Paleo Rotation Plane Adjustment

15th March 2016


 ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA
(Header photo not part of numbering sequence).

Photo 1

  
This photo has been culled from Part 42. It shows the diamond-shaped base of the comet’s body lobe. The main line we’re concerned with here is the brown one, which traverses the diamond. It’s the newly adjusted paleo rotation plane line and it now runs down the centre of the diamond instead of kicking over at a slight angle which used to take it about 5° lower, towards the bottom of the left hand flattened diamond tip. The other colours will be introduced and discussed throughout this post, along with this header photo, reproduced where necessary. Any longer, narrative keys for photos are concluded with ‘/////’.

Photo 2- the old paleo rotation plane version (larger brown dots) and today’s rotation plane (dark blue).  
Photo 3- the ESA regions map.   
INTRODUCTION

The paleo rotation plane line is the same as the equator, just like today’s equator line on the comet is today’s rotation plane (and around 12° offset from the paleo version). The paleo line is based on longitudinal stretch signatures that can be traced round the comet. These were summarised in Part 26 (from photo 7 onwards) and discussed in detail from Parts 20 to 25. There were eleven signatures then. Now there are seventeen, hence the adjustment. 

The reason it’s called the rotation plane is that this line lies in one plane which also rotates within its own plane. It helps us to keep in mind that the greatest magnitude of tensile force due to spin-up is directed along this plane: from the centre of gravity that lies in the plane to the long-axis tips of the comet. Those tips are the centre of Apis at one end and the Hatmehit cliff at the other. 

The Hatmehit cliff would have been the long-axis tip even when the head was clamped on the body. It’s referred to a lot in this post when discussing the rotation plane and its precession. However, Aker and the Khepry diamond tip are referred to as well. This is because the body lobe diamond appeared to be quite happily obeying all the same stretching behaviours along its own long axis while the head was herniating above the Aker end of the body. 

The top of the head at Hatmehit was indeed the true long axis tip but Khepry and Aker were near enough to that stretched end to be obeying the same stretching rules as the ideal long axis through the entire comet. Those ‘stretch before shear’ rules applied when the head was still attached, herniating and preparing to shear. In fact it may well be that the herniating behaviour of the head meant its runaway stretch decoupled its deformation scenario from that of the body below. The body continued relentlessly stretching into its characteristic diamond shape while the head bulged in a more fluid manner. After all that is the expected behaviour in a herniation- excess, poorly attenuated stretch. 

AN UNASHAMED PLUG FOR STRETCH THEORY

If you are new to stretch, herniation and shearing, the above paragraph may sound incredulous. However these three phenomena were proved beyond doubt in Parts 1 to 29 with 250,000 words of detailed NAVCAM photo description, several hundred annotated photos, and a relentless focus on the finest details of 67P’s morphology, right down to the 15-metre scale. As of this post we have moved 13 parts further on with six separate areas of 700-metre crust-sliding, identification of the paleo rotation plane and how it precessed and proof that the three large sink holes used to be one (now delaminated into three).

Stretch theory explains the morphology of every region on the comet with complete ease, and an elegant consistency between the various dynamical mechanisms. It’s now so far advanced that it would nearly double the number of regions due to understanding the dynamics for many sub-regions within the existing named ones. 

THE PALEO AND CURRENT PLANES CROSS AT THE LONG AXIS

The idea of maximum tensile force due to spin-up being directed through the centre of gravity to the long-axis tips wouldn’t necessarily be the case for every rotating body. For example, it wouldn’t apply if the rotation plane line didn’t run through the long-axis tips. But in the case of 67P it did so for the paleo plane and also does so for the current plane. 

That might seem like an impossibility at first blush. How can they be running in different planes and directions and yet both run through the long-axis tips? Well, the two planes have to intersect somewhere, along a single line. And that line just so happens to be along the long axis of the comet. It’s because the rotation plane precessed after the head lobe sheared and rose on the stretching neck. It precessed anticlockwise (looking down on the head). The precession was about the long axis so the long-axis tips are common to both the paleo plane and current plane. The axis tips at Apis and Hatmehit were the gimbals for the precession axis, i.e. the long axis. This is why the two rotation plane lines criss-cross with almost pinpoint accuracy at Apis and at the central V-apex of the Hatmehit cliff. 

In reality, the paleo line stretch signatures straddle quite a way either side of the actual line so it’s more like a band of maximum stretching round the comet. But the crucial fact is that these signatures all straddle the actual line symmetrically so however wide they are, their centres all sit on one line: the paleo rotation plane line or paleo equator. 

For an explanation of the dynamical mechanism that would give rise to the band around the long axis stretching preferentially and therefore exhibiting the seventeen signatures, please see the appendix. 

The crust did whatever it could to accommodate the stretch and did so mostly via rifting and delamination with some bending. However, it’s becoming apparent that some sections were able to stretch too, specifically, lower onion layers that are now exposed. All these methods of stretch accommodation are to be seen in the seventeen paleo rotation plane signatures. 

FIVE NEW PALEO PLANE SIGNATURES IN THE HEADER PHOTO  
Header reproduced. 

There are five features in the header, other than the newly adjusted paleo rotation plane, that are important too. All five are newly identified paleo rotation plane signatures in the light of the adjustment which will described in detail under the next sub-heading. These five new signatures are listed below:

1- The Khepry flattened diamond tip. The slate blue line defines the true length of the flattened diamond tip on the left. The fourth Babi cuboid, dotted fuchsia, makes the tip look wider but the flattened tip really is defined by the slate line. That length is almost the same as Apis, which constitutes the flattened tip at the other end of the diamond. 

