab A tore away (slab A, sited on Landing Site A; Part 9). The orange, dotted line marks one probable protrusion that has drooped over completely and is now lying flat against the surface. The edge of the Anubis missing slab would have taken on the imprint of these body protrusions.

This indicates that there was a lot of upheaval along this top perimeter of Anubis and the best fit for the concertinaed head protrusions is to a point that’s just behind that drooping body protrusion. The body protrusions appear to have resisted detachment along with the slab because they are the resilient rims of craters and sited just beyond the sudden, 90° turn in the body surface topography.

The concertinaed head protrusions might just as easily have been left behind on the body, intact and unstretched, alongside the body protrusions. For this reason, it could well be that the matching point for these head protrusions was also imprinted on the narrow edge of the slab that departed long ago.

Indeed, this fact has profound implications for this post’s main match in the header photo. It allows us to venture into the third dimension, thus further corroborating the match. Some eagle-eyed readers may have spotted that the red match line on the head lobe is actually following a ridge with a constant depth (around 50 metres) like a rebated rim and yet it appears to match just a one-dimensional line on the body that starts just to the right of that right hand body protrusion. One would expect it to match to a corresponding 50-metre-wide shelf on the body, not a line.

The triangular head protrusion is integral to this rebate and the fact that it may have seated against the edge of the Anubis slab gives us a clue to answering this paradox: the whole of the rebated rim was likely attached to the edge of the Anubis slab. The angle is correct- the rebate is angled inwards at 90° to the surface of the head and, for that matter, to the body as well, just like the edge of the slab would have been. In other words, this rebated rim is just another version of the body protrusions and when the head was seated on the body, the rim would have continued on from its body protrusion counterparts. Together, they would have formed the vertical edge of the tray that contained the Anubis slab.

The width of both the rebated head rim and all the body protrusions is the same, about 50 metres. These are two different sets of features that point strongly to the missing Anubis slab being 50 metres thick. So the expected 50-metre-wide shelf on the body was indeed there, but it was integral to the slab that departed.

That one-dimensional red line in the header photo, constituting the body match, would therefore correspond to the bottom of the edge of the Anubis slab just before it lifted off. It also means that the red line on the head lobe should really be matched to the top edge of the missing slab and not the red body line. But the slab is long-gone so the body line was used as a proxy for convenience. The true match to the red body line is in fact the inner edge of the rebated head rim, that is, the line in the shadows that is running parallel to the outer edge of the rebate that’s dotted red (see next photo). It’s a testament to the faithfulness of the matches that the outer edge of the rebate could be used as a proxy for the inner edge and yet still match to the body line so dramatically. In reality, if you seated the head back down onto the body, the head dotted line would be hovering 50 metres above the body dotted line, twisting and turning along the entire length of that faithful match. Together, they would define both the perimeter line and the thickness of the Anubis slab.

Put another way, the rebated head rim, as we see it today, is itself the imprint of the edge of the Anubis slab.

The following photo with a rather alarming array of colours is included as an attempt to explain the above. It’s taken from a slightly different angle from the header photo and shows up the head lobe’s rebated rim more favourably. Red- shows the inner and outer rims of the head rebate and their corresponding paths when the head was seated on the body. The bottom body line is the same as it is in the header photo and corresponds to the inner head rim. It runs just behind the mauve-dotted formation and is extended beyond its header photo position as far as the bottom of the green-dotted body protrusions. This line traces the bottom edge of the Anubis slab. The upper body line corresponds to the outer edge of the head rim and is therefore floating in ‘mid air’ and faithfully following the line of its lower counterpart. It traces the upper edge of the missing Anubis slab. It is extended beyond the header photo position to the point where the upper edge of the slab would have married to the upper edges of the green body protrusions.

Light blue- this should be treated as part of the red line. It’s annotated in blue simply because the path of the inner head rim at this point isn’t quite as clear as for the rest of the rebate- it could be further to the lower left and so is more provisional. The body line has been changed to blue as well, just to show where it sits but this line isn’t so speculative as it matches the outer head rim as per the header photo. This fact suggests that the blue line on the head is indeed in the right place but nevertheless, it’s difficult to tell where the rebate turns to become the neck.

Dark Blue- please ignore this. It’s a rogue dot.

Other colours are as for the previous photo, except that there is a large, yellow dot between and behind the first two body protrusions. This denotes the probable seating position of the triangular head protrusions when concertinaed together. Its position was plotted by measuring the distance from the uppermost head protrusion to the sharp downward turn. This was then transferred to the body line.

The mauve-dotted match isn’t exact. There is missing material that was sandwiched between them and there is an issue with the apparent angles which suggest one is at 90° to the other. However it may just be a perspective issue on a feature that ran at 45° through the slab-body join.

