tokens: error margin at three different observatory sites. When dealing with PRV data that supplies the photon-weighted mid-point time and yet no flux curve, the simplest assumption is that the flux was uniformly distributed in time. 2 This allows us to add a second-order correction to the calculated barycentric correction, v (〈 t 〉). To obtain 〈 v 〉, we can either subtract the result of equation ( 10 ) or get the difference from a simple numerical simulation as in Section 4 . In fact, if we do not apply a second-order correction to v (〈 t 〉), we implicitly assume that all photons arrived in the same instant at the photon-weighted mid-point time. We argue that the assumption of a uniform flux distribution is much more realistic. Fig. 5 shows how the second-order errors of three different flux scenarios are all closer to the uniform scenario than zero. In Fig. 7 , we calculate the second-order error using real exposure meter data from 1315 observations with EXPRES (see Blackman, Ong Fischer 2019 ), combining all colour channels to one. The data was obtained during commissioning between March 2018 and February 2019. No exposures were longer than 20 minutes, and as a result the second-order errors are relatively small. We plot the real second-order errors against the errors estimated with equation ( 10 ) for a uniform flux curve. The plot shows that within 1 cm s −1 , the uniform flux approximation is indeed a realistic assumption, and much more realistic than setting the error to zero. There is no indication that longer exposure times would change this picture. Figure 7. For nearly one year of EXPRES observations, we compare the actual second-order error of each measurement with the uniform flux approximation. The multichannel exposure meter data have been binned to one channel. EXPRES mainly observes bright targets, so the exposure times are short (≤1200 s), resulting in errors of only a few cm s −1 . Nevertheless, the data show that the uniform flux curve is a good approximation if we for some reason do not have access to the exposure meter flux curve when we want to calculate the second-order error. In the rare case of dealing with data that completely lacks information about the temporal flux distribution, there is no way of knowing if the individual observations have large first-order barycentric errors. One can in principle use equation ( 8 ) to estimate the RV error bars, but it requires a qualified guess at the offset (〈 t 〉 − t 0 ). In our experience, a typical offset is of order 5 per cent of the exposure time, with some larger, negative offsets from when the star was lost on the fibre before the end of the exposure. The actual distribution depends on the instrument and the local sky conditions. 6 CONCLUSIONS This paper describes how to correctly apply a barycentric correction to an exposure using the exposure meter flux curve or an equivalent measure. Rather than following the common practice of computing a single value at the photon-weighted
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