This length parity is no coincidence because both flattened tips arose as a consequence of the symmetrical tensile forces of stretch acting on them. The forces were symmetrical because the diamond-shaped base is symmetrical and owes its shape to those forces being at play during the stretch event. Those forces worked on crust of a similar thickness and nature at either end of the diamond. That crust fractured in a symmetrical manner that was in keeping with the symmetry of the forces. Hence, the two tips of the stretched diamond sheared away from their surrounding crust in the same manner.

The tensile forces became flexion forces as they rounded the diamond tips. That is, they became flexion forces for any crust that happened to be straddling the tip. The rate of change from tensile to flexion was roughly the same at both ends. With this force change acting on similar crust at both ends too, the two flattened tips broke in the same locations. These locations were where the flexion forces either side of each flattened tip centreline became sufficient to snap the crust. And the flattened tip centrelines were where the paleo rotation plane line ran. Hence the similar length of crust forming each flattened tip and their straddling the paleo line exactly. Each flattened tip is a stub of crust that protected the diamond tips from becoming pointed. 

This phenomenon would never be noticed without having the stretch scenario in mind. Similar signatures abound all over the comet and they too will only ever be noticed with the stretch scenario in mind. Numbers 2 and 3, below, are two more examples. 

2- The kissing point. The green dot denotes the kissing point of the notional pie-shaped crust pieces in Part 42. This new paleo rotation plane signature is described in more detail and in context in several places further down.   
3- The finger. This is the finger-like protrusion to the right of the ‘Khepry’ name. This is brown and outlined red by ESA as part of the Khepry region. The main chunk of thicker finger is a pointed shape that’s touching the seventh brown dot from the left and is outlined in green in photo 5, below. Its long protrusion to its right slopes down to a somewhat squared-off tip. 

The reason for the rather detailed shape description is that it’s also prepping the reader for the similarly shaped seating point. That will be presented in a main blog part soon. 

This is another paleo plane signature because it originally kissed the green dot kissing point which is also the lowest point in the Imhotep depression. The finger slid exactly down the brown line due to the tensile force of stretch. It suffered sub delaminations along the way, fanning away, up and down from the line. The finger remained intact purely because it slid straight down the centre, plumb on the paleo rotation plane line all the way. That’s why it’s so thin. It’s also the reason for its long, sloping tip extension looking decidedly smooth, bare and icy: anything either side of the brown paleo plane line got torn away and tugged up or down (see Part 42). 

There’s no reason for you to wait three weeks for the relevant blog part to make the exact, detailed matches to the finger. The upper slide match is there for anyone to see. Anyone with just a little time and patience to study the 20-30km-distant NAVCAM photos or the now available OSIRIS pictures will see it. Part 42 gives all the information on where to look. Describing it now is beyond the scope of this paleo plane post. 

4- The V shape of tensile force ridges. This isn’t annotated on the header because it’s not visible there but it is clear in photos 4 and 5, below. This V shape corroborates the finger’s slide direction. It comprises two ridges that fan out from the finger in a V shape. 

The V straddles the paleo line and its two tips are attached to the two ends of the flattened diamond tip at Khepry. The ridges betray the tensile stress force lines that ran from the two Khepry perimeters running up the front, or bow, of the body lobe. The force lines ran from those two resilient strong points to the finger. They were strong points because they are at either end of the resilient piece of crust that didn’t snap and became the Khepry flattened tip (see ‘1’ above). That force was applied due to the comet (and therefore the diamond) stretching due to spin-up. It would have been applied when the finger was being tugged from the kissing point (item 2, above). 

In other words, the tug from the kissing point resulted in the finger’s slide down the line of the paleo rotation plane and the signature of the tensile force of the tug is the V shape of the two ridges behind the finger. The Khepry tip was the workhorse but the real force came from core material pushing the Khepry tip out to stretch the diamond along its long axis (the paleo plane). This was therefore a perfect triangular pie-shape being pulled away from the centre of the pie:

Photos 4 and 5- the finger and its V-shaped tensile force lines. Each comes with its unannotated version below it. Photo 4 is culled from Part 42 so its unannotated version is still dotted but without the tensile V. Unannotated versions are supplied for you to assess the validity of the observations.     
   
 
Photo 4 is from the NAVCAM, credits below as usual. 

Photo 5 is from OSIRIS. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA/A.COOPER

Key for both photos:

Brown- paleo rotation plane/equator. 

Yellow- short axis of the body diamond. 

Green V shape- the tensile force V from the finger to the Khepry flattened tip. It follows a different path, on one side, between the two photos. In one photo it joins the fourth Babi cuboid but there’s a smaller-dot green line that follows an almost invisible V line to the flattened diamond tip end point. This line is more visible in the OSIRIS close up from the other direction so it’s dotted with the bigger dots. In that close up, the bifurcation that’s going to the cuboids is now demoted to small dots. It’s a small difference in path but open to some interpretation between the two options, according to the lighting. 

Larger green dot near the apex of the V- this is the finger itself. It’s a sharp, stubby point. Its top surface looks fairly smooth. In the close up there are very small green dots going round the perimeter of the finger. This shape identification isn’t speculation- it matches not just to its kissing point but, as mentioned above, to another place on Imhotep. That’s because, as stated in Part 42, the Imhotep crust slide was radial and involved two layers. So some seating areas at the kissing point originally had two nested layers on them. The matching crust pieces to those seating points are now flung in different directions, radially from the kissing point and across Imhotep. The finger is one of them. It matches via its ice signature too. The match is unequivocal.

Bright green dot at the axis crossing- the kissing point for the finger and five other sections of slid crust.

