ball bounces along a flat surface, uniform gravity, perfectly elastic collisions with the floor. trajectory is sequence of congruent parabolas truncated by the floor.
add a ceiling (cap, lid, cover, roof) also with elastic collisions. assume velocity high enough to hit the ceiling. trajectory remains truncated parabolas but more complicated.
add inverse square gravity, traveling around a (great) circle, without a ceiling. assuming less than escape velocity, trajectory is a necklace of congruent truncated ellipses.
add a circular (spherical) ceiling.
how much time does the ball spend at each altitude? (derivative with respect to height of how much time below an altitude.) this models a gas so diffuse that no gas particles collide.
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