Galilean cannon

At first sight, the behavior seems highly counter-intuitive, but in fact is precisely what conservation of momentum predicts.

The principal difficulty is in keeping the configuration of the balls stable during the initial drop.

Early descriptions involve some sort of glue/tape,[2] tube, or net[3] to align the balls.

[4][5] In this device, a heavy wire is threaded through all of the balls to keep them accurately aligned - but the principle is the same.

[6] Assuming elastic collisions, uniform gravity, no air resistance and the sizes of the balls being negligible compared to the heights from which they are dropped, formulas for conservation of momentum and kinetic energy can be used to calculate the speed and heights of rebound of the small ball: Solving the simultaneous equations above for v2′, Taking velocities upwards as positive, as the balls fall from the same height and the large ball rebounds off the floor with the same speed, v1 = −v2 (the negative sign denoting the direction reversed).

A Galilean cannon with proportions similar to the Astro Blaster
A Galilean cannon made from a basketball and a handball
Plot of maximum ideal rebound height ratio ( r h ) vs mass ratio ( r m ) for a two-ball Galilean cannon