# How large could Hyperion be and stay porous?

Hyperion is porous, with a density of 0.55 g/cc; a little more than half that of water.

A body with Earth's gravity and the density of Hyperion would be huge. But the question for this stack: in celestial bodies, does porosity scale up? Is there a limit to how large a porous celestial body can be before the pores crunch down? Are there enough celestial bodies that are porous to even deduce a rule?

• There is one close vote, but questions about the structure of solar-system bodies are not off-topic here. However, this one is also on-topic on the Astronomy stackexchange site as well. If you don't get an answer here, you might consider asking for it to be migrated there. Actually, if you are interested in the physics of it, you might even ask on the physics SE site, but there you might be asked to provide some information about the strength of the material.
– uhoh
Nov 6 '17 at 14:36
• That's a pretty crazy looking object for sure, I had no idea such a thing existed. +1 for asking such an interesting question!
– uhoh
Nov 6 '17 at 14:37
• The very definition of a planet is that its own gravity makes it round - which means its gravity must be strong enough to make it crumble. Thus, a porous planet is somewhat contradictory. Yes, there is a limit to the size a porous body can be. Those pores have a certain structural integrity, and once gravity is stronger, they start collapsing (the inner most ones first). Not sure how to determine their stbility, though, otherwise calculating how big such a body could be is easy. Nov 6 '17 at 15:03
• We see pores at the surface, but nobody knows how deep they go. The Earth is porous too for groundwater. We are lucky that the pores did not crunch down.
– Uwe
Nov 6 '17 at 16:17
• The pores seem to consist of water ice. On such a small body, the water ice will sublimate. But on a large body with an atmosphere, water ice will behave different.
– Uwe
Nov 6 '17 at 17:49

tl;dr- Apparently rocky planets can have porous crusts down to some significant depth, beneath which porosity ends due to lithostatic overburden pressure, while smaller objects like Phobos may have significant internal voids.

Apparently Saturn's moon, Hyperion, has a porosity $>40\%$:

Hyperion is Saturn’s largest known irregularly shaped satellite and the only moon observed to undergo chaotic rotation. Previous work has identified Hyperion’s surface as distinct from other small icy objects but left the causes unsettled. Here we report high-resolution images that reveal a unique sponge-like appearance at scales of a few kilometres. Mapping shows a high surface density of relatively well-preserved craters two to ten kilometres across. We have also determined Hyperion’s size and mass, and calculated the mean density as 544 ± 50 kg m-3, which indicates a porosity of >40 per cent. The high porosity may enhance preservation of craters by minimizing the amount of ejecta produced or retained, and accordingly may be the crucial factor in crafting this unusual surface.

"Hyperion's sponge-like appearance" (2007-07-05) [references omitted]

A moon of Mars, Phobos, was once thought hollow, though now its porosity estimated at $30\% \pm5\% ,$ which apparently suggested large internal voids:

[1] We report independent results from two subgroups of the Mars Express Radio Science (MaRS) team who independently analyzed Mars Express (MEX) radio tracking data for the purpose of determining consistently the gravitational attraction of the moon Phobos on the MEX spacecraft, and hence the mass of Phobos. New values for the gravitational parameter (GM = 0.7127 ± 0.0021 × 10−3 km3/s2) and density of Phobos (1876 ± 20 kg/m3) provide meaningful new constraints on the corresponding range of the body's porosity (30% ± 5%), provide a basis for improved interpretation of the internal structure. We conclude that the interior of Phobos likely contains large voids. When applied to various hypotheses bearing on the origin of Phobos, these results are inconsistent with the proposition that Phobos is a captured asteroid.

Apparently Earth's moon's crust has an estimated porosity varying from $10\%$ to $20\%$, though it drops off around $10\, \mathrm{km}$ to $20\, \mathrm{km}$ down due to "lithostatic overburden pressure":

The Gravity Recovery and Interior Laboratory (GRAIL) mission is providing unprecedentedly high-resolution gravity data. The gravity signal in relation to topography decreases from 100 km to 30 km wavelength, equivalent to a uniform crustal density of 2450 kg/m3 that is 100 kg/m3 smaller than the density required at 100 km. To explain such frequency-dependent behavior, we introduce rock compaction models under lithostatic pressure that yield radially stratified porosity (and thus density) and examine the depth extent of porosity. Our modeling and analysis support the assertion that the crustal density must vary from surface to deep crust by up to 500 kg/m3 . We found that the surface density of megaregolith is around 2400 kg/m3 with an initial porosity of 10–20%, and this porosity is eliminated at 10–20 km depth due to lithostatic overburden pressure. Our stratified density models provide improved fits to both GRAIL primary and extended mission data.

And relatively recent (2017) research suggests that Mars's crust might be similar to Earth's moon's in terms of density/porosity:

NASA scientists have found evidence that Mars’ crust is not as dense as previously thought, a clue that could help researchers better understand the Red Planet’s interior structure and evolution.

A lower density likely means that at least part of Mars’ crust is relatively porous. At this point, however, the team cannot rule out the possibility of a different mineral composition or perhaps a thinner crust.

“The crust is the end-result of everything that happened during a planet’s history, so a lower density could have important implications about Mars’ formation and evolution,” said Sander Goossens of NASA’s Goddard Space Flight Center in Greenbelt, Maryland. Goossens is the lead author of a Geophysical Research Letters paper describing the work.

The researchers mapped the density of the Martian crust, estimating the average density is 2,582 kilograms per meter cubed (about 161 pounds per cubic foot). That’s comparable to the average density of the lunar crust. Typically, Mars’ crust has been considered at least as dense as Earth’s oceanic crust, which is about 2,900 kilograms per meter cubed (about 181 pounds per cubic foot).

"New Gravity Map Suggests Mars Has a Porous Crust" (2017-09-13)

Then as for Earth, here's a density plot:
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showing that the sudden jump in density beneath the crust at the Moho discontinuity. Presumably any significant porosity tends to end at that boundary.

"Planetary Satellite Physical Parameters" lists the densities of many smaller solar system bodies from which porosity ranges might be inferred for smaller bodies, though it doesn't directly list porosities.