3D shape, cartography, and geoid of Comet 67P C-G Options

[Phil Stooke]

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

[Gerald]

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.

[Y Bar Ranch]

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.

[ngunn]

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.

[Y Bar Ranch]

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.