Slate blue- the Khepry flattened tip.

Fuchsia- the four Babi cuboids that slid across Babi (Part 40). They’re viewed here from below. In the header, the lower-left one looks like part of the Khepry flattened tip. It is nearby but it’s set back. It has a separate morphological history (it used to sit 800 metres over the horizon with the other three cuboids) and is therefore not part of the flattened tip. True, the green line V apex looks as if it’s attached to that end cuboid. However, there’s an abundance of evidence that this cuboid tore its way down the side of Aker, ripping out frayed edges as it went. If the green V in photos 4 and 5 really does go to the cuboid, it might be simply the tensile force ridge being more pronounced towards its anchor point at the ‘resilient edge’ of Khepry. Seeing as the cuboid ground hard against the Khepry perimeter too, it would look as if the two are attached. 

///// end of the key for point 4, the V shape of tensile forces.   
5- The red slide. The two red lines in the header show the matching Imhotep rift lines corresponding to the red slide which was first presented in Part 42. It’s more detailed in Photo 4 and will be still more detailed in Part 43. It’s a 700-metre rift that opened up in line with the stretch tensile force vector. So the two matching (red) perimeter lines of the rift are at right angles to the force vector which runs along, and parallel to, the paleo rotation plane line. And the rift straddles the paleo line itself symmetrically. 

The right hand line doesn’t extend as far ‘down’ as the left hand one even though it’s stated above that the rift straddles the paleo line. That’s for two reasons. Firstly, the square-ended protrusion slipped down from its seating before moving left across Imhotep (the cause of the two parallel lines across the flat plain). Secondly, the last short section of presumed seating match at the bottom of the right hand line is obscured by the mess left by the slide of the circular pancake. The pancake slid down in the header photo. It matches to the depression with the green dot. Its mini matches can be found on the Imhotep crust slide page in the menu bar. That page is just a preliminary repository for a small selection of Imhotep slide matches. 

Along with the orange slide (also in Part 42) that concludes all the colour explanations for the header. This also concludes the descriptions of the five newly discovered paleo rotation plane signatures that are visible on the base of the comet. 

THE REASONING FOR THE PALEO PLANE ADJUSTMENT

Eight strong paleo plane signatures get added here, including the five above that are visible on the base of the comet. Two others are round the corner, so to speak, at Aker and are presented below. The final one is in effect visible in the header. It’s the diamond itself so it’s not annotated in the header. 

Two spurious paleo plane signatures from the original list of eleven are taken away and their removal is wholly responsible for the realignment of the plane. Three of the eight replacements have been discovered, lying along the correct plane, as a result of the realignment. The other five were already known as possible candidates waiting for an explicatory mechanism, always being eyed with a view to this possible 3°-5° change. 

So the two discarded signatures negated any reason for the old path going through them and the 5 known candidates grabbed the line over because they were all in a straight line of their own. The final three along that line then jumped out, hiding in plain view, like every other signature on the comet since Part 1. 

The two discarded paleo signatures are spurious because they’re at the south pole where the photos were always long-distance and low res until recently. The recent photos have flagged up the deceptive character of this area which is where the two supposed hinge gouges are…or were. They were described in Part 20. They’ve been discarded because they are not gouges. This is discussed below. So we now have nine of the old paleo rotation plane signatures instead of eleven, before adding the eight new ones. That makes seventeen and it’s a much stronger paleo line as a result. It also looks more correct in a topographical sense both when looking at the actual comet and the ‘cylindrical projection’ map. In other words, one paleo stretch feature flows into and/or tugs on the next. 

The cylindrical projection map from the other paleo rotation plane page is reproduced further below with the corrected line based on the seventeen signatures. This updated version looks even more intuitively correct now because it’s a symmetrical sine wave running either side of the existing rotation plane. Moreover, it intersects the current plane at the long-axis tips. That betrays the precession of the rotation plane about the long axis after head lobe shear. The long-axis tips would be the most likely gimbal points for such a precession. It could hardly be neater. 

The 17 stretch signatures along this near-perfect line could be exhibiting stretch in any random direction but instead they’re showing it to have been along the line as would be expected if they were betraying the preferential stretching of the paleo rotation plane line. See the appendix for an in-depth study of why it’s a preferential stretch over and above the other areas flanking the paleo line. 

Looking at the header photo, the assumed paleo rotation plane line used to run from the same position at the right but crossed the comet’s base at an angle so as to arrive at the lower end of the opposite flattened tip (i.e. the bottom of the slate blue line). This was because the former list of eleven stretch signatures (Part 26) for the paleo plane seemed to dictate that it should veer over that way so as to pick up the head lobe hinge gouge (Part 20) at Anhur and continue on seamlessly to the head lobe v shapes (Parts 27-29). 

Photo 6- the supposed hinge gouges   
Large yellow dots- ‘gouges’ on head and body which nevertheless have matching V shapes as if the head and body were once sandwiched together before the large volumes were ground out. The reasoning was half right. The head and body do match via the V’s (Part 30) but the supposed gouges are an artefact of the delamination of the V’s after head shear. No material (or nowhere near as much material) was lost. It just slid up the head and down the body. That’s why there are two lines of deep gouges down the left side of Aker (dotted light blue). The body V’s slid and ripped their way down the perimeter. It’s the reason there are so many matching V’s spread so far apart. This head shear, delamination and slide is identical in nature to the Babi/Ma’at shear, delamination and slide symmetrically placed on the other side of Aker (Parts 40 and 41).

Brown- the newly adjusted paleo rotation plane line running neatly down the middle of Aker and Khepry. 

