In their 1966 book, Intelligent Life in the Universe, Carl Sagan and Iosif Shklovsky state that "a natural satellite cannot be a hollow object." How do we know this is absolutely true?

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    $\begingroup$ How could such a hollow satellite form? Even if some process caused the core to shrink, the outer part would collapse under its own gravity. $\endgroup$ – BillDOe Nov 29 '16 at 0:57
  • $\begingroup$ Not sure, but presumably, yes - that's what I'd conclude, as well. However, the full Sagan quote is puzzling. Located on page 373, it reads, "Thus, only one possibility remains. Could Phobos be indeed rigid, on the outside - but hollow on the inside? A natural satellite cannot be a hollow object. Therefore we are led to the possibility that Phobos - and possibly Deimos as well - may be artificial satellites of Mars." $\endgroup$ – CBobRobison Nov 29 '16 at 3:32

I'd caution that absolute statements are not good things in science. When Sagan says a natural satellite cannot be hallow, it is an absolute statement, but there's no way to 100% prove it true.

That being said, everything we know about planet/satellite formation tells us that the chances of a satellite forming as a hollow structure (or becoming hollow afterwards) is pretty much nil.

There is still much debate on the specifics of planetary formation, but the general process seems to be that small rocks and particles start to form, then they coalesce into bigger chunks and slowly that planetesimal grows in size. This type of formation process does not allow for the center to be hollow since it is the center which forms first! You cannot form the "edges" of your hollow planet and have those edges come together.

Moons and satellites can potentially have a different formation path. Look at our own moon for example. It is hypothesized that a Mars-sized proto-planet crashed into the Earth, flinging out a large amount of material. Much of this material then coalesced into our current Moon. Again, this process doesn't really allow for making something which is hollow.

Aside from the difficulty in forming a hollow satellite, you also have the challenge of maintaining the structure. Gravity constantly pulls everything to the center of the body. If there's nothing at the center, there's nothing preventing the outer shell from collapsing. It is technically possible that the satellite could not collapse, but that would require it to be fairly small and be perfectly structured such that the structural integrity of the rock forming the shell could withstand the crushing gravitational forces. Really though, such an object would have to be intelligently designed as the chances of it forming perfectly like that are non-existent. There's no possible way an object like Phobos could maintain itself without collapsing if it were hollow.

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