English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Stellar Doppler velocimetry determines a star's radial velocity $v_r$ viameasurement of a redshift, $z$. At precisions below 10 m s$^{-1}$ conversionbetween the two quantities is complex, and care must be taken to properlyaccount for the effects of relativity. One particular aspect of the problemthat bears repeating is that the one-dimensional version of the relativisticDoppler formula, which does not distinguish between the motion of the sourceand the observer, is incorrect in this context, and indeed does not evenprovide the correct coefficient for variations in the second-order termsinvolving $\beta$. Nonetheless, it is often useful to report a redshift in themore familiar units of velocity without a rigorous calculation, and much codealready exists that does this. In these cases it is important to clearlydocument which formula is being used, and I recommend simply (and explicitly)using the approximation $v_r \approx cz$. This choice is trivially inverted,does not misrepresent the degree of relativistic rigor that has been applied intranslating between redshift and radial velocity, and is, I believe, the mostcommonly followed convention in astronomy and cosmology.  I also briefly discuss the differences between the Wright & Eastmanbarycentric correction procedure and the Lindegren & Dravins barycentric radialvelocity measure.

The 1D Relativistic Doppler Formula is an Incorrect Approximation in Precise Radial Velocity Work