Derive a formula that gives a correction to the observed radial velocity of a star for the influence of the annual motion of the Earth

Derive a formula that gives a correction to the observed radial velocity of a star for the influence of the annual motion of the Earth for the case when the star is at the pole of the ecliptic.

This correction is always zero, since at any moment the Earth’s orbital velocity is perpendicular to the star’s line-of-sight velocity (to the line of sight connecting the star to the observer).

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