Dark blue- end portions and long axis crossing point of the current rotation plane (equator). The long-axis crossing is at a single point and marked with a single blue dot. You can see it crosses both the paleo plane (paleo equator) and the long axis tip at the top of the Hatmehit cliff with pinpoint accuracy.

Light blue- the lines of gouges down the exposed sides of the Aker perimeter. 

Red- reading the key to this photo in Part 20 it’s apparent that the red line was thought to match the long, bottom yellow line, which is correct (although it may match to the V above the bottom one- the overwritten yellow line is an up-to-date correction and the more recent Part 30 fits the overwrite to that next body V up). So the correct match for the delamination itself was made back in Part 20 without knowing about delaminations and despite thinking some mass had been ground out. I now remember having great puzzlement over how these two such disparate yet obviously matching V’s could ever have ‘crunched’ down through so much body to meet up. I knew nothing of sliding at that point. The green dot key is copied over below and shows the red and yellow V’s were thought to fit.

“Green- (requires zooming) denotes matching striations in the curved extensions of the top and bottom strata. These are small scale matches within a large scale match. ” (from Part 20).

/////

There’s another reason the ‘gouges’ were accorded greater importance. At the time of writing Part 26, there were no definitive paleo plane signatures recognised on the main part of the body lobe base, just the tentatively suggested low point (now the bright green kissing point) and the diamond itself. But the low point of the depression was suggested simply because it was known to be almost exactly central to the comet’s base. It was suspected not to be quite the coincidence it seemed to be but a mechanism was needed to promote it to paleo signature status. Now we know it’s low because it was the site of maximum outgassing at the initial tearing where the crust pieces kissed (Part 42). So the low point was crying out as a paleo plane signature if only the mechanism for its formation could be fully explained. 800-metre crust slides weren’t even dreamt of in the Part 26 era. Now they’re proven (Parts 30, 32, 33, 34, 38, 40, 41, 42). Part 42 is the one that explains the kissing point so it’s now placed centre stage, literally, at the intersection of the adjusted paleo rotation plane and the diamond’s short axis. It’s about 200 metres from the centre of the base and right on the adjusted paleo line between the two flattened tips. 

In addition to the low point, the symmetrical nature of the body’s diamond shape seemed to dictate that one day the paleo plane would get shunted over to the diamond’s centreline and the paradox of the awkward run across the base solved. The solution is simply that the supposed hinge gouges at Anhur/Bastet aren’t gouges after all but a delamination and slide.

The head lobe ‘gouge’ did seem to mirror the body gouge as if they’d ground against each other and they do mirror each other but that’s because the head feature was the place that the body feature tore from before delaminating and sliding. The head feature delaminated upwards and the body feature, downwards. Part 30 shows that they tore from each other and therefore were once fitted together- just like the Ma’at-Babi tear and slide on the other side of Aker/Bastet (Parts 40 and 41). 

That’s very interesting in itself and proves that these two features aren’t gouges. But since their delamination/slide signatures aren’t gouges, they are no longer paleo plane signatures either. Indeed, the fact that the same type (and area) of tear and delamination happened symmetrically on the other side of Aker/Bastet behoves us to consider Aker, straddling the symmetry line, as the true hinge. 

That neat prow shape of Aker at the tip of the body lobe was of course always beckoning as being the true line of the paleo plane but the gouges seemed compelling enough at the time and the paleo line was still running up just outside the Aker perimeter so it almost followed the long axis. Now, in the absence of any countervailing evidence and in the light of the Babi and Anhur slides literally ripping their way down either side of it, Aker is shoved into the limelight anyway. Its photogenic prow is just a bonus signature. 

Now that Aker is the supposed head lobe hinge, it would mean that the bottom rim of Bastet on the head lobe was hingeing against the top rim of Aker on the body as the head was lifting off. The hypothesised head tip on the hinge would presumably be short-lived and just prior to the head then slipping out of its hinge and rising in a translational manner straight up from the body. 

It also follows that the paleo line gets shunted over with the hinge as well, to run up the centre of Aker. When this line is traced round to the base of the comet as shown in the header, the line runs neatly from flattened tip to flattened tip of the body diamond, bisecting both tips. This constitutes, in effect, a 3°-5° swivel of the paleo line from the ‘bottom’ of the Khepry flattened tip, as it’s depicted in the header, to its centre. The axis of swivel adjustment is the midpoint of the opposite tip (Apis) which remains on the old paleo line, unchanged. This means that the old line of paleo stretch signatures beyond Apis, remains unchanged too. It’s only the Aker/Khepry end where the line gets shunted over. 

The paleo signatures have now become much more solid. Like Aker, the diamond-shaped base was always beckoning as a signature but the gouges pulled the line over. The symmetrical diamond shape is a stretch signature in itself and should be bisected by the paleo plane in the absence of any countervailing evidence. The only countervailing evidence was the gouges and they’ve now been discarded as being spurious. And by moving to the centreline of the diamond it’s allowed us to find the actual paleo stretch signatures that are strung across it. These are, from the Khepry tip to Apis:

1- the Khepry flattened tip

2- the tensile stress V shape attached to the finger.

3- the finger.

4- the Imhotep rift

5- the pie shape kissing point in the depression.

Apis itself is included in the nine signatures beyond the kissing point. That makes nine plus five. Adding the diamond itself, the Aker ridge (prow) and the symmetrical Bastet layers, we have 17 signatures. 

Incidentally, the original number of eleven was sometimes quoted as ten because the Hapi fracture plane was left out by mistake. 

