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Recent discovery of a satellite orbiting Dinkinesh made me wonder how fragile that system must be. Based on the numbers and photos given by NASA, I estimate that binding energy of the two bodies is of order of 100 GJ, which seems like almost nothing.

Do we know even smaller, gravitationally bound systems? For how long can they last, especially in the dense asteroid belt?

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  • $\begingroup$ A grain of dust orbiting the earth has a pretty small binding energy. Do you want to add conditions on the size of the bigger object? $\endgroup$
    – mmesser314
    Commented Nov 6, 2023 at 1:20
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    $\begingroup$ @mmesser314 good point, I think by smallest I mean the smallest total mass of the two bodies. $\endgroup$
    – user1079505
    Commented Nov 6, 2023 at 2:02
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    $\begingroup$ @mmesser314 A dust particle orbiting the Earth has small energy, but to perturb its trajectory gravitationally you would still need another large body, to compete with Earth's gravitational field. Having two small bodies orbiting around each other seems more difficult, and thus interesting. $\endgroup$
    – user1079505
    Commented Nov 6, 2023 at 2:09
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    $\begingroup$ Actually, your question gave me an idea how to search, yielding this link: ssd.jpl.nasa.gov/sb/sats.html But I don't know how to go through this long list yet! $\endgroup$
    – user1079505
    Commented Nov 6, 2023 at 2:16

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Some asteroids or comets are not solid bodies. Instead they are collections of rubble, weakly held together by gravity. The smallest such body is probably the system you are thinking of.

JPL's Small-Body Satellites page you linked is a good place to look. Follow the links to Small Bodies > Database query.

Create a query with a constraint GM < 1. This restricts it to the smallest masses. Make the output be GM and name. When the output appears, click on the GM column to sort by mass. Investigate which of those are rubble piles. Note that most bodies in the database are binaries.

It isn't what you asked, but you might find this interesting. Using sensitive torsion balances, it is possible to directly measure the gravitational attraction of kilogram masses. If you want to do this yourself, you can buy a Cavendish balance.

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    $\begingroup$ Selecting GM < 1 and #sats > 0, the smallest object I get is 185851 (2000 DP107) ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?des=185851&view= It is slightly bigger than Dinkinesh, but also lighter (assuming Dinkinesh being S-class with density of ~2.7 g/cm²). Thank you! $\endgroup$
    – user1079505
    Commented Nov 6, 2023 at 4:06
  • $\begingroup$ @user1079505 I just did a SBDB query for bodies with satellites, with defined GM. It only returned 4 results. BTW, there's also an API, listed on ssd.jpl.nasa.gov/api.html $\endgroup$
    – PM 2Ring
    Commented Nov 6, 2023 at 5:16
  • $\begingroup$ Oh, wow! I heard the term "rubble piles" many times in this context, but it never occurred to me that it's a collection of physically separate smaller objects held together by nothing but gravity! I always imagined it referred to something like a collection of tougher rocks loosely held together by this frail matrix of finer-grained material. $\endgroup$
    – Filip Milovanović
    Commented Nov 6, 2023 at 16:57
  • $\begingroup$ Wait, judging by this Wikipedia article and taking into consideration what you've written here, it looks like "rubble pile" can refer to both cases, and everything in between as well? $\endgroup$
    – Filip Milovanović
    Commented Nov 6, 2023 at 17:02
  • $\begingroup$ "Some asteroids or comets are not solid bodies." I cannot understand this statement. The asteroid however small it is, are solid matter, hence they are solid bodies. My thinking is that if we say the entity is not solid body, then it doesn't have any solid matter e.g. the sun. Maybe I am wrong in my thinking, so please correct me. $\endgroup$
    – Nilay Ghosh
    Commented Nov 11, 2023 at 7:14

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