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H:usa:m’s 2 Theoratical Visibility Criteria of Area of Lune of Crescent Of Luna [moon] A gift of “I:D 29\09\14380AH Prediction of the Visibility Of Crescent after the Conjunction with in 60h of Conjunction is a Complex Problem of Applied Astronomy. There are may Criteria [Equations and Inequilities] which are drvrloprd by different Excogitators in the field of Astronomy. Some of them are empirical and some of them are theoretical. But to the best of my information none of them have used the formula of Area of Lune[Hila:l] of Crescent Of Luna [Hila:l]. So for the first time some formulae [Commonly known as Criteria/Criterion] are presented on 29-09-1438 AH 0r 25-06-2017CE in these regard. Astronomists are requested to improve them and to use them for actual computation and calculation . I have made these formulae free to all without any copy right since I am personally want to annuleCopy Right Law legally . Since it is an obstacles in spreading Knowledge and science. But the best way to protest against it is not to violate it but to argue against it and never to apply it on my own works. First Formula:
H:usa:m’s First Theoratica; Visibility Criterion of Area of Lune of Crescent Of Luna [moon] Let A be the Area of Lune of Lunar Crescent A=A(R,r) Let B be the Brightneess of the Lune of the Luna’s Crescent. Let
Amin be the minimum Area of the Lune of Luna required for visibility of Lune of Crescent of Luna .
Let
Bmin
be the minimal Brightness of Lune of Crescent of Luna for the Visibility of Lune of Crescent.
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2 Let For any Value of Area of Lune less than Amin Visibility of Luna: is impossible for any value of Brightness of the Lune of Crescent , how so ever large it may be or how so ever small it may be. Let the time of observation of Crescent is not more then 60h after the birth of New Moon. Let the observation is at a place on earth at the Best Time. Let For any Value of B of stated above Lune less then Bmin Visibility of Lune of Crescent stated above is impossible for any value of A, how so ever large it may be or how so ever small it may be. Then under the above sentenced five conditions the formulae [First H:sa:m’s Formula in inequation] is as follow. A> Amin , and B > Bmin
Visibility is theoretically certain if (A)(B) > (Amin )( Bmin ) => [(A)(B)] / [(Amin )( Bmin )]>1 => LOG [ [(A)(B)] / [(Amin )( Bmin )]]>LOG (1)-----------------1 If = سLOG [ [(A)(B)] / [(Amin )( Bmin )]] -------------------- 2 Then visibility is Certain for 1< س----------
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If 1 > س-------------- 4 Visibility is Impossible A(R,r) = [1/2]Π [r]^2 – Rsin (r/R)+r ([R^2]-[r]^2)^(1/2) https://www.youtube.com/watch?v=aQJgz-PwPoY https://www.youtube.com/watch?v=rkrseBU21CU س
= SI:N =SEEN
Any one who uses Lune Area Criteria or derive any other criterion using Area of Lune [Either on Plane or Sphere is requested to use the letter Husa:m]
س
Brightness is the Brightness as mensioned in Shaefer’s Paper and Sang Yao’s Paper
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as it is the Part of Noun
3 1] A Model for the Brightness of Moon Light by Schaefer etc. 2] Moon Night Sky Brightness, Simulation For Xinglang Station by Sanf Yao etc. Portals for modifications are open. Area of Lune may be derived by one self by Geomatry. I Have used a Lune on a Plain, Area of Sperical Lune or Sphere may also be used.
H:usa:m’s Second Visibility Criterion of Area of Lune of Crescent Of Luna [moon] Let All the conditions of the conditions of the H:usa:m’s first Criterion be assumed. Then the B/A is the Brightness Per Unit Area of the Lune. Let 1 [ = سBmin ]/[ Amin ] 2 [ = سB ]/[ A ] Log [1 س/ 2 > ] س1 Then visibility is Certain.
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