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- Thread starter L0r3n20
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- #2

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The quantities you quoted are directly relatable to the energy and angular momentum, so yes.

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The module of the angular momentum can be expressed as L = m v b (being b the impact parameter) but what about the energy? I mean if the projectile is at an infinite distance it has only kinetic (therefore positive) energy, so I cannot find any bounded state. What am I missing?The quantities you quoted are directly relatable to the energy and angular momentum, so yes.

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If the particle can reach infinity, it obviously is not in a bound state by definition.

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But what if it starts from infinity moving towards the Sun?If the particle can reach infinity, it obviously is not in a bound state by definition.

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If it is at infinity it is not in a bound orbit, precisely because of what you mentioned.

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Ok, i get it but I was wondering if a particle coming from infinite be captured by an attractive potential and bound into a closed orbit.

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Of course it can be captured if it interacts with another body and transfers enough energy to it (part of my research deals with the possible capture of dark matter particles by the Sun.), but this requires additional interactions beyond the motion in the central potential.

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Thanks, I really understood! :)

Of course it can be captured if it interacts with another body and transfers enough energy to it (part of my research deals with the possible capture of dark matter particles by the Sun.), but this requires additional interactions beyond the motion in the central potential.

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