Some of these signatures are related like the finger to its tensile force V, or the four coloured anchors on both head and body that used to be sandwiched as one before head shear. However, if they’re not distinguished, they’ll likely get left out by mistake in future. The finger will be treated as a separate item anyway because it’s intimately related to the other chunk of radially slid crust on Imhotep and the kissing point that’s common to both. 

It should also be noted that the depression in Imhotep straddles the rotation plane but is slid a tad east along it, away from being central to the body diamond shape. In that sense it is a paleo line signature but it’s more like a duplicate signature to its low point that’s already been logged as a signature. So it’s a duplicate signature as opposed to the looser, “related signature” designation. The depression is described in detail in Part 42. It bears the hallmarks of being an area of very high activity. 

THE CONTINUATION OF THE PALEO LINE FROM THE NEW AKER HINGE TO THE FLATTENED TIP. 

Photo 7- The Aker hinge and its environs.     
Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA/A.COOPER

Red- the Aker hinge.

Brown- the Aker prow (it ends at the top perimeter of Khepry).

Blue- the exact locations of the divots on the left perimeter of Aker and torn-away tips on its right perimeter. 

Large Fuchsia- the four Babi-slide cuboids and the seating of the fourth (left hand) cuboid above at Hapi. 

Small fuchsia- the slide path of the fourth cuboid, ripping the perimeter of Aker, outwards then down.

Yellow- circles that match to the head at Bastet (Part 21).

Slate blue- (at the bottom). The Khepry flattened tip viewed from above. 

Green- the end of the tensile V ridge that extends to the fourth cuboid. 

Since we’ve established that the head lobe hinge was probably at Aker, it could be assumed to be in the most intuitive position: along the whole of that top rim of Aker. It’s the almost architectural, flattened V-shape with an even ~70° turn from the ‘horizontal’ all the way along it. And of course, it’s at the tip of the body diamond. That is, the upper, Aker edge of this end of the body diamond, not the lower edge of the same tip at Khepry- the Khepry tip is the left hand, flattened tip in the header, seen from below. 

There’s additional evidence for this being the hinge, in the form of signatures of catastrophic outgassing. They take the shape of circles along the supposed hinge at the top of Aker and circular/cylindrical features directly above them at Bastet that match, circle-for-circle (Part 21). Fluted dykes run between the head circles and two of those match to the body, between their corresponding circles. The body circles exhibit slurry-like signatures on their outside (outside of the shear line) as you’d expect if slurry were being ejected just prior to head shear and departure. Also, the surfaces of Aker and Bastet look crumpled as if their surfaces were slightly compacted with the compaction force running along their surfaces from the hinge ridge (not straight down onto their surfaces like a steamroller). That would be consistent with the hingeing (Part 10). There can’t have been much pressure on the hinge because the head lobe was on the point of departing, but if it was tipping on that edge, the force would have been concentrated along the two surfaces, crumpling them. Incidentally, the bigger original gouges were explained by a larger shunt forward of the head before lift-off and also a tip towards the south pole. If Aker was the hinge, it seems there was less or no forward slide but the southward tip may still have applied during or just after lift-off.

If the head lobe hinge is moved to Aker, it allows the paleo plane to follow the Aker prow down the centre of Aker. That shallow ridge is the downward, 3-D projection of the flattened V-shape at the hinge. Or, to be exact, the ridge follows the 3D projection of the central apex of the V into a sloping line. That ridge itself then becomes a stretch signature because it’s suggestive of this section of spared crust at the body tip being bent out just a tiny bit as it yielded to the flexion force (as described above for the Apis and Khepry flattened tips). The very small bend of the ridge is consistent with the flexion forces not being sufficient to snap the crust right on the tip but it betrays the attempt to do so. 

The flexion forces ended up operating successfully either side of the tip and that’s why we have two straight tear lines (or rather, snap lines) running almost vertically down the sides of Aker. Those lines are equidistant from the shallow ridge that is the prow. The prow was the centreline of the flexion forces so it was the line of the attempted snap that only succeeded in causing a neat, shallow bend. After the actual snaps down both sides of Aker, the Babi/Ma’at and Anhur/Bastet delaminations were free to slide up and down because they were the sections of crust that snapped from the Aker crust. And they now had free-moving edges along the snap line. This is why the exposed edge of the snapped Aker crust has a succession of similar gouge lines down either side. The right hand set were gouged by the fourth Babi cuboid sliding down and grinding against the exposed perimeter of Aker. The left hand set were gouged out by the symmetrical slide (not a cuboid) at Anhur. The force vector betrayed by the gouges is clearly downward towards the base of the comet, especially the frayed pieces of Aker on the Babi (right hand) side. These pieces fanned out sideways and slightly downwards as the fourth cuboid was dragged past them in the Babi cuboid slide (Part 40). The two straight lines of gouges down the Anhur side are uncannily similar to the jumping gouges you get when you drag a solid object over something soft, like scraping fingernails over plastic as you try in vain to open vacuum-packed items. 

The newly adjusted paleo rotation plane would continue on from the shallow Aker ridge to bisect Khepry too before turning the corner and striking out across the base at Imhotep. That would mean that on moving round to the ‘bottom’ of the comet to view the paleo plane’s path across the base, we’d see it coming round the corner at Khepry and bisecting the Khepry flattened tip. That’s why in the header photo the paleo rotation plane has been adjusted 3°-5°(clockwise in that ‘upward’ view from below the base). It now goes straight across the long axis of the diamond-shaped base and therefore bisects it.

