QUOTE (fredk @ Dec 29 2014, 10:25 PM)
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Shouldn't the rotating frame be the relevant frame for any "wind" effects? The material in the jets will be rotating with the comet, at least shortly after the material leaves the vent.
Actually, as soon as an particle loses contact with the rigid, rotating body of the comet, it is immediately in the inertial frame and just in a nice orbit around the comet. The only thing that keeps it in the rotating frame is some force holding together as a single piece with the comet. Once that is gone, it's gone. At that point the well known physical forces rule--inertia and gravity being the main ones. In short, once the particle leaves its vent, it is in orbit around 67P, with whatever initial velocity & direction the vent has given it.
[WARNING: Super-long, detailed post ahead. If you just want the conclusions, skip to the last three paragraphs, or just look at the picture.]Because I'm a Curious George, I ran a few quick simulations in Orbiter. All simulations were started near the Philae 1st impact site, just because it was a convenient and relevant location. 67P rotation direction, speed, and other details correspond to best-known ESA data. Gravitational weirdness isn't modeled precisely but that won't affect the gist of the argument and examples below.
Results:
- Example 1: Launched straight up in rotational frame at 0.1 m/s--simulating a vent on the surface launching a particle straight up at 0.1 m/s. Result: Flies about 40 minutes, ends up about 100 meters exactly in the opposite direction of the comet's rotation at the point it launched (ie, directly west of its starting point).
- Example 2: Launched straight up in rotational frame at 0.2 m/s. Result: Flies about 77 minutes, ends up about 200 meters directly west of its starting point.
- Example 3: Launched straight up in rotational frame at 0.3 m/s. Result: Flies about 133 minutes, ends up about 300 meters directly west of its starting point.
In short, the particle goes straight up, the comet rotates under it, the particle lands at a point directly west (ie, anti-rotation) of the place it started.
If you think about it, this makes perfect sense. I won't try to explain the rotational dynamics here, but has to do with how far the point is from the axis of rotation, and how fast, therefore, the point must move in order to keep up with a certain rate of rotation. And it is the same basic reason the ice skater rotates faster when the arms & legs are drawn in tightly, and slower when they are thrown out wide.
Now--what if you launch with both upward *and* westward velocity? Since the comet rotates eastward at 0.33 m/s, any westward velocity of the particle up to 0.33 m/s actually reduces the particle's total velocity in the inertial frame. So you get results like this--keep in mind that 0.33 m/s westward velocity equals 0 m/s in the inertial frame:
- 0.1 m/s upward, 0.33 m/s westward (in rotating frame): Travels about 300 yards westward.
- 0.2 m/s upward, 0.33 m/s westward: Travels off the head of the comet and ends up in the neck area.
- 0.3 m/s upward, 0.33 m/s westward: Travels off the head and lands on the foot of the comet.
- 0.4 m/s upward, 0.33 m/s westward: Goes much higher off the side of the head, but still lands in the neck/foot area.
- 0.7 m/s upward, .33 m/s westward: Ends up in a very high orbit, max altitude about 7 km. (We're very close to escape velocity now.)
- 1.0 m/s upward, 0.33 m/s westward: Above escape velocity; we're gone.
Contrariwise, if you launch your particle in the EASTWARD direction, your horizontal velocity *adds* to the 0.33 m/s rotation of the comet. So for example if you launch your projectile at 0.33 m/s eastward, you immediately have 0.66 m/s horizontal velocity--which is almost escape velocity right there. Examples:
- 0.0 m/s upward, 0.33 m/s eastward (in rotating frame): Enters a high orbit, about 6 km max altitude.
- 0.1 m/s upward, 0.33 m/s eastward: Again a high orbit, about 6.5 km max altitude.
- 0.3 m/s upward, 0.33 m/s eastward: High orbit, about 11 km max altitude
- 0.5 m/s upward, 0.33 m/s eastward: Escape velocity; it's gone.
End result is, there is a just a narrow range of eastward velocities that end up actually landing just eastward of the starting point. Most eastward-bound particles end up westward of their starting point *or* in a big orbit or escaping.
