The absolute visual magnitude as function of the observed colour (B-V), also
named Hertzsprung-Russell diagram can be described through five equations; that
in presence of calibrated stars means eight constants. The developed framework
allows to deduce the remaining physical parameters that are mass, radius and
luminosity. This new technique is applied to the first 10 pc, the first 50 pc,
the Hyades and to the determination of the distance of a cluster. The case of
the white dwarfs is analysed assuming the absence of calibrated data: our
equation produces a smaller χ2 in respect to the standard
colour-magnitude calibration when applied to the Villanova Catalog of
Spectroscopically Identified White Dwarfs. The theoretical basis of the
formulae for the colours and the bolometric correction of the stars are
clarified through a Taylor expansion in the temperature of the Planck
distribution.Comment: Pages 35, Figures 1
