Motion of massive particles and geodetic precession in the spacetime of a Galilean rotating observer in the Schwarzschild background

We investigate the motion of a particle in a Galilean rotating frame in Schwarzschild background. We obtain the related geodesic equation, constants of motion, centripetal and Coriolis forces, effective potential and geodesic precession in this frame. We compare the results with the corresponding results in the rotating observer spacetime in the Minkowski background. By considering the Schwarzschild background instead of the Minkowski background for the Earth-rotating observer, corrections of order 10-9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10<^>{-9}$$\end{document} appear in some cases.