ÇCLINE
Calt;RF;AL;W;E2;S1;B;C;COSD1;SIND1;BB;Y1;PHI1;LAMDAE;A;H;LL2;N;SINH;COSH;f
[1] ¹ Adopted astronomical constants
[2]
AlphaÓÖ298.257 ¹ Earth flattening factor
[3]
RearthÓ6378.14 ¹ Earth equatorial radius in kilometers
[4]
DayRatioÓ1.002738 ¹ Ratio of mean solar day/mean siderial
day
[5] ¹
[6]
fÓ(1000âRearth)Ö(Calt+1000âRearth) ¹ Fractional increase in radius vector for altitude AMSL
[7] XÓXâf × YÓYâf × XPÓXPâf × YPÓYPâf × l1Ól1âf × l2Ól2âf
[8] ¹
[9] ¹ Compute TOPOCENTRIC Shadow Geometry
[10]
SIND1ÓSINDâWÓÖ(1-(E2Ó(2âAlpha)-Alpha*2)âCOSD*2)*0.5
[11]
BÓ(XâSINDâMUPâS1ÓÜÖ10800)-YP
[12]
CÓXP+((YâSIND)+l2âtanf2âCOSD)âMUPâS1
[13]
COSD1Ó(1-Alpha)âWâCOSD
[14] ¹
[15] ¹ Compute CENTERLINE
Circumstances
[16] RED
LOGÓ1=âBBÓ1-(X*2)+(Y1ÓWâY)*2
¹ Eliminate pts below horizon
[17]
PHIÓÐ3Ü((1-E2)*-0.5)â3ÜPHI1ÓÐ1Ü(Y1âCOSD1)+SIND1âBBÓBB*0.5 ¹ Latitude
[18]
DELTATDEGÓ360âDELTATÖ86400
¹ Delta-T in degree
[19] SINHÓÐ1Þ(XÖ2ÜPHI1)Ä1
¹ Sine Hour Angle
[20] COSHÓÐ1Þ(((-Y1âSIND1)+BBâCOSD1)Ö2ÜPHI1)Ä1
¹ Cosine Hour Angle
[21] HÓSINH ASC COSH
¹ Vector Resolved Hour
Angle
[22]
LAMÓ(LAMDAEÓ(ÜMUÖ180)-H)-(ÜÖ180)âDayRatioâDELTATDEG
¹ Longitude
[23]
DURÓ(120âLL2Ól2-BBâtanf2)ÖNÓ((AâAÓC-BBâS1âMUPâCOSD)+B*2)*0.5 ¹ Duration
[24] TYPÓ'T*A'[2+âLL2]
¹ Type Code: T, A, *
[25]
WIDÓRearthâ2âLL2Ö((BB*2)+(((XâA)-YâB)*2)ÖN*2)*0.5
¹ Umbra width
[26]
ECCÓ2ÜALTÓ(SINDâ1ÜPHI)+COSDâ(2ÜPHI)â2ÜH
¹ Shadow eccentricity &
alt.
[27]
AZÓÐ3Ü(((1ÜPHI)â2ÜH)-(2ÜPHI)âtansd)Ö1ÜH
¹ Shadow azimuth (degrees)
[28]
AZDÓ(180â1=âX)+90+(ÖÜÖ180)â-Ð3Ü(((1ÜPHI)â2ÜH)-(2ÜPHI)âtansd)Ö1ÜH ¹ Shadow azimuth (degrees)