HEAD-TIP ALIGNS EXACTLY ALONG THE ROTATION PLANE AND NECK FRACTURES EXACTLY STRADDLE IT.
(This post is twinned with Part 11)
Photo 3: A closer view. Notice the most obvious fracture of all, running above the yellow line fracture. Also other fainter fractures are visible in line with the fourth blue dot from the top and just below the fifth blue dot. All are roughly parallel and at 90 degrees to the rotation plane.
At the end of Part 7 I mentioned how the forward position of the future head lobe, when still attached to the body, would lead to a greater tensile stress at the back of its neck. I was using the rubber duck analogy where the head is naturally set towards the front of the body. But I was describing it in its pre-stretched form with the head tucked onto the body like a dome. This would mean that the future neck area, the back of the dome where it attached to the body, was under the most strain under spin-up. It follows that this would be the most likely place to fail and tear away from the body first. It would also very likely become the most tipped-up portion of the head once the stretch was completed.
This scenario would make sense only if the head and body were aligned along the rotation plane, meaning the duck was continuously doing forward somersaults. That’s the only way the head could experience the tipping-forward strain prior to its shearing away. This is because there would be a tendency for the head (the dome) to slide to the end of the rotation axis before lifting away. If the head/dome were sitting on a lubricated plane, it really would slide forward to the axis extremity. But of course, it would have been attached to the body with some degree of shear resistance to the sliding force. The only other way it could succumb to the force, in the absence of a slide, was to tear along the back of the dome/neck and tip forward.
Once fully broken away, this tipping-forward force would act in concert with the ‘lifting’ force (the so-called centrifugal force) to lift the head directly away from the body and continue tipping it forward as it lifted. The centrifugal force would provide the lift. The tipping force would reduce somewhat as the head lifted away because the fulcrum for the tipping (front of the neck) would have broken free and be rising as well.
It should be said here that in reality the tipping force is actually a vector component of the centrifugal force but it’s beyond the scope of this post to talk about vector summing of forces.
As you can see from the header photo, the head lobe is indeed tipped up exactly along the rotation plane. The blue dots show the comet longitude line that corresponds to that plane. The rotation plane is the xy plane of the comet, which is at 90 degrees to the rotation axis, the z axis. You can see the x axis pointing downwards and, together with the y axis (mauve dots), it forms a cross shape that can only sit in one plane and that is the rotation plane. The z axis points to the left, out of frame. It is the spinning axis, the axle if you like and is by definition at 90 degrees to the xy rotation plane.
The lighter blue dot in the middle of the blue dotted line is where the y axis pierces the body and continues through the core to the centre of gravity and out the other side of the comet. This proves that the blue dotted line is on the xy rotation plane.
The header photo is a still taken from a video posted on the Rosetta blog. You can see the original video here, which shows all the axes labelled as the comet spins:
I tilted the header photo so that it looked very roughly similar to how it would look if you sat on the ecliptic plane to observe the comet, i.e. with the z axis of rotation at 41.6 degrees to the ecliptic. In the video it’s spinning on its side with the z axis straight up which would be ecliptic north and the xy rotation plane would therefore be at one with the ecliptic plane. I think that was done so that all parts of the comet would be presented as it rotated.
So we have a head that’s tilted up at the back and exactly in line with the xy rotation plane. This is what you would expect from stretch theory, in fact it’s almost a prerequisite. However, in addition to this compelling evidence there’s the fact that the fractures exactly straddle the rotation plane and do so at near enough 90 degrees. This has all the hallmarks of the stretching process putting too much strain on the material to yield plastically all the way through the stretch. So it fractured across several weak spots at the same time as it stretched. Those fractures were naturally going to appear at 90 degrees to the direction of the stretching force vector.
The head-tipping would probably have contributed to the fractures too. We know it swivelled anticlockwise by about 5 degrees (looking from above; mentioned in Part 3 with photo) and that must have been after detachment. That means tipping probably occurred as well, despite having a less solid fulcrum at the front.
Moreover, the quasi-circular cross sectional profile of this strange portion of the neck and its pinched appearance is indicative of the pinching you see when two plastic lobes are pulled apart, like pulling apart bread dough. You could take the analogy further and say that if there’s not enough water in the dough to stretch plastically, fractures will appear at 90 degrees to the stretch, curving around the cross sectional profile.
Parts 7 and 8 explain how a supposedly brittle comet might stretch like dough, and this link is a further piece of evidence that backs up that hypothesis. It’s wholly relevant to 67P and mentions the authors’ prediction for the fine-grain structure of 67P- ice pebbles (paywalled but abstract is long and informative).
Part 11 will see how contact binary theory fares at explaining the head tip and fractures being exactly along the rotation plane.
Photo and video still credits:
Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0