FYKOS Year 34 Series 3 Problem 3 — kaboom, kaboom · FYKOS 34 #34.3.3

Physics · mechanics

Problem

Imagine placing a large number of satellites on the geosynchronous orbit. Coincidentally, a runaway series of collisions occurs and forms a thin spherical layer homogenously scattered with ten million shards with an average size of

x = 10\,\mathrm{cm}

. Assume that the velocity directions of the individual shards are oriented randomly in the plane tangent to the sphere. On average, how much time passes between two collisions?

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