Quick answer: No....Just fishing Billy T, but if as you say "the hotter the core the faster the reaction rate" would this not make the core susceptible to potential overheating if environmental factors such as the hypothesized geomagnetic /Earth COG instability were to occur?... Would they be as sensitive to gravitational COG instabilities as the USSR systems may have been? ...
You speak basically non-sense about "gravitational COG instabilities." I would like you to be more specific as to what that even means and the time scale for a significant movement of the Earth's center of gravity.
Let me note that yes the CoG does move mainly along the Earth's spin axis (not magnetic axis, which is a somewhat different) with great regulatity in a full cycle period of 12 months. I.e. the mass of snow and ice in the Northern Hemisphere increases in winter. This shift has been happing for a very long time as the spin axis of earth is tilted 23.5 degrees from the orbit plane's normal. (Thus Earth has seasons.)
What other shift you can suggest that is even 0.000,1 as great or as fast?
Also note the Earth/moon barycenter orbits the sun in nearly perfect ellipse and has for an equally long time (as the ~23.5 degree tilt.) The separation between earth and moon, is slowly increasing, and has been for millions of years. (I.e. every since the moon "belonged to the earth." I don't know when or how Earth got its moon, but there had to be some "third body" involved. Before earth got ist moon, the spin axis may have significantly different from the current 23.5 degrees, but probably not by 10 degrees.)
Again, to not appear so ignorant, please be more specific as to what significant movement of the Earth's center of gravity you refer to, what causes it, what tiny fraction of the seasonal shift it makes, and what is the time scale for your postulated shift, which is important to GW.
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