SUMMARISING THE NEW AND OLD PALEO SIGNATURES

The hinge adjustment over to Aker is corroborated by the ridden-up head lobe strata that fall either side of the neck when viewed head-on from Aker. There’s a good photo and explanation of this in Part 29- the ‘coats wrapped round the chair’ analogy. This is really another way of saying the delaminations at Bastet/Anhur and Ma’at/Babi were symmetrical either side of Bastet/Aker (as mentioned further above). But it’s an easier way of visualising it and the proxy for that symmetry is the Aker hinge that sits in the middle, acting as the symmetry line between the two sides. So that’s the way it’s described in the summary below. It’s the first of the new signatures. 

The new signatures, arranged in prograde order (i.e. along the direction of rotation):

1- the Aker hinge. This is a proxy for the head strata straddling the Bastet head/neck symmetrically, either side of the hinge. 

2- the Aker prow, or shallow ridge. 

3- the Khepry flattened diamond tip.

4- the V-shaped tensile stress ridges from the Khepry tip to the finger. 

5- the finger that was attached to (4) and kissed (7).

6- the rectangular Imhotep plain (because it’s a 700-metre rift at right angles to the paleo line, straddles it and has matching perimeters).

7- the symmetrical body diamond. It’s placed here in the sequence because its centre point (axis crossing) lies between the Imhotep plain centre point and the kissing point. 

8- the crust ‘kissing point’ in the Imhotep depression.

And perhaps the main point is that all these signatures’ centre points lie along one line and betray longitudinal stretch along that line, not in some other random direction. 

When the paleo line is continued on round the comet from its bisecting of the Apis flattened tip, it picks up the remaining nine paleo plane stretch signatures described in Part 26 and bisects every one. They numbered eleven before the two ‘gouges’ were demoted. They’re listed under the heading below, also in prograde order from Apis onwards, and include Apis. Since Apis constitutes one of the long-axis tips, it seems appropriate to designate this as number one of all seventeen signatures anyway. So, after number nine there is a ‘****’ to show these are the old signatures and then the eight new signatures from above are added below that and are renumbered, from ten to seventeen. 

THE NEW LIST OF 17 PALEO ROTATION PLANE SIGNATURES

1- the flattened tip (Apis).

2- the red triangle.

3- the four coloured body anchors.

4- the fracture plane that fits to the ‘vertical wall’ 1km above it. 

5- the four coloured anchor head matches.

6- the vertical wall.

7- the head lobe V’s.

8- the spidery Hatmehit V’s.

9- the Hatmehit slab hinge. 

****

10- the Aker hinge.

11- the Aker prow (the ridge running down Aker). 

12- the Khepry flattened tip.

13- the V-shape of tensile force ridges.

14- the finger attached to (13). 

15- the Imhotep plain. 

16- the body diamond shape. 

17- the kissing point. 

We now have 17 paleo rotation plane signatures that run all the way round the comet and take in its long axis as expected with stretch theory. Furthermore, they’re evenly spread. In fact, there’s hardly a section of paleo line that doesn’t now exhibit such a longitudinal stretch signature. That too is to be expected if the signatures were strung along a band that stretched more than anywhere else on the comet (see the appendix for the explanation of this preferential stretching). Only central Bastet is apparently bereft of such paleo line signatures and that may be because they haven’t yet been noticed. Its crumpled surface is interesting but not a strong signature. Part 21 noticed a matching ridge to the Aker prow that slopes off up Bastet erratically but towards the next signature (the Hatemehit V) so that may get some more scrutiny. The ridge is rather bent but Bastet shows signs of bulging and crumpling on the hinge. Nevertheless, it’s not as worthy as other signatures. 

THE ESA CYLINDRICAL PROJECTION 

 
Photo 8

The ESA cylindrical projection of the comet is reproduced above. It’s annotated with the line of the newly adjusted paleo rotation plane as well as the old one (from the old paleo page) that dipped lower to the south to pick up the two gouges. The old plane is in small brown dots and the new adjustment is in large brown dots. Their exact paths will be discussed further down as we get familiar with the distorted look of the cylindrical projection. 

The portion of old line on the left still stands. This section incorporates signatures one to four. After the neck gap, the whole of the rest of the line is realigned. The old line of small dots shadows the adjusted line and is simply left for reference. The new, smooth curve below the equator on the right is adjusted according to the eight new signatures in Part 42 and this page. The six large brown dots that run above the equator across the head lobe have been adjusted down because the top head lobe V apex was misidentified in the old version. 

The annotation also includes the seventeen paleo plane stretch signatures in very small bright green dots. So if in any doubt the new improved line is the one with green dots along it. They start with Apis at number one on the left and finish with the kissing point at number 17 on the right. The cylindrical projection is reproduced further down, along with the list for easy cross-referencing. 

Two things should be borne in mind when reading the projection. Firstly, the line running horizontally through the centre (0° latitude) is today’s equator. The whole point of the projection is to centre it on the equator because that is the rotation plane of today’s comet. Secondly, as stated several times before, the equator is essentially the same as the rotation plane in that it’s the line on the comet’s surface at which the rotation plane emerges- and that’s the case both for today’s equator running straight across the projection and the brown-dotted paleo plane/equator. The only reason the paleo line runs in a curve on the projection is because it’s distorted by the longitude lines remaining parallel when in real life, they converge at the poles. It’s also distorted by the fact that the cylinder that the comet’s surface was projected onto is then cut along the 180° longitude line, unrolled, and presented flat for us to look at. 

The current rotation axis runs at 90° to the current rotation plane/equator which means that as you look down on any one of the longitude lines, you know that the rotation axis is hiding exactly behind that line. There are 12 longitude lines, 13 including the duplicated 180° line that was cut to unroll the cylinder. This doesn’t mean there are 12 rotation axes- if we roll up the cylinder again and sellotape up the 180° line, it means that every time we walk another 30° round the cylinder to peer down on a longitude line and ponder on the rotation axis buried exactly below it, we are now looking at the same central rotation axis every time due to our ‘orbiting’ the cylinder. 

