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Physics

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  • $\begingroup$ I have no idea what you mean by the statements "The total "available energy" that the gravitational attraction has is theoretically infinite!" and "Two material points with positive mass are basically an infinite source of energy". You can store arbitrability large quantities of potential energy in arbitrarily large and distant masses, but there is no sense in which gravity provides an inexhaustible, "infinite" source of energy. Even when falling toward each other from a theoretically infinite distance, objects collide with a finite velocity - the escape velocity. $\endgroup$
    – Nuclear Hoagie
    Commented Sep 28, 2023 at 19:21
  • $\begingroup$ Sure, but the escape velocity depends on the radius of the planet ;) What happens if the planet has no radius and is just a point particle…? If you plug zero radius in the formula for the escape velocity, you see that the escape velocity becomes an interesting number $\endgroup$
    – Lorenzo Pompili
    Commented Sep 28, 2023 at 19:45
  • $\begingroup$ I agree that the escape velocity provides an upper bound to the available energy when the radius of the planet is non zero, this is similar to what I wrote in the parentheses and in the final remark at the end. $\endgroup$
    – Lorenzo Pompili
    Commented Sep 28, 2023 at 19:50
  • $\begingroup$ With zero radius, we find that the escape velocity exceeds $c$ - that alone should tell you this is no longer an application for classical physics. Objects do not accelerate to infinite velocity or obtain infinite kinetic energy when they fall into black hole singularities of zero size. $\endgroup$
    – Nuclear Hoagie
    Commented Sep 28, 2023 at 19:57
  • $\begingroup$ @NuclearHoagie the OP explicitly asked to ignore relativistic effects, the expansion of the universe, etc. Also, mathematically, the energy a particle can get when colliding with a gravitational singularity can approach infinity in classical mechanics, and I am reasonably sure this is the case also in general relativity even though the velocity is bounded by $c$ (objects with positive mass still need infinite energy to accelerate to speed $c$), although I could be wrong. $\endgroup$
    – Lorenzo Pompili
    Commented Sep 28, 2023 at 20:13