IPB

Welcome Guest ( Log In | Register )

13 Pages V  < 1 2 3 4 5 > »   
Reply to this topicStart new topic
3D shape, cartography, and geoid of Comet 67P C-G
fredk
post Aug 10 2014, 06:38 PM
Post #31


Senior Member
****

Group: Members
Posts: 3772
Joined: 17-January 05
Member No.: 152



QUOTE (Gerald @ Aug 10 2014, 06:03 PM) *
Projections go along the field lines of gravity.

Why along the field lines (and with respect to an equipotential surface)? That would rely to some extent on knowledge of the internal mass distribution, which may be significantly nonuniform, and at the very least would require nontrivial numerical modelling to determine. It would strike me as a good property of a projection to depend only on the geometry of the body's surface.

But all of this is probably moot since such bodies have been mapped in the past. In practice, I'd guess the projection would be tailored to the body, since some projections may not work for bodies when the surface "folds back on itself".
Go to the top of the page
 
+Quote Post
Gerald
post Aug 10 2014, 07:11 PM
Post #32


Senior Member
****

Group: Members
Posts: 1876
Joined: 7-December 12
Member No.: 6780



QUOTE (Harder @ Aug 10 2014, 08:38 PM) *
... I noticed you follow the Rosetta blog, too. Unless another Gerald is at work there! ...

I admit, I couldn't help to extend the funny metaphorical thought experiment about the Philae descent and landing (with limited type setting options).
But names don't need to be unique, necessarily.

QUOTE (fredk @ Aug 10 2014, 08:38 PM) *
Why along the field lines..?

Because it corresponds to the intuitive and physical concept of "up" and "down".
Notions like slope / steepness, depression, hill, etc. make a sense. It's kind of generalization we are used to from Earth on a physical basis, not merely geometric.

Technical difficulties to find the field of gravity are going to be reduced by the orbital measurements. These measurements allow even to determine the interior mass distribution to some degree. But an estimation would do the job, too.

The surface shouldn't fold back to itself (conjectural to some degree at this point), since the gravitational potential should be defined uniquely, at least for the non-rotating body.
The body itself may be layered or contain overhangs, of course.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Aug 10 2014, 09:43 PM
Post #33


Martian Cartographer
****

Group: Members
Posts: 7262
Joined: 5-April 05
From: Canada
Member No.: 227



The up and down can be incorporated into topography by mapping height (and slope etc.) relative to the equipotential surface (with or without rotational accelerations included - with them, it corresponds to what Peter Thomas has called Dynamic Topography) - there's a literature on this especially by Peter Thomas and colleagues.

There is no one best way to map a non-spherical object, just as there is not for a sphere. In fact, we need lots of maps in different projections, and using different versions of the shape, to explore the range of possibilities, most of which few people have ever thought about in detail. For instance, the shape model used to establish locations and drive the projection might be any of these:

True topographic shape
Equipotential surface
Convex hull
Triaxial Ellipsoid (best fit)
Sphere
- also other possible shapes such as a cylinder could be considered, especially for more elongated objects.

For anything but the first, the actual surface would be projected onto the shape model along radii or surface normals (body or model), then that shape drives the map projection.

Although simple cylindrical maps contain severe distortions they are very useful as intermediate steps in mapping and they are easy to import into many mapping and visualization systems. My Itokawa mosaic, for instance, includes many distortions and one small area where the mosaic is not unique (radii exit the surface and reconnect with it, as we may see at 67P as well. But there are ways to cope with these issues and you have to start somewhere.

"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."

ESA can choose its own method of mapping, no international agency has any role in it except the IAU Working Group for cartographic coordinates and rotational elements - the coordinate system should conform to their guidelines. But mapping - no. The field is still very immature and no standards exist, nor should they until we have much more experience with different methods.

Phil


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
JohnVV
post Aug 10 2014, 11:38 PM
Post #34


Member
***

Group: Members
Posts: 824
Joined: 18-November 08
Member No.: 4489



the problem at this time is we do not have a mesh to work with
-- yes one could use "Blender" and hand carve a cube into something that looks like it

now a cube map has advantages ( sometimes) for some shapes

a hi-passed map for a mesh of Vesta ( old map 2006 data) in a uv mapped cubemap
( from a normal by Chris Laurel)
north,90 to180,0 to 90,
-90 to 0,-180to -90, south


the new DEM hi passed for comparison
-- in Simple Cylindrical projection


now vesta is a bad example it is rather spherical ( i just happen to be working on this asteroid right now)

so for 67p a SimpleCyl. map will not work well . BUT it is a good intermediate format and so is sinusoidal

Go to the top of the page
 
+Quote Post
Y Bar Ranch
post Aug 11 2014, 02:16 PM
Post #35


Junior Member
**

Group: Members
Posts: 34
Joined: 28-July 07
Member No.: 2984



QUOTE (SteveM @ Aug 8 2014, 05:42 PM) *
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.

