Application of Gauss averaging method to the analysis of the possibility of a celestial body deviation using a microthrust

Abstract

A method of a correction of a celestial body (asteroid) trajectory is considered: maintenance of a small acceleration using a microthrust. Euler equations of osculating elements variations are written in a moving frame of references in which x-axis is directed along the velocity vector of the asteroid, and z-axis is directed along the angular momentum vector. Applying Gauss averaging method under the condition that components of disturbing acceleration are constant we construct a system of 5 differential equations for slow variables, and after solving them the fast variable (e.g. mean anomaly) can be found by a simple quadrature. Equations for semi-major axis, eccentricity, and mean anomaly are integrable in quadratures. The complete system of averaged equations is integrable in quadratures if the disturbing acceleration lies in the orbital plane. As an example we consider an asteroid 50 m large having the density 1 g/cm³. A 1 newton thrust during 8 months is sufficient to assure its deviation at a safe distance.