Reconstruction of Schaefer' Formula for the Visibility of Crescent of Luna

Reconstructio n of the Schaefer Criteria of Visibility of Crescent of Luna by H:usa:mullah Schaefers formula is a good formula for the speculation of the visibility of Crescent/Hilal of Luna/Qamar/Moon. But this formula is hidden and even a man like F-t-h:i: was unable to find it. I have tried to reconstruct and resurrect the formula. Any error in the formula can only be ascribed to the Reconsturtor and not to the original Deriver of the Formula.

Dedicated to all who are interested in Visibility of Crescent of Luna from Planet Earth.

25/09/1438 AH

Schaefer’s Formula is not found in general. The reasons for hiding the formulae are speculated but they are beyond the scope of the present work. Even a man like F-tu:h:I was unable to find it.I Have tried to reconstruct the formulae. Any error in the formula can only be ascribed to me and not to Schaefer.

In the reconstruction I have used some “Arabic Letters.

The Formula is as follow:= ‫ = س‬Log ε (‫بب‬/‫)ب‬-------------(1)

Where ‫ س‬is pronounced as Seen [Si:n] ‫ ب‬is

Pronounced as Baa [Ba:]

‫ بب‬is

Pronounced as Baa Baa

Criteria Visibility is Certain for

1< ‫س‬

Visibility is Impossible for 0> ‫س‬ Visibility is Probable for 1>0<‫س‬ Where ‫=ب‬

B act -----------------(2)

‫= بب‬B

req

B act =B- B0(Z) ---------------(3) B0(Z)=B zen [10exp(-0.4)K(X-1)]X------------(4) K>0.03 [Constant]----------------------(5) B=(0.263)(a(exp(Q-V))))--------(6a) Or B=(34.08)exp(20.7233-0.92104V)-------------------(6b) V=21.37710 Constant----------------------(7) X=(1-0.96(sin(Z)^2))exp(-(1/2)), Z is Zenith--------------------(7) Zm is the Zenith of Luna ------------------------------(8)

Q=10+(2.5)Logε (3600)^2 -------------------------------(9) a= (100)exp(0.2) ---------------------------(10) Bμ= f(ρ)I*[10exp(-0.4)KX(Zm)][1-10exp(-0.4KX(Zm))---------------(11) X(Z)=(1-0.096((SinZ)^2)exp(-1/2)--------------------------------(12) I*=10exp(*0.4)(m+16.57)------------------------(13) m= -12.73+0.26|α|+(4(10)exp(-a)|α|^4----------------------(14) α= Phase Angle.

Bm= Dark night Brightness calculated as an average-----------------(15) X(Z)=[Cos(Z)+0.25e (exp(-11Cos(Z))exp(-1)------------------------(16) ΔV=(-0.2)Logε [[Bmoon+B0(Z)]/B0(Z)]-------------------------(17) Bmoon = Bμ-----------------(18) .ε=10 0r e --------------------------(19) [Not specified but assumed to be 10, Log at the base 10]

For any confusion in equations consult the followings.

1] Moon Light Brightness Simulation for Xinglang Station by Sang Yao. 2] A Model for the Brightness of Moon Light by Schaefer and Bredley.