zonde said:
Say binding energy of H-molecule.
Ok. Then the answer is that, since the binding energy contributes to the externally measured mass of the H molecule (the "contribution" is actually negative), it will affect the H molecule's behavior as a source of gravity. In practical terms this won't be observable for a single H molecule, but if you imagine, say, a large planet whose atmosphere is made up largely of hydrogen, like Jupiter, if you try to estimate its mass by adding up the masses of all of the H molecules, you will need to take into account the electromagnetic binding energy of each H molecule (i.e., the fact that its mass is slightly less than the sum of the masses, considered in isolation, of the protons and electrons making it up).
However, considering a case like the planet Jupiter also brings up another point. Jupiter's externally measured mass also has an
additional "binding energy" contribution (which is negative) because it is a gravitationally bound system. In other words, suppose we have, say, ##10^{60}## or so isolated hydrogen molecules and we want to make a planet out of them. The mass of those molecules when we start out, since they are all isolated and their mutual gravity is negligible, will be ##10^{60}## times the mass of an individual hydrogen molecule--which is less than the mass of the same number of isolated protons and electrons, because of the binding energy we talked about above. But if we now take those molecules and form them into a planet, the final mass of the planet will be smaller--we will have to extract energy from the system in the process, and this extracted energy is the gravitational binding energy of the planet. So gravitational binding energy for a large, gravitationally bound system is not quite the same as the binding energy of individual molecules.
zonde said:
Let's say that binding energy of H-atom is radiated away while the atom remains as a part of larger body.
Binding energy is negative, so it won't be radiated away. You would have to
add energy to an H atom to separate its proton and electron (the amount of energy required, in the case of an H atom in its ground state, is 13.6 electron volts).
If we suppose that the H atom in question is somewhere in the atmosphere of Jupiter, say, and we add energy to it to ionize it (separate the proton and electron), we now have a system consisting of a free proton and a free electron, whose mass is larger (by the aforementioned 13.6 electron volts) than the mass of the H atom was. But the system as a whole is still bound gravitationally to Jupiter and contributes to Jupiter's externally measured mass. The question is, where did the 13.6 electron volts come from that were used to ionize the atom? If it came from some source internal to Jupiter, then this whole process would have no effect on Jupiter's externally measured mass. But if it came from somewhere outside Jupiter, then the whole process, seen from the outside, amounts to adding 13.6 electron volts to Jupiter's externally measured mass.
