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Except for ice, acetic acid, bismuth and gallium and a few other things materials generally shrink when they cool and solidify, so I'm pretty sure Earth has as well.

It probably wouldn't be measurable over a period of years, but models of the Earth's current and historic rates of heat flow can probably be used to estimate a rate of change of Earth's average size and possibly oblateness.

Right now WGS84 uses 6378137.0 meters for Earth's equatorial radius and a flattening at the poles of about 1/298.257222.

How fast might those change over any given million years?

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    $\begingroup$ Perhaps relevant question: earthscience.stackexchange.com/q/18534/15419 $\endgroup$ – BMF Mar 1 at 5:01
  • $\begingroup$ @BMFForMonica Thanks! That's close but I don't think it's a duplicate. It's possible that an answer can be written here based on estimating the slopes shown in Figure 2 of the link in an answer there if we assume that most of the change is due to the mantle. But I'm not sure if those assumptions are correct. $\endgroup$ – uhoh Mar 1 at 5:06
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    $\begingroup$ keep in mind the earth is slowly gaining mass due to meteors. Its a small effect but on the scale involved likely bigger than thermal changes. $\endgroup$ – John Mar 2 at 2:55
  • $\begingroup$ @John good point! ;-) $\endgroup$ – uhoh Mar 2 at 2:57
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    $\begingroup$ @a_donda I guess at 10k reputation deleted posts are still displayed. In Stack Exchange nothing is ever really deleted, it just "fades from view" for most users. When I saw "linked article" in your comment and didn't see a linked article in my question, I scrolled down and saw it. i.stack.imgur.com/b8Lvq.jpg $\endgroup$ – uhoh Jul 29 at 23:38
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(From the answer linked in a remark under the question by @BMF, which I only realized after having saved this answer. So, in principle, a double post, but I was asked to undelete :-))

Earth's thermal history may give some hints, not sure if this is an actual answer to the question. It seems like Earth's radius depends on the layering of mantle convection, and that though there where significant changes during the Archean and earlier, today's (since the late Archean) shrinking rate is slow (12km less in radius in 2.5Gy).

Source: https://www.sciencedirect.com/science/article/pii/S167498711200148X

Questions that remain:

What about the core ?

And is mass loss or gain from astronomical processes significant enough ?

I would like to add that WGS 84 is a reference ellipsoid, and height values can be (are) given as positive or negative numbers. They can be updated every now and then by satellite. Also, I would assume that tectonic processes or local anomalies by far outweigh any signal from thermal shrinking, over the course of next centuries or even millennia (speculation).

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