  The Earth's velocity relative to the Sun in galactic coordinates is required
in the rate calculation for direct detection experiments. We provide a rigorous
derivation of this quantity to first order in the eccentricity of the Earth's
orbit. We also discuss the effect of the precession of the equinoxes, which has
hitherto received little explicit discussion. Comparing with other expressions
in the literature, we confirm that the expression of Lee, Lisanti and Safdi is
correct, while the expression of Lewin and Smith, the de facto standard
expression, contains an error. For calculations of the absolute event rate, the
leading order expression is sufficient while for modulation searches, an
expression with the eccentricity is required for accurate predictions of the
modulation phase.
