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A nucleus $A$ can be split into two smaller nuclei $B$ and $C$. It is well known that the sum of the masses of $B$ and $C$ will not equal the mass of $A$ due to the nuclear binding energy and the relativistic mass-energy equivalence.

My question: In theory will object feel the same gravitational attraction towards $A$ and they will towards the constituent nuclei $B$ and $C$? My guess is the answer is yes.

My follow up question: Has this effect been directly observed experimentally? My guess is that the claim that the masses differ is often supported by mass spectroscopy experiments, but in these cases the intertial mass of the particles is being measured by looking at the dynamics of the particles in interaction with electromagnetic fields. I'm curious if any experiment or observation has observed the change in gravitational forces of some matter (i.e. the gravitational mass) due to binding energy involved in the configuration of the matter.

I know there are tests of the equivalence principle showing the inertial and gravitational masses are equal, but have such tests been performed while varying the binding energy present (and thus mass missing) in the test particles?

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Precision gravimetry experiments tend to have uncertainties of $10^{-4}$ in the best cases (though a few experiments have done better). A binding energy of a few MeV, compared to a mass of tens of GeV, is not really accessible.

This sounds like the sort of idea that E. Fischbach would have explored during his equivalence principle phase in the late 1980s and early 1990s. Fischbach is brilliant but incautious; read the literature skeptically.

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  • $\begingroup$ Yes, I'm aware of the relatively poor precision of precision gravity experiments, that largely motivated the question. I'll skeptically look into Fishbach's work. $\endgroup$
    – Jagerber48
    Commented Sep 20, 2023 at 1:30
  • $\begingroup$ @Jagerber48 Yes, a large dose of scepticism is required. The Fischbach group have some rather controversial theories, and numerous critics. See physics.stackexchange.com/a/267458/123208 & physics.stackexchange.com/a/75077/123208 $\endgroup$
    – PM 2Ring
    Commented Sep 20, 2023 at 2:48
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    $\begingroup$ @PM2Ring I gained more respect for Fischbach after my graduate research group (but not me) was involved in a null result inspired by the 2008 sun-earth distance thing. I'm thinking specifically of an equivalence principle proposal that gravity might depend on strong isospin. The deep dive into the literature of measurements from drop towers and in evacuated mineshafts and in vertical access tunnels in dams (where the water reservoir acts as a variable semi-infinite mass) was educational; I recommend it. $\endgroup$
    – rob
    Commented Sep 20, 2023 at 4:03
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In addition to the answer from Rob, for your first question: The source of curvature (with curvature creating the effect of gravitational attraction) is the stress-energy tensor. This tensor not only depends on the mass but also on the momentum of the system.

Although at the moment of the splitting of the nucleus $A$, a part of its mass is converted into kinetic energy of $B$ and $C$, the stress-energy tensor still takes into account the contribution from the latter. So, just at the moment of splitting, the gravitational attraction would still be the same (but as the particles fly away, the system's configuration would change drastically, hence changing the overall mass distribution).

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