Effect of the gyro's quadrupole moment on the relativity gyroscope experiment

We show that the quadrupole moment of the gyro affects the drift rate of the presently planned Stanford gyroscope experiment by $\left(\frac{{0.0254}^{\prime \prime }}{\mathrm{yr}}\right)sin2\alpha$, where $\alpha$ is the angle between the gyro's spin axis and the orbit plane. Thus, if the gyro's spin axis is off by more than one degree from being either in the orbit plane or perpendicular to the orbit plane the drift rate will exceed 0.001″/yr, which is the expected accuracy of the experiment, and, hence, this predictable drift rate will have to be taken into account to preserve the expected accuracy of the experiment. We also calculate the precession of the orbit of the gyro due to the gyro's quadrupole moment and find it two orders of magnitude smaller than the precession of the orbit due to the gyro's spin.