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
ABSTRACT
Arithmetic Lunar Calendar is based on the concept of Leap Years and the average motion of the Moon. However, the actual motion of the Moon varies greatly due to various factors which cause the observational calendar to be different from the arithmetic calendar. Whereas, the Calendars based on prediction criterion of Yallop are the closest to the observational calendar. In this work, we compare these calendars with the actual observational calendar in practice in Pakistan for the years 2000 to 2004. It is found that on average 95% observations are according to the Yallop's criterion. The disagreement is the result of either the bad weather due to which the new Lunar crescent could not be sighted and the Lunar month began one day late, or too optimistic claims of observation and the Lunar month began one day earlier than predicted. On the other hand the disagreement between the Arithmetic Calendar and the observational one is 54%.