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["Calendrical and Astronomical Calculations based on Hilchot Kiddush HaChodesh"]
["Programmed and compiled by Dr. Irv Bromberg, Toronto, Canada  <http://individual.utoronto.ca/kalendis/hebrew/>",{"$nulls":4},"Revised 2022-03-10"]
["http://individual.utoronto.ca/kalendis/hebrew/RMBM-seasons.htm"]
["\"CC\" refers to the book \"Calendrical Calculations\", 3rd edition, by Nachum Dershowitz and Edward M. Reingold, see <http://www.calendarists.com>."]
["Chabad's on-line copy of Hilchot Kiddush HaChodesh is at <https://www.chabad.org/library/article_cdo/aid/947915/jewish/Kiddush-HaChodesh.htm>."]
[]
["The zodiac signs as referenced by Rambam always refer to each 30° ecliptic longitude division, measured eastward from the solar position at the northward equinox."]
["Due to precession of the equinoxes, these signs are not the same as the astronomical or astrological zodiac constellations that share the same names."]
[]
["Chapter","#","English Terms","עִברִית","Decimal #","Separated #","Comments"]
[null,null,"Epoch Dates"]
["CC",null,"Hebrew Epoch","תְחִלָת החשבון",{"$f":"HebrewToFixed(1,7,1)","v":-1373427},null,"days counted before Gregorian epoch"]
["CC",null,"Check Date",null,{"$f":"FixedToHebrewString(E12)","v":"Yom Sheini, 1 Tishrei, 1"},null,"just after sunset, location undefined"]
[]
[11,16,"Rambam Epoch","הַעִקָר שממנו מתחילין לחשבון זֶה",{"$f":"HebrewToFixed(4938,1,3)","v":429979},null,"days counted from Gregorian epoch"]
["CC",null,"Check Date",null,{"$f":"FixedToHebrewString(E15+0.25)","v":"Yom Chamishi, 3 Nisan, 4938"},null,"just after sunset in Jerusalem"]
[]
[null,null,"Target Date and Time",null,null,"Years 3, 6, 8, 11, 14, 17, and 19 in each 19-year cycle are leap years."]
[null,null,"Hebrew Year since Creation","שָׁנָה עִברִי יְצִירָה",5782,{"$f":"IF(modulus(7*hYear+1,19)<7,,\"Non-\")&\"Leap Year (\"&amod(hYear,19)&\" of 19)\"","v":"Leap Year (6 of 19)"}]
[null,null,"Hebrew Month","חוֹדֶשׁ עִברִי",7,"Nisan=1 Iyar=2 Sivan=3 Tammuz=4 Av=5 Elul=6 Tishrei=7 Cheshvan=8 Kislev=9 Tevet=10 Shevat=11 Adar=12 Adar2=13"]
[null,null,"Day of Hebrew Month"," יום שֶׁל חוֹדֶשׁ עִברִי",1]
[null,null,"Time of Day",null,"18:30:00",null,"HH:MM:SS after mean sunset (disregard AM / PM if Excel displays it)"]
["CC",null,"Fixed Day Number (rata die)",null,{"$f":"HebrewToFixed(hYear,hMonth,hDay)","v":738040},null,"days counted from Gregorian epoch = 1"]
["CC",null,"Moment",null,{"$f":"FixedDay+TimeOfDay","v":738040.7708333334},null,"at Jerusalem"]
[null,null,"Check Hebrew Date",null,{"$f":"FixedToHebrewString(moment)","v":"Yom Shlishi, 1 Tishrei, 5782"}]
["CC",null,"Gregorian Date",null,{"$f":"FixedToGregorianString(moment)","v":"Tuesday, September 7, 2021"}]
["CC",null,"Julian Date",null,{"$f":"FixedToJulianString(moment,TRUE)","v":"Tuesday, August 25, MMXXI AD"}]
["CC",null,"Julian Day Number",null,{"$f":"MomentToJD(moment)-2/24","v":2459464.9375},null,"at Prime Meridian"]
["CC",null,"Days Elapsed from Hebrew Epoch",null,{"$f":"moment-hEpoch","v":{"v":2111467.7708333335,"d":"2111467.7708"}},null,"from mean sunset"]
[null,null,"Days Elapsed from Rambam Epoch",null,{"$f":"moment-RMBMepoch","v":308061.7708333334}]
[11,16,"Year with regard to contracts","שָׁנָה לשְׁטָרות",{"$f":"hYear-3449","v":2333}]
[11,16,"Years after destruction of the Second Temple","שָׁנָה מחוּרבָּן בַּיִת שֵׁנִי",{"$f":"hYear-3829","v":1953}]
[]
[6,null,"Traditional Molad","מולד"]
["mine","It is improper to translate or regard the molad as a \"lunar conjunction\" or even a \"mean lunar conjunction\".  It is just Hebrew calendar arithmetic.  See: <http://individual.utoronto.ca/kalendis/hebrew/molad.htm>."]