The paleo line is somewhat similar to those satellite ground tracks you see curving in a sine wave either side of the Earth’s equator on a Mercator projection map. If they follow a sine wave, it really means they are following a great circle orbit round the Earth. The paleo plane almost follows a sine wave either side of 67P’s equator, which is a very good sign that it is in one plane, though not a circle of course. 

It’s not actually expected necessarily to follow an exact sine wave because, unlike the case of a spherical globe, the paleo plane is following bumps and dips in the comet’s surface which are of course unique along its path. Meanwhile, today’s plane follows its own unique bumps and dips. But seeing as the two planes are angled at 12°-15° degrees to each other, the two lines track over surfaces that are on average very similar in radius from today’s reference point which is today’s centre of gravity. Hence the sine wave. That is, a sine wave with two gaps. The gaps correspond to the neck, which didn’t exist when the paleo plane held sway and caused the seventeen signatures. So it’s only when you disregard the neck and slide the three portions of the paleo line along the current equator to meet up that they marry into a true sine wave. That sine wave betrays the paleo plane as a true plane. 

The numbering sequence, above, that runs from Apis at number one to the kissing point at number seventeen will help greatly in reading off the location of the seventeen signatures that are dotted on the cylindrical projection map, reproduced below. That’s because the projection begins on the left at 180° longitude and just to the left of the long axis extremity at Apis. This is to be expected because the projection is centred almost on the opposite long axis tip and Apis is 180°, half of the equator angular distance, away from that tip. The right hand half of the map then continues along the remaining 180° of equator to ‘join’ back up with the 180° line that started at the opposite end. So it runs, practically speaking, from Apis to Apis. That’s why it’s called a cylindrical projection- if you printed it out, you could roll it into a cylinder with the two 180° ends sellotaped along their lengths. That would make it start to resemble the 3D comet. The only other rather obvious anomaly is then the two large holes at either end of the cylinder. Those are the result of keeping the longitude lines parallel all the way to the top and bottom when in reality they all kiss at the poles. That distorts Hapi and the south pole beyond recognition. The projection is useful only for reading features nearer the centre, say, up to 50° north and 50° south. That incorporates the head lobe and Imhotep which are clearly recognisable and not very distorted. This is fortunate because the adjusted paleo plane that’s annotated on the projection diverges by a maximum of only 15° from the central, present-day equator line.

It looks as though ESA have followed convention by notionally designating a long-axis tip as 0° longitude (and latitude i.e. 0°,0° the prime meridian) but that convention allows for a landmark near the long axis tip and along the equator line to be chosen for practical purposes like navigation. The prime meridian is in Hatmehit, just west of the long axis tip so it appears this is what ESA have done. I do remember a reference rock in Hatmehit being mentioned in one of the scientific papers. 

The equator itself is dictated by the rotation plane which is in turn dictated by the rotation axis. So humans can’t decide where the equator is but they can choose a protocol for positioning the prime meridian along it. What they chose is very close to the long axis tips. 

We can use their 180° line and 0° line as a reference to slide along east (right) a few degrees to the actual long axis tips. The first dot to the right of 180° is Apis and the first dot to the right of 0° is the Hatmehit slab hinge V apex. These are the long axis tips and you can see that the large-brown-dotted paleo line goes plumb through both. The current equator line goes plumb through the Hatmehit tip too and just misses the Apis tip centre point by 5° or about 150-200 metres. This proves that the rotation plane precessed about the long axis after the head lobe lifted off. The sine wave neatly criss-crossing the straight equator line at the long axis tips is the smoking gun: the two rotation planes intersect along a single line that is the long axis and so the clockwise precession had to be about the long axis. 

THE CYLINDRICAL PROJECTION REPRODUCED WITH THE LIST OF 17 SIGNATURES

The list under the photo applies to the 17 small, bright green dots along the newly adjusted paleo rotation plane. Number 1 is on the left at Apis and number 17 is on the right at the kissing point. The dots are much smaller than the signatures and are done that way so as not to obliterate what they are depicting. They won’t be all that useful for anyone who isn’t familiar with the shape and formation of the signatures as shown in Part 26 (photo 7 onwards), Part 42 and signatures 10-14 from this page. But this depiction does show that their centre points all lie along a near-perfect sine wave.   
1- the flattened diamond tip (Apis).

2- the red triangle (apex tip).

3- the four coloured body anchors (centre point). Also the base of the red triangle. 

4- the fracture plane that fits to the ‘vertical wall’ 1km above it. 

5- the four coloured anchor head matches (centre point).

6- the vertical wall (centre point w.r.t. its base).

7- the head lobe V’s (just the apex of the top V).

8- the spidery Hatmehit V’s (middle of their centreline). 

9- the Hatmehit slab hinge (its central V apex). This dot is a bit yellowy for some reason (just right of 0°,0°).

10- the Aker hinge (its central shallow V apex).

11- the Aker prow (bottom of the ridge running down Aker). 

12- the Khepry flattened tip (centre point).

13- the V-shape of tensile force ridges (centre point)

14- the finger attached to (13). 

15- the Imhotep plain (centre point).

16- the body diamond shape (centre point).

17- the kissing point. 

The appendix follows the photo credits. 

PHOTO CREDITS

NAVCAM:

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

To view a copy of this licence please visit:

http://creativecommons.org/licenses/by-sa/3.0/igo/

OSIRIS:

Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

All dotted annotations by Scute1133.

