Nice question. The velocity, i.e. speed and direction, of our earth can be determined by observing a small anisotropy in the cosmic background radiation. This anisotropy is attributed to a Doppler shift due to the motion of Earth-MilkyWay system moving with respect to "the rest of the universe".
See for an explanation and a nice picture.
LeeH
(published on 07/03/2013)