[6,2,"Divisors of 1080 (parts per hour = חלקים) = ",{"$f":"Divisors(1080,0)","v":"2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080"}]
[6,3,"Traditional Molad Interval","חדשה שֶׁל לְבָנָה",{"$f":"29+12/24+(44+1/18)/1440","v":29.53059413580247},{"$f":"\" \"&momenttodc(MoladInterval,5)&\"  =  \"&momenttodc(MoladInterval,6)&\"  =  \"&momenttodc(MoladInterval,9)","v":" 29 days 12 hours 44 minutes 1 part  =  29 days 12 hours 793 parts  =  29 days 13753 parts"}]
[6,5,{"$f":"\"Remainder in Excess of \"&QUOTIENT(E37,7)&\" Weeks\"","v":"Remainder in Excess of 4 Weeks"},"שְׁאֵרִית חוֹדֶשׁ הַלְבָנָה",{"$f":"modulus(MoladInterval,7)","v":1.5305941358024704},{"$f":"\" \"&momenttodc(E38,5)&\"  =  \"&momenttodc(E38,6)&\"  =  \"&momenttodc(E38,9)","v":" 1 day 12 hours 44 minutes 1 part  =  1 day 12 hours 793 parts  =  1 day 13753 parts"}]
[6,4,"12 Lunar Months",null,{"$f":"12*MoladInterval","v":354.36712962962963},{"$f":"\" \"&momenttodc(E39,5)&\"  =  \"&momenttodc(E39,6)&\"  =  \"&momenttodc(E39,9)","v":" 354 days 8 hours 48 minutes 12 parts  =  354 days 8 hours 876 parts  =  354 days 9516 parts"}]
[6,5,{"$f":"\"Remainder in Excess of \"&QUOTIENT(E39,7)&\" Weeks\"","v":"Remainder in Excess of 50 Weeks"},"שְׁאֵרִית שָׁנָה פָּשׁוּטה",{"$f":"modulus(E39,7)","v":4.3671296296296305},{"$f":"\" \"&momenttodc(E40,5)&\"  =  \"&momenttodc(E40,6)&\"  =  \"&momenttodc(E40,9)","v":" 4 days 8 hours 48 minutes 12 parts  =  4 days 8 hours 876 parts  =  4 days 9516 parts"}]
[6,4,"13 Lunar Months",null,{"$f":"13*MoladInterval","v":383.8977237654321},{"$f":"\" \"&momenttodc(E41,5)&\"  =  \"&momenttodc(E41,6)&\"  =  \"&momenttodc(E41,9)","v":" 383 days 21 hours 32 minutes 13 parts  =  383 days 21 hours 589 parts  =  383 days 23269 parts"}]
[6,5,{"$f":"\"Remainder in Excess of \"&QUOTIENT(E41,7)&\" Weeks\"","v":"Remainder in Excess of 54 Weeks"},"שְׁאֵרִית שָׁנָה מְעוּבּרֶת",{"$f":"modulus(E41,7)","v":5.89772376543209},{"$f":"\" \"&momenttodc(E42,5)&\"  =  \"&momenttodc(E42,6)&\"  =  \"&momenttodc(E42,9)","v":" 5 days 21 hours 32 minutes 13 parts  =  5 days 21 hours 589 parts  =  5 days 23269 parts"}]
[6,"end 8","Molad Epoch","מולד תוֹהוּ (בהר\"ד)",{"$f":"TraditionalMolad(0)","v":{"v":-1373426.7837962965,"d":"-1373426.7838"}},{"$f":"\" \"&momenttoclock(MoladEpoch,5)&\"  =  \"&momenttoclock(MoladEpoch,6)","v":" 5 hours 11 minutes 6 parts  =  5 hours 204 parts"}]
