  We study the effect of tidal interaction between two compact bodies in an
eccentric orbit. We assume the tidal fields to be static. Therefore, we ignore
the dynamic tides and resonant excitations. Using the results, we find the
analytical expression for the phase shift of the emitted gravitational wave. In
the process, we find that in the leading order, the initial eccentricity $e_0$
and the dimensionless tidal deformability $\Lambda$ couple as $\sim
e_0^n\Lambda$, where $n$ is a positive number. We only focus on the dominant
contribution, i.e., $e_0^2\Lambda$. We also compute the accumulated dephasing
for binary neutron star systems. We find that for optimistic values of
eccentricities $e_0 \sim .05$ and $\Lambda \sim 600$, the accumulated dephasing
is $\mathcal{O}(10^{-4})$ radian, requiring a signal-to-noise ratio $\sim 7000$
to be observable. Therefore, these effects can be measured in binary neutron
star systems with large eccentricities if the signal-to-noise ratios of the
systems are also very large. Hence, in third-generation detectors, it may have
an observable impact if the systems have large eccentricities. We also explore
the impact of this effect on extreme mass-ratio inspirals (EMRIs). We find that
even for supermassive bodies with small values of $\Lambda \sim 10^{-3}$, this
effect has large dephasing in EMRIs $\sim \mathcal{O}(10)$ radian. Therefore,
this effect will help in probing the nature of the supermassive bodies in an
EMRI.
