Study of Danjon limit in moon crescent sighting

About 70 years ago “André Danjon” a French astrophysicist showed that as elongation of the moon decreases the arc length of crescent gets less too. By studying the recent observational data, he concluded that at 7 degree elongation, the length of arc (cusp to cusp) will reach zero degree. Today, this value is named as Danjon limit, which points to the limit at which the moon crescent is formed. Danjon believed that the effective factor for occurring this limit was the shadows of moon’s mountains. Later researchers have obtained different values for this limit. In this research based on the new data, the decreasing dependence of length of arc versus elongation was obtained. The results show that the Danjon limit is about 5 degrees. The effective factors to form the Danjon limit are then given and discussed. By considering the effects of astronomical seeing and shadows of lunar features, the values of the arc length were calculated and compared with the observational data curve. The results of this study show good agreement with the observational data. The present research shows that the above-mentioned effects can reduce the length of arc. The effect of libration and roughness of the lunar terrain of the moon in forming the moon crescent were also considered, and the possibility of observing thinner crescents by photometric model and breaking the Danjon limit were given.