Methods of calculating crescent length

ABSTRACT

A number of authors have described the reasons for the shortening of the length of new lunar crescent. McNally devised a mathematical technique to find the shortened length of crescent using his formula for the width. Recently Sultan has also developed a mathematical technique to calculate the length of crescent on the basis of Blackwell contrast threshold. In the present paper a technique for calculating the "observed length" of the new lunar crescent based on the lower limit on the visible width of crescent is developed using q-value criterion of Yallop. This technique is than used to calculate the crescent length for a number of observations reported in literature since the time of Schmidt of Athens. Finally a comparison of the observed crescent lengths is done with the calculated lengths using our technique and the calculated lengths on the basis of the formulas due to Sultan and McNally. The results of this work are consistent with the observed lengths whereas those due to others are generally inconsistent