PHOTO CREDITS
Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0

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8 thoughts on “67P/Churyumov-Gerasimenko. A Single Body That’s Been Stretched- Part 17.

  1. I can’t leave this post uncommented! These new matches are very long, have many matching points, and are corroborated with separate images. It took me way less time to familiarise myself with the matching shear line points this time. The consistent thickness of the crust is a very interesting new development. I think the crust is more obviously concentric rather than parallel to the strata. Thus you have strata which more easily fracture along those plains, while at the same time you have the crust which can also fracture along the crust/mantle border, thus across the strata plains, which I think Anubis is at an angle to the strata plains.

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    • Marco

      I’m pleased the match is obvious to others. Did you understand the multicoloured photo i.e. the one showing the top and bottom edges of the Anubis slab, sitting on the body and joining to the bright green body protrusions? That one is difficult to visualise, I know.

      I left a comment on Elisabetta Bonora’s site, Aliveuniverse. While I was writing it, something occurred to me so I included it in the comment. Basically, all the ground-based observations that have noted fragmentation in comets can see the fragments only because their own mini-coma betrays their existence. This sets up a mindset that only sees fragmentation and precludes stretching because all they witness is fragmentation. However, as we know, the ‘centrifugal’ force is proportional to the radius. This means that there remains a nucleus with insufficient tangential velocity at its extremities to shed any more fragments. But being on such a cusp, there is still plenty of rotational force left for stretching that residual nucleus.

      This radial reduction of the forces almost requires the nucleus to stretch if it has just shed fragments that are just beyond that cusp. I sort of touched on that somewhere else but the new slant in the Aliveuniverse comment is the fragmentation mentality that is borne of only ever seeing fragments. This leads them to think that fragmentation is the only game in town and that all comets must be brittle, ergo, they can’t stretch.

      But there is currently no method of catching a stretching nucleus in the act as it also sheds fragments. The nucleus will have a coma throughout the shedding event and it (probably*) won’t change in such a way as to evidence stretch. The evidence of fragments doesn’t preclude the possibility of stretch at all. It applies to a completely different mechanism- and it could well be the loose crust being sloughed off, leaving the fluffy, porous centre to stretch.

      *actually, I think it might change enough to evidence stretch but if it does, the researchers haven’t seen that change for what it is or might be. The jets often describe a helical trail in the tail due to any prominent jets being at an angle to the axis of rotation (as most jets are). This means that if there is a significant change in this helical property for the nucleus during the fragmentation event, it’s a possible sign of stretching. I think the researchers may put this down to newly exposed jets showing up the rotation period that was always there but doing so more clearly. In fact, if stretching is the culprit, that rotation period wasn’t always there, it’s a new, slower rotation period due to stretching.

      This in turn leads me to question whether the observed spin up/spin down episodes of ~20mins per orbit is always to do with asymmetrical outgassing, especially if accompanied by a fragmentation event. True, such a fragmentation event needs asymmetrical outgassing in order to occur, but it may have happened over centuries and then they observe a sudden slowdown due to stretch during a fragmentation event and put it all down to outgassing around that time. This would especially be the case if the spin was measured several years apart and the fragmentation occurred, unwitnessed in between those two readings.

      The same principle would apply to neck-collapse and a consequent spin-up, like the ice skater. In that scenario there may be no fragmentation at all.

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      • That last sentence is calculably wrong, which is what I have been trying to explain on previous occasions. An Ice skater has to physically perform work to pull her arms in, and that energy is converted to rotational kinetic energy. Similarly for the comet lobes, work has to be performed to speed up the lobes as they collapse inwards, just to conserve angular momentum. This is the crux of it though *mutual gravitational potential energy is not enough to provide the work required* (do the maths yourself, if you like) . To put it another way, stretch is not reversible.

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      • Marco

        If the comet were spun down to zero rotation, which is a theoretical possibility, there would be no angular momentum to conserve. In that special case, if the neck were removed, the head would fall onto the body due to the mutual gravitational force. If the neck were in place, it would be subjected to considerable extra compression from the head lobe (and integrally, from its own mass) and would certainly compress a little more and possibly collapse onto the body along with the head. There would be no angular momentum to conserve, just potential energy turned to kinetic energy and thence to heat in the collision.

        If this is the case for a spin-down to no rotation then it will also be the case for an infinitesimally small rotation period and in fact, for discernible, slow periods. This is why I believe the head will subtly rock around on its neck as any small amount of spin-down occurs in a reverse of the outgassing spin-up.

