Relativity Gyroscope Experiment at Arbitrary Orbit Inclinations

We carry out a calculation of the "indirect" quadrupole moment effect (given by "averaging" the de Sitter term, ${\overrightarrow{\mathrm{\Omega }}}_{\mathrm{DS}}$, over a period of the motion) for "distorted" elliptical orbits of small eccentricity at arbitrary inclination to the earth's equator. Combining this with other effects enables us to calculate the total gyro precession. We then discuss the question of what is the optimum orbit for the relativity gyroscope experiment.