3D shape, cartography, and geoid of Comet 67P C-G |
3D shape, cartography, and geoid of Comet 67P C-G |
Aug 6 2014, 02:11 PM
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#1
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Solar System Cartographer Group: Members Posts: 10229 Joined: 5-April 05 From: Canada Member No.: 227 |
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 -------------------- ... because the Solar System ain't gonna map itself.
Also to be found posting similar content on https://mastodon.social/@PhilStooke Maps for download (free PDF: https://upload.wikimedia.org/wikipedia/comm...Cartography.pdf NOTE: everything created by me which I post on UMSF is considered to be in the public domain (NOT CC, public domain) |
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Aug 6 2014, 02:44 PM
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#2
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Junior Member Group: Members Posts: 30 Joined: 6-September 12 From: Denver Member No.: 6641 |
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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Aug 6 2014, 03:47 PM
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#3
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Member Group: Members Posts: 593 Joined: 20-April 05 Member No.: 279 |
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Aug 6 2014, 04:06 PM
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#4
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Senior Member Group: Members Posts: 1669 Joined: 5-March 05 From: Boulder, CO Member No.: 184 |
A 2D map of C-G seems like a tough order; the projection math alone... 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). -------------------- Steve [ my home page and planetary maps page ]
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Aug 6 2014, 04:46 PM
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#5
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Member Group: Members Posts: 495 Joined: 12-February 12 Member No.: 6336 |
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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Aug 6 2014, 04:52 PM
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#6
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Senior Member Group: Members Posts: 2346 Joined: 7-December 12 Member No.: 6780 |
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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Aug 6 2014, 05:02 PM
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#7
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Senior Member Group: Members Posts: 1669 Joined: 5-March 05 From: Boulder, CO Member No.: 184 |
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. -------------------- Steve [ my home page and planetary maps page ]
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Aug 6 2014, 05:23 PM
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#8
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Senior Member Group: Members Posts: 2346 Joined: 7-December 12 Member No.: 6780 |
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Aug 6 2014, 05:38 PM
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#9
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Senior Member Group: Members Posts: 1669 Joined: 5-March 05 From: Boulder, CO Member No.: 184 |
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. -------------------- Steve [ my home page and planetary maps page ]
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Aug 8 2014, 07:47 PM
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#10
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Member Group: Members Posts: 107 Joined: 1-August 14 Member No.: 7227 |
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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Aug 8 2014, 08:04 PM
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#11
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Solar System Cartographer Group: Members Posts: 10229 Joined: 5-April 05 From: Canada Member No.: 227 |
Not a pain, it just means the cartographers have long-term employment!
Phil -------------------- ... because the Solar System ain't gonna map itself.
Also to be found posting similar content on https://mastodon.social/@PhilStooke Maps for download (free PDF: https://upload.wikimedia.org/wikipedia/comm...Cartography.pdf NOTE: everything created by me which I post on UMSF is considered to be in the public domain (NOT CC, public domain) |
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Aug 8 2014, 08:06 PM
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#12
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Senior Member Group: Members Posts: 2106 Joined: 13-February 10 From: Ontario Member No.: 5221 |
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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Aug 8 2014, 10:00 PM
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#13
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Solar System Cartographer Group: Members Posts: 10229 Joined: 5-April 05 From: Canada Member No.: 227 |
I think you're right, the lobes would collapse together as the neck was eroded.
Phil -------------------- ... because the Solar System ain't gonna map itself.
Also to be found posting similar content on https://mastodon.social/@PhilStooke Maps for download (free PDF: https://upload.wikimedia.org/wikipedia/comm...Cartography.pdf NOTE: everything created by me which I post on UMSF is considered to be in the public domain (NOT CC, public domain) |
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Aug 8 2014, 10:05 PM
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#14
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Junior Member Group: Members Posts: 88 Joined: 8-May 14 Member No.: 7185 |
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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Aug 8 2014, 10:17 PM
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#15
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Founder Group: Chairman Posts: 14434 Joined: 8-February 04 Member No.: 1 |
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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