Does this even make sense? Just how immense would that be?
What do you mean by "gravitational binding energy"?
That concept doesn't make sense in the case of a galaxy? It's the amount of energy needed to liberate all the particles of a body beyond the ability of gravity to pull them back together.
Basically, how much energy would it take to "blow it up" or pick it apart piece by piece.
Gravitational binding energy of a galaxy is simply the energy needed to move each particle (star) in it to infinity - is equivalent of escape velocity.
For each small element of radius simply find the mass inside that radius, then the gravitional potential energy of a star at that radius is just = G m_star m_galaxy /R
You have to then recalculate the remaining mass of the galaxy at each step
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