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Unbound in this context means, that the distance from the particle orbiting (e.g. earth) to its focal point (e.g. sun) is not bound and can become infinite.

In a bound orbit, this is not possible. The orbiting particle will always be closer to its focal point than a maximal radius. It can not escape to infinity.

This also works for an infalling particle, where the radius is not bounded from below and can become 0, i.e. it collides with the focus. In this case, there is no minimal radius. (technically, there is one, but it is 0).

To summarise: unbound means, either the orbiting particle escapes to infinity or collides with it's focal point at some time.

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