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I have heard sometimes that "X is too small to have an atmosphere/geologic activity" so that got me wondering: Is there a minimum mass or volume needed for an (old) object to have geologic activity? What would it be?

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  • $\begingroup$ This is actually an interesting question! Even small bodies will be active if they are young enough - a 10 km fragment from a planetary collision will be very active for a short time at least. So implicit in the quote is a presumption of "oldness" somehow. $\endgroup$
    – uhoh
    Dec 20, 2023 at 23:52

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It may sound like an easy question, but it is not. The first thing one needs to agree on is what constitutes "geological activity". Having an atmosphere might not be a precondition for that.

In the case of Moon-quakes they are mostly attributed to thermal expansion and shrinking or tidal activity, and the regolith cracking due to these processes. These can reach up to magnitude 5 - something quite noticable, and definitely a geological process. However speaking of an atmosphere in the sense normally understood is difficult in the case of our Moon. Similar types of geological activity is observed, judging by surface features, (including the age of their surfaces based on crater density measurements) on the icy moons of Jupiter and Saturn, e.g. Io, Europa and Enceladus.

Even when Rosetta visited comet 67/P Churyumov-Gerasimenko, a body of just a few kilometres diameter, surface changes were observed, including cliff collapses. Sure enough, here the causes behind these processes were mostly the erosion of the surface due to the insolation. Yet these processes (maybe other than the evaporation itself) are often also considered geological processes.

Now, if your question is about plate tectonics, that's a far tighter constraint. You definitely need a differentiated body, and you might need the presence of water within the rock as well (That however is not a strong constraint). Plate tectonics on Earth are driven by the primordeal heat in the Earth's core and the gradient towards the surface - but how much exactly which of the associated processes contribute (like subduction, plumes, etc.) is still up to debate. Mars on the other hand is similar to Earth in most regards (especially rotation, and somewhat composition) except its size - and does not have plate tectonics anymore. Thus - without much calculation - the boundary in mass for plate tectonics over billions of years seem to be somewhere between these. Venus does not exhibit plate tectonics (probably due to its lack of rotation), but it shows some vulcanism, so the heat transfer favours other processes than here on Earth.

Lastly, if you want aeolian processes altering the surface which require presence of an atmosphere, the limit comes from the mass of the planet itself, and the surface temperature which defines the escape velocity for the gas molecules of the atmosphere, and thus its longevity over astronomical timescales. Here Mars gives one good lower boundary of a planet which still exhibits some atmosphere - and we regularily see planet-wide dust storms and on normal days dust devils, both reshaping and eroding the surface. Another, only slightly smaller example for the lower atmospheric boundary is the saturnian moon Titan. It features an atmosphere made from nitrogen and methane. It can hold an atmosphere denser than Mars, even 50% denser than Earth, despite being the smallest of the three as it is further from the Sun and thus the escape velocity for the atmospheric molecules is much smaller.

To allow assess the mass of the bodies talked about, in order of increasing mass:

  • Churyumov-Gerasimenko: $10^{12}$kg
  • Enceladus: $1\cdot 10^{20}$kg
  • Europa: $4\cdot 10^{22}$kg
  • Moon: $7\cdot 10^{22}$kg
  • Io: $9\cdot 10^{22}$kg
  • Titan: $1\cdot 10^{23}$kg
  • Mars: $6\cdot 10^{23}$kg
  • Earth: $6\cdot 10^{24}$kg

In summary: there are geological processes on all kind of bodies, from small comets up to the largest (terrestrial) planets - their relative importance differs, depending on size, solar distance and exposure to tidal forces.

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