An influence of the rotation and gravity of the Earth on beam dynamics and
spin motion is not negligible and it should be taken into account in
spin physics experiments. The Earth attraction manifests in
additional forces acting on particles/nuclei and in additional torques
acting on the spin. The additional forces are the Newton force and the
reaction force provided by a focusing system. The additional torques are
caused by the corresponding focusing field and by the geodetic effect. In
storage ring EDM experiments, this effect leads to the spin rotation about
the radial axis with the angular velocity [1]
$$
{\rm {\bf \Omega }}_g =\frac{2\gamma +1}{\gamma +1}\cdot \frac{{{\boldmath
\beta }}\times {\rm {\bf g}}}{c},
$$
where ${\rm {\bf g}}$ is the gravitational acceleration. The Earth rotation
manifests in the additional rotation of the spin with the angular velocity
$-{\boldmath \omega }~(\omega =7.27\times
 10^{-5}$ rad/s is the angular velocity of the
Earth rotation) and in a change of the Maxwell electrodynamics. The Sagnac
effect should also be mentioned. The corresponding change of electrodynamics
due to the Earth gravity is $\omega c/g\approx 2\,200$ times less
and can be neglected.

The electric and magnetic fields acting on the \emph{spin} in the Earth's rotating
frame coincide with the corresponding fields determined in the inertial
frame instantaneously accompanying a lab. In the two frames, torques of
electromagnetic origin which act on the spin also coincide. The effective electric and magnetic fields which governs the beam in the rotating frame are defined by
[2,3]
$$
{\bf B}={\bf B}',~~~{\bf E}={\bf E}'-{\bf B}'\times \left( {\boldmath
\omega }\times {\bf r} \right),
$$
where ${\bf E}'$ and ${\bf B}'$ are the electric and
magnetic fields in the instantaneously accompanying frame. As a rule, the
difference between the conventional and modified Lorentz forces vanishes on
average in accelerators and storage rings due to the beam rotation.

\textbf{References}

\begin{enumerate}
\item A.J. Silenko, O.V. Teryaev, Phys. Rev. D \textbf{76, }061101(R) (2007).
\item A.J. Silenko, O.V. Teryaev, PoS (Baldin ISHEPP XXII), 105 (2015).
\item Y.N. Obukhov, A.J. Silenko, O.V. Teryaev, to be published.