  Our motion relative to the cosmic-microwave-background (CMB) rest frame
deflects light rays giving rise to shifts as large as L -> L(1+beta), where
beta=0.00123 is our velocity (in units of the speed of light) on measurements
CMB fluctuations. Here we present a novel harmonic-space approach to this CMB
aberration that improves upon prior work by allowing us to (i) go to higher
orders in beta, thus extending the validity of the analysis to measurements at
L > 1/beta ~ 800; and (ii) treat the effects of window functions and
pixelization in a more accurate and computationally efficient manner. We
calculate precisely the magnitude of the systematic bias in the power spectrum
inferred from the partial sky, and show that aberration shifts the multipole
moment by Delta L/L ~ beta<cos(theta)>, with <cos(theta)> averaged over the
survey footprint. Such a shift, if ignored, would bias the measurement of the
sound-horizon size theta_* at the 0.01%-level, which is comparable to the
measurement uncertainties of Planck. The bias can then propagate into
cosmological parameters such as the angular-diameter distance, Hubble parameter
and dark-energy equation of state. We study the effect of aberration for
current Planck, South Pole Telescope (SPT) and Atacama Cosmology Telescope
(ACT) data and show that the bias cannot be neglected. We suggest that the
small tension between Planck, ACT, and SPT may be due partially to aberration.
An Appendix shows how the near constancy of the full-sky power spectrum under
aberration follows from unitarity of the aberration kernel.