APPENDIX – THE MECHANISM BEHIND THE BAND OF PALEO SIGNATURES STRETCHING PREFERENTIALLY 

The width of the band of signatures reflects the fact that there are parallel rotation planes extending out from the rotation axis running through the comet (actually an infinite number). And the more central ones, close to the actual rotation plane run almost all the way to the long-axis tip as well and so mimic the rotation plane itself in doing their part to stretch the comet. They mimic the rotation plane not only in the parallel direction of their tensile stress forces away from their respective rotation axis ‘mountings’ but also their magnitude. But the magnitude is just a little less due to not taking in the long axis tips. 

Force magnitude is equal to the sum of all mR^2w units (let’s say, 1 kg packets of matrix) sitting in each ‘plane’ that’s one packet wide. However, only the actual rotation plane runs through the centre of gravity and all the way to the tips. So it has the greatest number of mass packets (m) and all the surplus ones are situated at a greater radius, R, beyond the neighbouring, parallel planes. The same argument of diminishing force applies to the successively shorter-radius planes moving further away from the actual central rotation plane. Those planes are all mounted further along the rotation axis, either side of the centre point. The centre point is the centre of gravity and classic rotation plane line axis. 

Hence, with more packets in total and all those surplus packets at a greater radius, the greatest stretch is around the rotation plane line with symmetrical diminishing either side of that line. That’s why the band of stretch signatures straddle the rotation plane. 

Just one thing to note before continuing. The word ‘radius’ was used above to describe the diminishing radii of successively smaller, parallel planes. It was used very loosely because the shape of the planes isn’t circular (implying the diminishing concentric, circular planes of a sphere- its latitude lines). If the comet is duck shaped then these are diminishing duck-shaped planes and the biggest one is the paleo plane duck shape boasting the longest long axis from head to tail. But take a radius from the rotation axis in any direction and it will (almost) always be longer when traced along to the outer edge of the paleo plane (its equator or paleo line). That is it will extend for longer than a radius drawn in the same direction along the plane next door or the one after that, etc. We know this has to be the case because if we keep going we ultimately reach the poles at the ends of the rotation axis. And there we find the planes (that are still parallel to the giant rotation plane at the centre) are an inch across. 

The above description is simplistic in that it assumes the outer sections (planes) that are rotating near the ends of the rotation axis, and at a smaller radius, won’t get tugged by the long axis stretch as well. Also, there’s a wide ellipse of core material within the band of stretch signatures. Portions of that ellipse were rotating near the axis as well, i.e. at the same radii as the flanking planes. So surely there’s a whole, wide cylinder of rotating core that the long-axis stretch is pulling on? Why should it pull preferentially on the middle section of the cylinder and less so the two ends out on the extremities of the rotation axis?

The following answer assumes there’s one notional cylinder but in reality there are many (an infinite number) of concentric cylinders obeying these rules more and more faithfully as their radius gets smaller and closer to the rotation axis. The cylinder is of course made up of the central, circular portions of all the planes, threaded along the rotation axis like polo mints making up a polo mint packet. 

Since we know the comet stretched even before shearing (Parts 26-29) the original diamond must have been a much stubbier diamond, possibly barely longer on its long axis than on its short axis. Let’s say it originally had sides set at 40° to the long axis. That would mean its long/short axis ratio would be about 1.2. For comparison, in the minimum case of a ‘square’ diamond, these values would be 45° and 1 respectively. For a 40° side, it means the force vectors exerted by the stretching mass at the tips and pulling on the central cylinder mass, were fanning out where they were ‘attached’ to the cylinder. The pulling forces fanned out from the central attachment line, straight down the long axis, to 40° at the ends of the cylinder. The force exerted on the ends of the cylinder would be 77% of the full force down the middle of the band (cos 40°= 0.766). The force at a 30° from the long axis would be 87% of the full force and at 20° (getting near to the band anyway) it would be 94%.

So the tugging on the outer parts of the central cylinder matrix was significantly lower than on the cylinder matrix inside the band, hence the runaway stretch of the central band. That band is betrayed by today’s paleo line stretch signatures. 

The inescapable result of stretch due to spin-up is that the short axis (which is almost synonymous with the rotation axis) donates core material to the growing long axis due to the centrifugal forces stretching the long axis. Since the cylinder was under much less influence from centrifugal forces than the long-axis tips were, and was also closer to the centre of gravity, it was much more inclined simply to collapse in passively towards the centre of gravity as core material was pulled from the volume at or near its cylindrical surface. And because the cylinder is really just a fatter representation of the short axis, this is how the short axis behaved in order to make its donation of core matrix material to the long axis. As the cylinder collapsed and decreased lengthwise (by probably at least 300 metres at either end) it had volume taken from its surface to feed the long axis. The long axis stretched by at least 600 metres, perhaps one kilometre, judging by the rift/delamination signatures at Imhotep (Part 42) and Hapi (Parts 37-40). 

And all that redistribution of core material eventually led to the head lobe herniating, shearing and rising on the neck.

It doesn’t matter if current models don’t allow this. 67P definitely did allow it. Observing the actual comet in question in exquisite detail is the only way to establish this unassailable fact. Citing papers on other comets and poring over phase diagrams will inform us but not prove what is happening on the comet we spent €1.4 billion to go and look at. Presenting ‘bicycle speed’ contact binary models that turn out to be ‘baby crawling speed’ at 1/16th the specific KE for the comet in question is remiss to say the least. Rewriting the history of the solar system based on the resulting “unequivocal” contact binary would be a mistake on an epic scale. 

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