- If the particle has just a bit of eastward velocity, the rotation wins out and the particle ends up going a bit westward instead.
- If the particle is going with substantial eastward velocity, it's likely to enter a high orbit (meaning it will eventually land on some random point of the comet) or even reach escape velocity. The fact that the eastward velocity of the particle is added to the 0.33 m/s rotation velocity of the comet, plus the fact that escape velocity is somewhere around 0.75 m/s makes this inevitable.
- That leaves us with just a very narrow range of moderate eastward velocities that result in the particle landing just to the eastward of the starting point.
- By contrast, there is a rather large range of westward velocities that end up landing westward of the starting point.
With all that in mind, we can pretty well characterize the distribution of particles from a plume in the area of the head of 67P, such as the one Bill nicely identified
here. (I'm going to argue with Bill's interpretation here--but please don't take that to mean I don't appreciate his very beautiful and persuasive interpretation. Quite the contrary! His clear and persuasive summary helped me a lot in clarifying my own thinking about how these plumes must work.)
- Particles leave the plume in relatively random directions. This is what you would expect from gases and/or particles escaping from a jumble of rocks or random vent openings. (Bill's theory depends on all plumes along a long fracture vent somehow having special piping that directs all the outgoing particles in one particular direction. That seems very, very unlikely to me.)
- All the particles with westward velocity end up deposited west of the plume (unless they have too much velocity--then they may end up in orbit or escaping).
- All the particles directed upwards end up west of the plume (again--too high velocity & they will orbit or escape instead).
- Particles with slight eastward velocity end up west of the plume.
- Particles with too much eastward velocity end up in high orbits or escape (and this is far more likely for eastward-escaping particles than westward).
- Only a specific, narrow range of eastward velocities end up deposited just eastward of the plume.
Results:
- All the above means that the vast majority of particles deposited near the plume are deposited to the westward of the plume; relatively few to the eastward.
- There is indeed a clear westward bias to the velocity of the particles.
If you look at Bill's beautiful diagram
here, you can see all that in action. Particles escape from the fracture vent (red line) in random directions. Most end up west of the fracture vent. Just a few end up to the east of it. (East is very nearly aligned with the green arrow in the diagram.)
Particles do travel north and south if by chance they have that velocity when leaving the vent--there is no bias for or against those directions. But it's mostly northwest & southwest of the fracture vent, with little northeast or southeast.
Bill interprets the 'dunes' as running parallel to the primary direction of the particles. But (drum roll please)--finally, my conclusion:
MY CONCLUSION It's clear now the that particles do in indeed (primarily/with a clear and fairly strong bias) move to the westward, which is 90 degree leftward of the blue arrows in Bill's diagram
here.
So again, we're left with the question of: Why do these dune features align perpendicularly to the primary/main direction of the particles?
I'm going to suggest (again) the that reason **might** be similar to the reason sand dunes grow perpendicular to the prevailing wind in some conditions (see
reference here--because the fracture vent on 67P's head is a relatively long line rather than a point source, and because particles move in various directions with just a bias towards westward and against eastward movement, conditions there are similar to those shown in Figure 1D (theta = 33 degrees) and 1E (theta = 30 degrees)--and the outcome also looks much the same).
Note that this is different from saying that the 'plume piles" form in exactly the same way sand dunes do. Sand dunes are created due to the action of the atmosphere moving and dropping sand, a situation that doesn't pertain to the comet. But here we have 'plume piles' developing transverse to the general direction of particle flow, in a way that looks mighty similar to the dunes that form under similar conditions. There **just might** be an underlying connection.
These parallel 'plume piles', generally perpendicular to the rotational direction, are found all over the head of 67P (see attached image). They strike me as quite a noteworthy and remarkable feature. I don't see any similar features in the neck area (wouldn't expect them--rotational velocity is lower), but I also haven't spotted any yet in the 'foot' area of the comet, where similar conditions to those on the head might be at work.