For a small separation from a circular reference orbit (mean motion n = √(μ/a³)), the relative position in the rotating frame (x radial outward, y along-track) obeys the Clohessy-Wiltshire equations: x¨ = 3n²x + 2n y˙, y¨ = −2n x˙. For a fragment released at the origin with speeds (x˙0, y˙0), the closed form is x = (x˙0/n) sin nt + (2y˙0/n)(1 − cos nt), y = (2x˙0/n)(cos nt − 1) + (y˙0/n)(4 sin nt − 3nt).

The −3 y˙0 t term is secular: a fragment pushed forward gains energy, moves to a larger orbit, slows down and drifts behind the station by 3 y˙0 T per orbit. Only fragments with y˙0 = 0 return to the station each period. The conserved quantity y˙ + 2n x is verified numerically.

Simplifications: the linear equations hold for separations much smaller than the orbit radius (tens of km at most), circular orbit, no drag, no J2, in-plane motion only. Educational physics only.