  Gravitational-wave astronomy allows us to study objects and events invisible
to electromagnetic waves. So far, only signals triggered by coalescing binaries
have been detected. However, as the interferometers' sensitivities improve over
time, we expect to observe weaker signals in the future, e.g. emission of
continuous gravitational waves from spinning, isolated neutron stars. Parallax
is a well-known method, widely used in electromagnetic astronomical
observations, to estimate the distance to a source. In this work, we consider
the application of the parallax method to gravitational-wave searches and
explore possible distance estimation errors. We show that detection of parallax
in the signal from a spinning down source can constrain the neutron star moment
of inertia. For instance, we found that the relative error of the moment of
inertia estimation is smaller than $10\%$ for all sources closer than 300 pc,
for the assumed birth frequency of 700 Hz, ellipticity $\geq 10^{-7}$ and for
two years of observations by the Einstein Telescope, assuming spin down due
purely to quadrupolar gravitational radiation.