Actually, the neck is not near a gravitational low. If you could hollow out a little sphere at where the center of mass is for the comet, at that point there'd be no gravity since the mass would be pulling from all directions equally. That's somewhere near the neck. Taking off and flying away from the neck perpendicular to the main axis is probably the lowest energy trajectory for departing (now I'm guessing).
Go to the top of the page
 
+Quote Post
djellison
post Aug 11 2014, 02:47 PM
Post #36


Administrator
****

Group: Chairman
Posts: 14013
Joined: 8-February 04
Member No.: 1



QUOTE (Y Bar Ranch @ Aug 11 2014, 07:16 AM) *
Actually, the neck is not near a gravitational low.


QUOTE
If you could hollow out a little sphere at where the center of mass is for the comet, at that point there'd be no gravity since the mass would be pulling from all directions equally. That's somewhere near the neck.


Are these not contradictory statements?
Go to the top of the page
 
+Quote Post
ngunn
post Aug 11 2014, 02:48 PM
Post #37


Senior Member
****

Group: Members
Posts: 3433
Joined: 4-November 05
From: North Wales
Member No.: 542



QUOTE (Y Bar Ranch @ Aug 11 2014, 03:16 PM) *
Actually, the neck is not near a gravitational low.


I think there is confusion here between the scalar quantity gravitational potential and its gradient, gravitational field strength. The centre of the Earth, for example, is a low point in the gravitational potential. If you could dig a tunnel all the way there objects would certainly fall down it, even though on arrival they would have zero weight.
Go to the top of the page
 
+Quote Post
Gerald
post Aug 11 2014, 03:37 PM
Post #38


Senior Member
****

Group: Members
Posts: 1876
Joined: 7-December 12
Member No.: 6780



If you take a binary of two spherical bodies, the center of mass is in the middle of the line between those two bodies, but that's no gravitational low; it's more like a saddle; and it's a Lagrangian point (L1) at the same time, although the center of mass of two bodies doesn't need to be a Lagrangian point, in general. There are two lows at the respective centers of the two bodies.

For 67P/C-G there may also be two (or more) local gravitational lows, the deeper one near the center of the larger component.
The center of mass should be between the gravitational low of the larger component and the neck.
The neck should be near a Lagrangian point (a saddle in the field of gravity), which is between the local gravitational low of the smaller component and the center of mass.
At the center of mass there should be a net gravitational pull towards the local gravitational low of the larger component.

The center of mass is a point on the rotation axis.

Start with the Earth-Moon system as an easier-to-understand example, when reading the second paragraph a second time.
Go to the top of the page
 
+Quote Post
Y Bar Ranch
post Aug 11 2014, 04:02 PM
Post #39


Junior Member
**

Group: Members
Posts: 34
Joined: 28-July 07
Member No.: 2984



QUOTE (djellison @ Aug 11 2014, 09:47 AM) *
Are these not contradictory statements?

Not contradictory, more like a non sequitur. huh.gif
Go to the top of the page
 
+Quote Post
Y Bar Ranch
post Aug 11 2014, 04:08 PM
Post #40


Junior Member
**

Group: Members
Posts: 34
Joined: 28-July 07
Member No.: 2984



QUOTE (Gerald @ Aug 11 2014, 10:37 AM) *
If you take a binary of two spherical bodies, the center of mass is in the middle of the line between those two bodies, but that's no gravitational low; it's more like a saddle;

That's what I meant to express. A small perturbation from the saddle point not exactly on the upward isoline and its downhill to one of the two lobes.

So escape velocity from the saddle point is likely lowest for the comet and it would dissipate at a higher rate, and any spray that doesn't make it off the comet from the neck is likely pulled to one of the lobes, adding to the saddle-ness of the saddle point. So for an asymetrical body, it seems that process is unstable and the asymmetry would grow, i.e., more necking.

There's probably an unstable process between the two lobes too, with one having a higher rate of dissipation and the heavier one stealing some of the lighter one's mass. But this is more guessing on my part.
Go to the top of the page
 
+Quote Post
Gerald
post Aug 11 2014, 04:36 PM
Post #41


Senior Member
****

Group: Members
Posts: 1876
Joined: 7-December 12
Member No.: 6780



QUOTE (Y Bar Ranch @ Aug 11 2014, 06:08 PM) *
That's what I meant to express. A small perturbation from the saddle point not exactly on the upward isoline and its downhill to one of the two lobes.
...

That's really hard to tell at the moment, since the local gravitational lows are probably within the nucleus. Since the surface of the larger component is farther away from its local gravitational low than the surface of the neck is away from the line between the two(?) gravitational lows, we've two opposite effects which may or may not cancel out.

