Sorry, I’m drifting a bit. Let me try to regain my bearings.
My second objection in this thread to geocentricism–the theory that the earth is stationary–is that the earth is not a rigid body, that one part of it moves relative to another part of it. I asked trth_skr what part of it is stationary, and he replied that it is the center of mass. I have two problems with this reply:
(1) To define a stationary coordinate system, you need three points. One of these would be the earth’s center of mass; the other two are not defined–at least not that I know of; trth_skr hasn’t answered me yet.
(2) The center of mass is defined as the average of the positions of a large number of atoms, weighted by the mass of each atom. How do we define the set of atoms to be included in this average? Before a meteor hits the earth, it is obviously not part of the earth and should not be included. After it hits the earth, it is part of the earth and should be included. At what point do we make the changeover and include the material from the meteor in the center of mass calculation? What non-arbitrary criterion do we use?
I apologize for the mention of the momentum. It appears at the moment to be a red herring, although the question of how the impact of a meteor locally on the surface of the earth can instantaneously affect the velocity of galaxies billions of lightyears away remains to be settled.
I will try and answer your questions. I will use this post.
(1) No, you need three axis. Any time we create a coordinate system, this is somewhat artificial. There is a difference between making a coordinate system transformation and doing a calculation (i.e., on the geosynchronous satellites), say using general relativity and actually having a detailed physical model of the system. In the case of my assertion about geosynchronous satellites, this is simply a coordinate transformation. I would suspect that the best approach would be to constrain the average center of mass of the earth in 3 translational directions, as well as constrain the rotational motions, all to zero. The calulation, if properly done, will calculate the necassary reaction forces within the earth to maintain that constraint.
(2) In the case of a detailed model, you may want to account for mass changes, etc. In that case, I would think a good approach would be to choose a zero time, calculate the center of mass at zero, then as time advances, uipdate the center of mass. Of course this would be extremely complicated, but in principle, not impossible.
Now the model would also have to account for the effect of changing center of mass. This is where modelling the earth as gyroscopically stabilized (per MWT) comes in. As long as the center of mass does not change too much from its intital position, the gyroscopic stabilization should keep it stable.
A huge asteroid hitting the earth will cause a huge earthquake, made up of some fraction of the energy of the asteroid impact, plus some fraction of the change in position of the center of mass of the earth. Due to Mach’s principle, the rest of the universe will absorb some of the energies. I suspect the earth will absorb a fair amount of the direct impact energy, but the universe can change configuration ever so slightly to absorb any change in the center of mass, but this is a guess.
Keep in mind that in a rotating/translating earth frame, an impact will change the velocity of the earth’s translation (and possibly apply a torque cahnging angular velocity). In a fixed earth frame, it will change the precession dynamics and possibly the rotation velocity. Keeping in mind the infintessimal mass of the earth, relative to the universe, the change would be almost unobservable.