Motion in rotating Earth: exact solutions and second-order effects of noninertial forces

Abstract

The motion of a particle evaluated from the noninertial frame of the rotating Earth with constant angular velocity ω is solved analytically without carrying out a priori approximations, that is, considering both the Coriolis and the centrifugal terms. Position vector solutions written in terms of generic initial conditions were obtained from a decoupled sixth-order equation of motion, obtained using a fully vectorial approach, without specifically resorting to coordinates. By comparing the exact solutions for the complete and approximate (ignoring the centrifugal term from the beginning) problems, great differences can be seen in the order of the decoupled differential equation as well as in the temporal dependencies of the noninertial terms of the solutions. Noninertial effects for the solution were classified according to the order of magnitude in ω, where first-order effects are oriented east-west and the second-order ones are oriented north-south.