The analysis of the dynamics of a ring system around earth

Abstract

This is an exercise which involves the assumption of a hypothetical ring system around Earth (at which point in its evolution is irrelevant); formulation of the initial conditions; determination of the internal and external forces that contribute, to its stability, or instability; analysis and estimation of the limits of its stability, and finally, approximation of the ring's survival time.
The strongest determinant of the survival time of a planetary ring system is the number of shepherd moons in external resonance with it. Since Earth is unable to provide the strong confining mechanism, the ring system suffers a brief lifespan (10⁵ years).