But I share the impression, that the surface of the nucleus isn't in perfect equilibrium between the several forces (gravity, inertial pseudo-forces, friction).
If there is some mass waste from the neck or from the smaller component towards the larger one, the field of gravity, and the rotation also change. Asymmetric loss of volatiles may change the angular velocity too.
This might eventually lead to ejection or collapse of some parts. As the comet gets closer to the Sun, I'd guess, we may see some dynamics.
Go to the top of the page
 
+Quote Post
ngunn
post Aug 11 2014, 04:42 PM
Post #42


Senior Member
****

Group: Members
Posts: 3433
Joined: 4-November 05
From: North Wales
Member No.: 542



QUOTE (Y Bar Ranch @ Aug 11 2014, 05:08 PM) *
So escape velocity from the saddle point is likely lowest for the comet and it would dissipate at a higher rate, and any spray that doesn't make it off the comet from the neck is likely pulled to one of the lobes, adding to the saddle-ness of the saddle point. So for an asymetrical body, it seems that process is unstable and the asymmetry would grow, i.e., more necking.


I really don't think that's true. Consider a body consisting of two perfect touching spheres. Place a small test sphere on the surface of one of them and where would it roll to? Towards the contact point for sure as that is the point of lowest potential on the surface of the body. Thus the neck would tend to grow thicker.
Go to the top of the page
 
+Quote Post
Y Bar Ranch
post Aug 11 2014, 04:50 PM
Post #43


Junior Member
**

Group: Members
Posts: 34
Joined: 28-July 07
Member No.: 2984



QUOTE (ngunn @ Aug 11 2014, 12:42 PM) *
I really don't think that's true. Consider a body consisting of two perfect touching spheres. Place a small test sphere on the surface of one of them and where would it roll to? Towards the contact point for sure as that is the point of lowest potential on the surface of the body. Thus the neck would tend to grow thicker.


It would do that only because it is constrained to roll on the surface of the two spheres.
Go to the top of the page
 
+Quote Post
Phil Stooke
post Aug 15 2014, 06:18 PM
Post #44


Martian Cartographer
****

Group: Members
Posts: 7262
Joined: 5-April 05
From: Canada
Member No.: 227



Ok... I have been taking some time out from what I should really be doing - finishing a book (Emily will understand this) - to play around with some ideas about what a map of 'the nucleus that dare not speak its name' should look like.

Let me preface this by saying - this is a horrible map, very distorted and inaccurate, and the Rosetta team will do much better soon and completely discredit me. This is only intended to illustrate roughly what a proper map might look like. It's cylindrical, so the projection is very distorted to begin with.

We had a video of a shape with a lat-long grid, so that forms the basis of my coordinate system. I took images from orientations which roughly matched frames from the video and overlaid them. Two sources of error immediately - the shape was based on low res images and will not fit high res images very well to begin with, and the overlay is only approximate due to different view directions, so it's hard to match positions properly. Then I copied areas grid cell by grid cell and pasted them and distorted them to fit the grid. Lots of problems and bad fits especially in the neck area, obviously.

The grid is spaced at 15 degrees like the shape model video grid. Longitude 180 is in the middle. A separate version is annotated to show where the main features are.

Phil

Attached Image


Attached Image


--------------------
... because the Solar System ain't gonna map itself.
Go to the top of the page
 
+Quote Post
Explorer1
post Aug 15 2014, 07:13 PM
Post #45


Senior Member
****

Group: Members
Posts: 1439
Joined: 13-February 10
From: Ontario
Member No.: 5221



Very impressive! The axis must be tilted quite a lot; given the length of the seasons it might be a very long time until much of the 'southern hemisphere' is in sunlight to fill in the black spaces.
Go to the top of the page
 
+Quote Post

13 Pages V  < 1 2 3 4 5 > » 
Reply to this topicStart new topic

 



RSS Lo-Fi Version Time is now: 24th September 2017 - 08:47 AM
RULES AND GUIDELINES
Please read the Forum Rules and Guidelines before posting.

IMAGE COPYRIGHT
Images posted on UnmannedSpaceflight.com may be copyrighted. Do not reproduce without permission. Read here for further information on space images and copyright.

OPINIONS AND MODERATION
Opinions expressed on UnmannedSpaceflight.com are those of the individual posters and do not necessarily reflect the opinions of UnmannedSpaceflight.com or The Planetary Society. The all-volunteer UnmannedSpaceflight.com moderation team is wholly independent of The Planetary Society. The Planetary Society has no influence over decisions made by the UnmannedSpaceflight.com moderators.
SUPPORT THE FORUM
Unmannedspaceflight.com is a project of the Planetary Society and is funded by donations from visitors and members. Help keep this forum up and running by contributing here.