        One thing is for sure. The head lobe is currently not moving with a tangential speed that is the equivalent to the tangential speed required for a circular orbit at that radius from the c of g. Yet it is describing such a circle as it rotates (but doesn’t currently orbit) about the c of g. It is therefore in a perpetual attempt to drop to a lower altitude (radius). It wants to give up PE for KE which might allow it to resume an elliptical orbit, which would have the current head lobe altitude as the apoapsis and some unspecified lower altitude as the periapsis. It would give up PE for KE as it approached periapsis and give up KE for PE as it returned to apoapsis. If the neck were weaker or not there, the head would ‘drop’ in the sense that the radius would reduce but, strictly speaking, it would assume this elliptical orbit that would arise from being ‘launched’ at that particular altitude and tangential velocity. It would then rise (increase radius) as it returned to apoapsis. The question is whether the lower altitude it is ‘seeking’ at periapsis is at a radius that’s inside the body in which case it would impact the body. That would mean it was in fact in a suborbital trajectory, just like ballistic missiles, launched at sub 8km/sec speeds from the Earth, except that it was launched from a point along that suborbital trajectory.

        I agree that energy is required for the lobes to approach each other and increase their combined rotation rate (like the skater) but whether or not the energy for this, derived from potential energy (gravitational force x distance), is sufficient is a quantitative rather than qualitative issue.

        The qualitative aspect is that, in the absence of a neck (or a neck with no compressive strength over and above what it currently exhibits), the lobes will surely approach each other and speed up their overall rotation. They may crash or assume the orbit described above, in which case their combined rotation period will oscillate as a function of the eccentricty of the orbit, slow at apoapsis, fast at periapsis.

        The quantitative aspect is in the nature of the neck, namely, its compressive strength: will it have the strength to resist the attempted approach of the two lobes due to gravitational attraction? At present, the answer is clearly “yes”. This may be because it is inherently strong enough to take the full weight of the head, whether spinning or not. Or it may be because the rotation is reducing that compressive force. If the latter is the case, when and if the comet is spun down via a reverse process of the asymmetrical outgassing spin-up, the neck won’t have the compressive strength to resist the increased net force, applied in compression. In that case, depending on just how insufficient the compression strength is and how it’s distributed in cross section, the head will collapse down towards the body to some degree and/or rock to one side.

        I suspect that, in reality, the neck might well be strong enough in compression to hold the entire weight of the head. So in this sense I’m in agreement with you when you say, “mutual gravitational potential energy is not enough to provide the work required”. However, if the neck is weaker than this ‘full load’ requirement, it will collapse to some unspecified degree when the spin-down passes below a certain rotation period threshold.

        As mentioned above, my suspicion is that in the real-world scenario we see the neck is, overall, strong enough to take the full weight. The cracks in the neck betray tensile forces due to the original stretch and head tip. Some of them may be due to the torsional forces due to the 15° anticlockwise rotation of the head. What I don’t see is slithers of neck, sheared away due to shearing in compression (as briefly mentioned in Part 11), so perhaps spin-down via asymmetrical outgassing has happened and the neck has resisted the extra force. Either that or spin-down due to outgassing hasn’t occurred yet and may never occur.

        If spin-down never happens, or the neck supports the head when it does, then stretch would indeed be irreversible. But if spin-down does happen and the neck can’t take the weight, then the lobes would approach each other to some degree, large or small, and so stretch wouldn’t be irreversible. The crux of the issue lies in the compressive strength of the neck.

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  2. I guess my question on the reversibility of stretch is really quantitative in nature. In a partial collapse of the neck which ends up speeding the rotation of the comet without the lobes rotating with respect to each other, the kinetic energy will increase in proportion to V^2 , the velocity will be in proportion to the distance of movement, and the gravitational potential difference will be in proportion to the distance of movement and thus the velocity due to the conservation of momentum. If I have my maths thinking right, the kinetic energy required is more than gravitational potential that would naturally be supplying the kinetic energy. Where is the extra kinetic energy coming from? In the reverse case, the excess kinetic energy is being attenuated by friction when stretching. I don’t think you can get this energy back in any easy, natural way except for stored elastic energy with tiny vibrations, perhaps.

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  3. I guess it would depend on the actual spin rate, mass, centre of mass of lobes. V^2 isn’t always “bigger” than V, but I’m betting it is at this current rate, and it isn’t the intuitive situation where centrifugal balancing gravity would be the dividing line between whether stretching or shrinking is irreversible. Might have to do the maths 😦

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  4. Reminds me of a trick question from my first year Physics. A large plasticine pendulum and a smaller one are swung towards each other at the same speed and they stick when they collide, and swing in the direction that the bigger pendulum was going. The naive physics students use the conservation of kinetic energy, but the clued in students realise that kinetic energy is not conserved in a plastic interaction, but that momentum is. The reverse cannot happen. The pendulum cannot redivide into two again passively, even though momentum would be conserved, because it involves an addition of kinetic energy.

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  5. My clue to this line of thinking was your 67P Equinox tidal stretching calculations, and the initial fact that gravity wasn’t being overcome by the addition of tidal forces.

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