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3D shape, cartography, and geoid of Comet 67P C-G
Phil Stooke
post Aug 6 2014, 02:11 PM
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Explorer 1 said:

"A 2D map of C-G seems like a tough order; the projection math alone..."


Don't worry! If you can put a grid on the surface (as we have seen already), you can warp that grid into any map projection you like. Mapping will be no huge problem - in fact I expect they have a rough one already (I've been playing with one myself).

Phil


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acastillo
post Aug 6 2014, 02:44 PM
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It would appear that the neck is an "erosional" feature (not sure if erosion is the right word), and maybe not the contact boundary between 2 separate bodies. At some point in the future, the neck will sublime away and the comet will split in two.
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AndyG
post Aug 6 2014, 03:47 PM
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QUOTE (acastillo @ Aug 6 2014, 03:44 PM) *
It would appear that the neck is an "erosional" feature...


Gravity must be very low there, caught as it is between two lumps o' rock. A higher chance for material to be lost, maybe?

Andy
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scalbers
post Aug 6 2014, 04:06 PM
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QUOTE (Explorer1 @ Aug 6 2014, 11:43 AM) *
A 2D map of C-G seems like a tough order; the projection math alone... wink.gif


Interesting though that a unique coordinate system (projection) is possible as seen in the rotating map. None of the overhangs appear to wrap back on themselves as seen from the central projection point. Thus a 2D map should be possible with access to the shape model (as Phil alluded to earlier).


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TheAnt
post Aug 6 2014, 04:46 PM
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QUOTE (acastillo @ Aug 6 2014, 04:44 PM) *
It would appear that the neck is an "erosional" feature (not sure if erosion is the right word), and maybe not the contact boundary between 2 separate bodies. At some point in the future, the neck will sublime away and the comet will split in two.


I concur, not that we have a final word yet but I do tend to think the shape is from melting and erosion, rather than 2 objects that have merged since that is a less likely scenario.

@AndyG: Gravity is nearly negligible, gas pressure define this environment with sublimation and active geysers, though I wonder if the latter could create a static charge.
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Gerald
post Aug 6 2014, 04:52 PM
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QUOTE (scalbers @ Aug 6 2014, 06:06 PM) *
Interesting though that a unique coordinate system (projection) is possible as seen in the rotating map. ...

That's possible with any simply connected object (no "handle-shaped holes") in 3d via a homeomorphism (continuous map).
For objects with holes, like doughnuts different coordinate systems are needed. The shape of the nucleus is strange, but fortunately not that strange.
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scalbers
post Aug 6 2014, 05:02 PM
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QUOTE (Gerald @ Aug 6 2014, 04:52 PM) *
That's possible with any simply connected object (no "handle-shaped holes") in 3d via a homeomorphism (continuous map). ...

Sounds good, though it seems to me that C-G would be more straightforward than some other simply connected objects. A latitude/longitude with respect to C-Gs center of gravity appears to be possible as a "planetocentric" or "cometocentric" coordinate. It would be a simple tracing of rays emanating from the central point and then intersecting the surface. Each ray has just a single intersection with the surface.


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Gerald
post Aug 6 2014, 05:23 PM
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QUOTE (scalbers @ Aug 6 2014, 07:02 PM) *
...Each ray has just a single intersection with the surface.

As long as there are no relevant overhangs (in the sense of the rays). I'm not quite sure whether this holds for the comet.
It could become a little more tricky.
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scalbers
post Aug 6 2014, 05:38 PM
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QUOTE (Gerald @ Aug 6 2014, 05:23 PM) *
As long as there are no relevant overhangs (in the sense of the rays). I'm not quite sure whether this holds for the comet.
It could become a little more tricky.

Good point. A closer look at the recent animation shows a few localized breaks in the grid lines. This correlates with some local topography that has addtional intersection points with the rays pointing at the center of gravity. Perhaps one would have to filter out these bumps in a shape model to come up with a reference shape that could be specified using a cometocentric coordinate. Then the actual surface can be compared with normals to this reference shape.


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mcgyver
post Aug 8 2014, 07:47 PM
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QUOTE (acastillo @ Aug 6 2014, 03:44 PM) *
It would appear that the neck is an "erosional" feature (not sure if erosion is the right word), and maybe not the contact boundary between 2 separate bodies. At some point in the future, the neck will sublime away and the comet will split in two.

Eyewitnessing it will be simply amazing.
On the opposite side, mapping an evolving body will be a pain!
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Phil Stooke
post Aug 8 2014, 08:04 PM
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Not a pain, it just means the cartographers have long-term employment!

Phil


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Explorer1
post Aug 8 2014, 08:06 PM
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Wouldn't the two lobes just gradually come back together together as the neck erodes, if their mass remains the same? Unless a decrease in radius forces C-G to rotate faster and faster (I guess we'll find out soon!)
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Phil Stooke
post Aug 8 2014, 10:00 PM
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I think you're right, the lobes would collapse together as the neck was eroded.

Phil



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Mercure
post Aug 8 2014, 10:05 PM
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I believe the centrifugal forces at the rotational rate of ~ 1 revolution per day are stronger than the combined gravitational attraction of the two lobes. If the neck breaks they would come apart, as I see it. Would be interesting to see calculations of the eventuality.
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djellison
post Aug 8 2014, 10:17 PM
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Rotation rate is 12.7 hours. The circumference drawn by the 4km length of the comet ( a 2km radius ) is 12.6 km

So very roughly - it's doing 1km/hr or 0.28m/sec. V^2/r is thus 0.000039 m/sec^2

Surface gravity is approximated as 10^-3 m/sec^2 3 orders of magnitude higher than the centripetal acceleration due to rotation.

Thus no - they would not fly apart. They would collapse together.

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