\documentstyle{article}
\title{Effects of the solid tides on the $P$ and $\dot P$ \\
of pulsars and their applications}
\author{Rong Jiangxiang, Xiao Naiyuan\\
Astronomy Department, Nanjing University, 210093, Nanjing China}
\date{}

\begin{document}
\maketitle

The observational effects due to the Earth's solid tides on the period $P$ and
its derivative $\dot P$ of pulsars are brought to light in this paper.

Let $P_0$ is the period of a pulsar in the rest frane, when it moves with a
radial velocity $V_{rad}$ relative to an observer, its apparent period $P$ is fit
to the expression

\begin{equation}
{P - P_0 \over P} = {V_{rad} \over c} \label{eq1}
\end{equation}

Aftera derivation, it can be approximated by

\begin{equation}
{1\over P}(\dot P - \dot{P_0}) = {1\over c}{dV_{rad}\over dt} \label{eq2}
\end{equation}

In practice, the revolution velocity of the Earth around the Sun and its rotation
velocity about its spin axis and other obvious effects are removed by
eq.(\ref{eq1}).

Because of the Earth's solid tides an observer on the surface of the Earth
oscilates with a nearly semi-diurnal period and gives rise to a velocity $V$
relative to his remote pulsars. The velocity components are (in spherical
coordinates):

\begin{eqnarray}
V_r & = & \sum_{n=2}^{\infty}{h_n\over g}\sum_{m=0}^n (\dot{A_n^m}E_n^m + \dot{A_n^{m*}}E_n^{m*}), \\ 
V_{\Phi} & = & \sum_{n=2}^{\infty}{l_n\over g}\sum_{m=0}^n(\dot{A_n^m}{\partial E_n^m \over \partial \Phi} + \dot{A_n^{m*}}{\partial E_n^{m*}\over \partial \Phi }),  \\
V_{\lambda} & = & \sum_{n=2}^{\infty}{l_n\over g}\sum_{m=0}^n [(-im\dot{A_n^m}E_n^m -\dot{A_n^{m*}}E_n^{m*})] 
\end{eqnarray}

where $A_n^m$ and $E_n^m$ are spherical harmonic functions, the formers vary with
the coordinates of the Sun and The Moon, while the latters depend only on the
geocentric distance $(r)$ and the geographic coordinates $(\lambda, \Phi)$ of the
station where the observer finds himself, and $A_n^{m*}$ and $E_n^{m*}$ are their
conjugate functions, respectively.

It is easy to derive $\dot V_r$, $\dot V_{\Phi}$, $\dot V_{lambda}$ from eq.(3).
The order of magnitude of $|V|$ is generally equal to $1.10^{-5} m/s$ and so

$$ {V_{rad}\over c} \approx 10^{-14} \sim 10^{-13}, {l/c}{dV_{rad}\over dt}
\approx 10^{-18} \sim 10^{-17} $$

and they are in some case within the precision of $P$ and $\dot P$, respectively.

It is proceeded to propose their application in two aspects: (1) Corrections to
observational data of pulsar in order to determine their $P$ and $\dot P$ more
precisely. (2) Analysis of $P$ and $\dot P$ of pulsars to examine the Eart-tide
models and to determine their parameters.








\end{document}
