[gzefwefw] colliding spheres amidst gravity

model a collection of spheres bouncing inside a container in a uniform gravitational field.  the spheres do not affect each other gravitationally.  the spheres collide elastically with each other, the floor, and sides of container.  there does not need to be a ceiling: in a uniform gravitational field, gravity does not get weaker with height, so there is no escape velocity.  what goes up must come down.

when do parabolic trajectories pass close enough for there to be a collision between spheres?  this seems annoying to calculate but doable.

one can measure density, temperature, pressure.  individual spheres can have different sizes, densities, and masses.

perhaps toroidal universe in the horizontal directions to avoid the need for sides.  or, universe of a spherical shell, still with a uniform gravitational field (future post kmhdhghk) directed toward the center of the shell.

next, consider spheres bouncing on the surface of a spherical planet in a spherically symmetric inverse-square gravitational field.  as before,the little spheres do not affect each other gravitationally but do elastically collide with each other.  finding when spheres collide seems even more annoying but still doable because all trajectories are conic sections.  probably need to solve Kepler Equation.  it may be many orbits before a collision.  add an elastic ceiling, a spherical dome enclosing the planet, to prevent spheres from escaping.  measure the pressure the spheres exert against the ceiling.

add a moon orbiting the planet and try to model tides.  unfortunately this becomes the 3-body problem, more difficult to calculate trajectories.