Surface Brightnesses in the U, B, V System with Applications of Formula and Dimensions of Stars

The surface brightnesses are expressed in the V system in terms of V0 and |d^| (the angular diameter) with the formula |sV = V₀ + 5 \,log d. sv| is derived for 18 stars from observation and the relation between sv and |(B-VB)₀| is obtained. The central problem is the determination of Mv from R (the linear radius) or vice versa; the formula |Mᵥ - sv + 5 \,log R = + 15.15| is basic for the solution thereof. The use of sv is compared with a method based on BC and T e currently employed in the same problem. The two methods are equivalent provided a certain condition is satisfied. Lines of equal radius have been drawn in a HR diagram having ( B–V ) 0 and M v coordinates and the radii of stars along the zero age main sequence are given. The mean absolute magnitude of δ Cephei has been derived in good accord with other modern determinations |(Mᵥ = -3.56).| The absolute magnitudes M v for the components of some eclipsing variables are derived and a mass-luminosity relation is drawn with small scatter. The dimensions of some supersupergiants belonging to the Magellanic Clouds are calculated; HDE 268757 is one of the largest known stars with a radius of 10.3 a.u. A check is made on a published list of BC and T e , using the results of this paper.