  Distances in cosmology are usually inferred from observed redshifts - an
estimate that is dependent on the local peculiar motion - giving a distorted
view of the three dimensional structure and affecting basic observables such as
the correlation function and power spectrum. We calculate the full non-linear
redshift-space power spectrum for Gaussian fields, giving results for both the
standard flat sky approximation and the directly-observable angular correlation
function and angular power spectrum. Coupling between large and small scale
modes boosts the power on small scales when the perturbations are small. On
larger scales power is slightly suppressed by the velocities perturbations on
smaller scales. The analysis is general, but we comment specifically on the
implications for future high-redshift observations, and show that the
non-linear spectrum has significantly more complicated angular structure than
in linear theory. We comment on the implications for using the angular
structure to separate cosmological and astrophysical components of 21 cm
observations.
