Photon-weighted barycentric correction and its importance for precise radial velocities

Understand

When applying the barycentric correction to a precise radial velocity measurement, it is common practice to calculate its value only at the photon-weighted midpoint time of the observation instead of integrating over the entire exposure.

• However, since the barycentric correction does not change linearly with time, this leads to systematic errors in the derived radial velocities.
• The typical magnitude of this second-order effect is of order 10 cm s$^{-1}$, but it depends on several parameters, e.g.
• the latitude of the observatory, the position of the target on the sky, and the exposure time.