In Simple Terms, mathematical or otherwise, how did Hertzsprung, for the FIRST TIME work out the distance of?

Question

In Simple Terms, mathematical or otherwise, how did Hertzsprung, for the FIRST TIME work out the distance of some Cepheid Variables to Earth without resorting to parallax method (that, anyway, would not have been accurate)?

Answer 1

The distance to rare stars such as Cepheid Variables is usually done by finding them in clusters with other stars.

The distance to the other, main sequence stars in the same cluster can be determined by fitting their colors (and possibly their spectra) and brightness to a main sequence locus.  Since the Ceheids are in the same cluster, they are presumably at the same distance.

Answer 2

He used statistical parallax - and made errors. His calculations put the Cepheids ten times closer as they really are.

His data was used for the relation between luminosity and distance of these special variable stars - and the relation got more and more refined over the years, by better measurements. The currently best measurement is from the Hipparcos satellite (1997).