A Quantitative Approach of the Orbital Uncertainty Propagation through Close Encounters

Abstract

The greatest impediment against collisional predictions of Near-Earth Asteroids with the Earth is their orbital uncertainty and its divergence in time. Repeated close encounters with terrestrial planets generate chaotic motions which make unpredictable the future orbits of these objects. This paper deals with a quantitative analysis of the orbital uncertainty propagation through close encounters. We approach this problem analytically (using the Opik’s formalism of close encounters) and numerically (through Monte Carlo simulations). We emphasize the progressive degradation of the orbital uncertainty from one encounter to another, identifying the way in which such an encounter acts to increase this uncertainty. Also, an oscillatory behaviour of the uncertainty is discovered and explained.