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Husa:m form of Schaefer’s formula of Luna’s Crescent. Wψ=rcosψ(1-cosE) =WcCosψ Bψ=rFmCosψ(1-CosE)[(A)^2](R)^2 (Brightness of Luna’s Crescent at displacement ψ from a cusp, r is the radius of Luna,Fm is the Maximum flux,E is the separation between sun and moon,a is the albedo of Lunar Surface,R is the distance between Earth and Moon,Wc is the theoritical Width of Moon from the middle/center, WcCosψ is thr reduced Width at angle ψ, Wm is the Width reduced by ARCV .) See :Shahid Quraishi’s Thesis:Shahid Page 177 refers to Quraishi and Khan 2007
Bψ=Fm {1/(R)^2}Wψ Note Shahid Quraishi did not provide any formula for Fm. It amy be empirically or practically be determined, who ever Husam has attempted to find one by equating to Shahid’s and Shaefer’s equations which are supposed to be approximately equal. Now according to Schaefer’s Reconstructed formula =سLog بب/ب = Log[ Bmoon/BReq] Let Bmoon=Bψ BReq= B0(Z) Now we get an other formula =سLog[ [WcCosψ((a^2)/(R)^2)Fm]/ B0(Z)] Now the Criteria is the same If 1< سVisibility is Certain 0> سVisibility is impossible 0<1> سVisibility is Probable Dedicated to any one who understands it. 1
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