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3D shape, cartography, and geoid of Comet 67P C-G
nprev
post Aug 8 2014, 10:20 PM
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The key variable between these scenarios is mass, which will presumably be known in time to a high degree of precision. (Probably not nearly as soon as it would be for a symmetrical body; Rosetta's navigators are probably gonna have an interesting time for quite a few orbits until they get a handle on the mass distribution of C-G).

EDIT: Whups, cancel that. What Doug said. Obviously the system's mass is constrained well within an order of magnitude already.


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ngunn
post Aug 8 2014, 10:22 PM
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Every irregular object eroded from the outside must eventually form a neck which breaks and the two parts will settle together, tumbled or not. How would they get the energy to fly apart again?
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nprev
post Aug 8 2014, 10:28 PM
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Could acquire more angular momentum from impacts over time; then the variable would become the shear strength of the 'neck'. But as Doug observed, it's not spinning fast enough.


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djellison
post Aug 8 2014, 10:37 PM
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If it were rotating fast enough to displace the two halves if the 'neck' were to disappear....then it would also be rotating fast enough to rip itself to shreds.

What I have in essence done is prove that the comet can exist (which is somewhat self evident)
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SteveM
post Aug 8 2014, 10:42 PM
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I'm not convinced by the emerging consensus that the neck is an erosional feature. It seems to me that the neck is near a gravitational low (i.e., "downhill" from the rest of the comet) and any loose material near the comet would be likely to settle there.

In previous passes by the Sun the comet would eject both volatile gases and particles of solids; some of them might not achieve escape velocity. The volatiles would be reheated on the surface and escape again but we would expect the solids to settle back in the lowest point, the comet's neck. This model predicts a dustier area near the neck with a comparatively lower concentration of volatiles.

We'll see what turns up but I'm not a geologist so what do I know.

Steve M
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djellison
post Aug 8 2014, 11:10 PM
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QUOTE (SteveM @ Aug 8 2014, 03:42 PM) *
I'm not convinced by the emerging consensus that the neck is an erosional feature


It's where the bulk of activity appears to be
http://sci.esa.int/rosetta/54471-comet-act...-2-august-2014/

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djellison
post Aug 9 2014, 12:08 AM
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QUOTE (Gerald @ Aug 8 2014, 03:36 PM) *
Hmm, according to the Wikipedia version, the escape velocity is estimated to 0.46 m/s, corresponding to about 0.33 m/s for a circular orbit.
So I'd say within the current uncertainty, respecting the rotation, the resulting surface gravity at the parts most distant to the center of mass is about zero.


No - the centripetal acceleration is 4 orders of magnitude less than the escape velocity.

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JCG
post Aug 9 2014, 01:11 AM
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QUOTE (Gerald @ Aug 8 2014, 01:36 PM) *
Hmm, according to the Wikipedia version, the escape velocity is estimated to 0.46 m/s, corresponding to about 0.33 m/s for a circular orbit.
So I'd say within the current uncertainty, respecting the rotation, the resulting surface gravity at the parts most distant to the center of mass is about zero.
A significantly more compact body with the same angular momentum would be torn apart.

This opens a scenario almost opposing the contact binary approach, meaning head and body could have been broken apart already by centrifugal pseudo-force, and kept together by the stretched "neck", which would give the "rubber" duck metaphor more sense than originally anticipated.
This way the inner of the comet would be exposed at the neck.
Additional momentum could have been provided by impacts or by YORP.


Back of the envelope:
Gravity /centripetal ~ GM/r^2//V^2/r ~ GpP^2 where G = grav constant of 6.67x 10^-11 (mks), p = density ~ 10^3 (mks) and P = period ~4.6x10^4 sec.
Ratio ~ 10^2
Gravity wins hands down. Tidal forces are insufficient.
Adjustments to Fg due to odd shape may cause ratio be somewhat less, but increasing density will go the other way.
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JohnVV
post Aug 9 2014, 01:28 AM
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QUOTE (jgoldader @ Aug 7 2014, 09:24 AM) *
Any chance of Gaspra? I did some work on that back before the Galileo flyby; it would be great to print it out.

