Circular, Elliptical and Parabolic Properties in Missile Shutting

Abstract

By analyzing the parabolic trajectories that follows the missiles shuttled with different angles but same velocity, we find there are three groups of conical sections that bellows to a pair of circular properties, one elliptic with two physical meaning, and other parabolic. We obtain each one from the conical sections, discussing his physical meaning and universal properties. Using one of such properties we show a method to obtain the safety parabola and the ellipse that joint the maximum height positions.