The law of conservation of momentum says that the momentum sum of a
closed system before an interaction of its objects remains the same
after an interaction of its objects.
Not quite correct. A closed system, at least in thermodynamics, is one that cannot exchange mass with its surroundings. That doesn't preclude the possibility of external forces acting on the system changing its momentum.
If an astronaut in space pushes another astronaut I would expect the
momentum of the two together to remain the same after the push
(because they're applying force to one another).
Yes, as long as the astronaut is far enough away from any gravitational forces. Then the momentum of the center of mass of the two astronauts will be unchanged, even if the momentum of each astronaut changes.
It is said that when a resting bomb sets off, the momentum sum of the
dispersing shrapnel should add up to 0 (the same prior to the
That is correct, provided the bomb is set off where there are no external forces in play, e.g, if the bomb is set off in outer space far from the effects of gravity.you ignore the external force of gravity.
However, when a resting bomb sets off and shrapnel disperses to
different directions, it's not these pieces of shrapnel that applied
the necessary force to one another to allow them to disperse, it's the
Yes, it is the conversion of the chemical potential energy of the bomb to the kinetic energy of the pieces (along with other forms of energy like heat and sound) that causes the pieces to disperse.
So why would I expect the momentum sum of the shrapnel to add up to 0?
It should rather be the momentum of the shrapnel AND the momentum of
the gas particles, because after all they are the ones who passed
their momentum unto the shrapnel.
It is the momentum of the shrapnel and the gas, as both have mass, that sums to zero. Insofar as conservation of energy is concerned, the only missing part is the increase in temperature of the shrapnel parts and gas which, together with the kinetic energy of the shrapnel and gas, equals the chemical potential energy of the bomb before the explosion.
Hope this helps.