Thanks!
Jeff

there is a 3d mesh ( low-res) for gaspra
http://forum.celestialmatters.org/viewtopi...p?f=4&t=636

my g-drive link to the mesh
https://drive.google.com/file/d/0B6ZYAd08tZ...dit?usp=sharing

QUOTE
Not a pain, it just means the cartographers have long-term employment!

Phil

well for 67P a Simplecylindrical map is " out the window"
the vid on youtube looks to be using a Simplecylindrical map
https://www.youtube.com/watch?v=CNGu7KbXzOs
you can tell by the STRETCHED green dots that look like lines

But a "cubemap " would work fairly well
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Greenish
post Aug 9 2014, 01:42 AM
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I had been curious about the gravity field so was googling about... this poster shows some of the weirdness of "which way is up" in a simplified contact binary scenario. It makes perfect sense, but I never considered that there could be the equivalent of Lagrange points near these bodies. Close-in "orbits" would certainly not be circular, even halos are possible. And the details near the neck... hard to know.

http://www.lr.tudelft.nl/fileadmin/Faculte...nglang_Feng.pdf
snip:
Attached Image


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machi
post Aug 9 2014, 01:53 AM
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According to my calculations gravity/centripetal ratio for r=2000 m and vrot=0.28 m/s is G/a=0.0143*Ro (density)
Comets could be very fluffy so density can be between 100 to 1400 kg/m3.
Ratio is then 1.5 to 20 (not ~100 or ~1000).


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Gerald
post Aug 9 2014, 02:10 AM
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QUOTE (JCG @ Aug 9 2014, 03:11 AM) *
Back of the envelope:
Gravity /centripetal ~ GM/r^2//V^2/r ~ GpP^2 where G = grav constant of 6.67x 10^-11 (mks), p = density ~ 10^3 (mks) and P = period ~4.6x10^4 sec.
Ratio ~ 10^2
Gravity wins hands down. Tidal forces are insufficient.

This would be bad for Philae, so I've looked, where the discrepancy may come from.
One reason is -- if I calculated correctly -- a factor of 1 / 3π for the density calculation in the spherical case.
The other one is the estimated density, which has been estimated as 10^2 kg/m.
Together we get a discrepancy factor of 30π, about 94.
Now add the non-spherical shape, and things are open again.

-- This shows, how important the ongoing gravimetric measurements are.
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Adam Hurcewicz
post Aug 10 2014, 05:16 PM
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OK, here is visualization from Celestia. I made model in Blender, texture is from Itokawa, orbital data from SPK/BSP od NAIF NASA/JPL

http://www.youtube.com/watch?v=kETzagV37ig


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Gerald
post Aug 10 2014, 06:03 PM
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For 67P/C-G, and similarly asymmetric bodies, I'd suggest a projection on an appropriate gravitationally equipotential surface, either respecting the centrifugal forces, or using the body at rest.
"Appropriate" means, the average height of the topography over the equipotential surface should be zero, if possible. As a constraint a surface should be taken, which consists of one component without singularities (and without overlapping itself, which is probably a corollary).
Projections go along the field lines of gravity.
The result is still a non-planar map.
This could be projected in a second step to planar tiles/stripes (mercator-like in a very general sense) by constraining the intrinsic curvature.
The width of the stripes would vary because of the varying intrinsic curvature.

... just to close this gap preliminarily, until an official decision is made.
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Harder
post Aug 10 2014, 06:36 PM
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thanks, Gerald, for your insights. I noticed you follow the Rosetta blog, too. Unless another Gerald is at work there! My own name (Peter Groeneweg) is a bit too difficult so on the ESA blogs I'm PeterG.

In my previous entry my use of the English language is perhaps "difficult" too, so let me say here what I really wanted to say: I feel privileged to be a member, a junior member to be more precise, of a forum that has experts like Phil in its ranks. No unmanned spaceflight subject seems too arcane for the forum!

A further thought: is a cartography system the province of ESA, or does it need endorsement by the international organization(s)? One thing seems sure: after the initial spectacular success at 67P/C-G I expect more missions to follow and a sound cartography system seems most useful to have by then.
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