Ehrenfest (1917/1920) studied the hydrogen in n dimensions and concluded for n> 3 that neither classical atoms nor planetary orbits can be stable, because the inverse square law of electrostatic and gravity becomes an inverse cube law. When n > 3 there are no stable orbits to the two body problem: an incoming light body attracted by a heavy one would either escape to infinity or get sucked into collision.
For n = 3 we get stable elliptic orbits or non-bound parabolic and hyperbolic orbits.
Collision only occurs when the lighter body heads directly towards the heavy body within 2R (R being the heavier body's radius), ie. the impact parameter is zero [2]
[1] https://doi.org/10.1002/andp.19203660503
[2] https://en.wikipedia.org/wiki/Impact_parameter
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