[6,8,"Hebrew Date of Molad Epoch",null,{"$f":"FixedToHebrewString(MoladEpoch)","v":"Yom Sheini, 1 Tishrei, 1"}]
[6,12,"Lunar Months per 19-Year Cycle","חודשי הַלְבָנָה למַחזוֹר",{"$f":"19*12+7","v":235}]
[6,12,{"$f":"E45&\" Lunar Months\"","v":"235 Lunar Months"},null,{"$f":"E45*MoladInterval","v":6939.689621913581},{"$f":"\" \"&momenttodc(E46,5)&\"  =  \"&momenttodc(E46,6)&\"  =  \"&momenttodc(E46,9)","v":" 6939 days 16 hours 33 minutes 1 part  =  6939 days 16 hours 595 parts  =  6939 days 17875 parts"}]
[6,12,{"$f":"\"Remainder in Excess of \"&QUOTIENT(E46,7)&\" Weeks\"","v":"Remainder in Excess of 991 Weeks"},"שְׁאֵרִית הַמַחזוֹר",{"$f":"modulus(E46,7)","v":2.689621913580595},{"$f":"\" \"&momenttodc(E47,5)&\"  =  \"&momenttodc(E47,6)&\"  =  \"&momenttodc(E47,9)","v":" 2 days 16 hours 33 minutes 1 part  =  2 days 16 hours 595 parts  =  2 days 17875 parts"}]
["CC",null,"Lunar Months Elapsed from Hebrew Epoch",null,{"$f":"hMonth-7+QUOTIENT(235*IF(hMonth<7,hYear+1,hYear)-234,19)","v":71501},null,"arithmetic is from \"Calendrical Calculations\" by Reingold & Dershowitz."]
["CC",null,"Molad Moment",null,{"$f":"TraditionalMolad(MonthsElapsed)","v":738040.227507716}]
["CC",null,"Fractional Portion of Molad Moment (time)",null,{"$f":"MomentToTimeOfDay(MoladMoment)","v":0.2275077160447836},{"$f":"\" \"&momenttoclock(MoladMoment,5)&\"  =  \"&momenttoclock(MoladMoment,6)","v":" 5 hours 27 minutes 11 parts  =  5 hours 497 parts"}]
["CC",null,"Molad Hebrew Date",null,{"$f":"FixedToHebrewString(MoladMoment)","v":"Yom Shlishi, 1 Tishrei, 5782"}]
[]
[7,null,"Rosh HaShannah","ראשׁ הַשָׁנָה",null,null,"See:  <http://individual.utoronto.ca/kalendis/hebrew/postpone.htm>"]
["CC",null,{"$f":"\"Months Elapsed from Epoch to Tishrei \"&hYear","v":"Months Elapsed from Epoch to Tishrei 5782"},null,{"$f":"QUOTIENT(235*hYear-234,19)","v":71501},null,"elapsed months expression is simplest for Tishrei"]
["CC",null,{"$f":"\"Molad of Tishrei for Hebrew year \"&hYear","v":"Molad of Tishrei for Hebrew year 5782"},"מולד תשרי",{"$f":"TraditionalMolad(E54)","v":738040.227507716}]
["CC",null,"Fractional Portion of Molad Moment (time)",null,{"$f":"MomentToTimeOfDay(E55)","v":0.2275077160447836},{"$f":"\" \"&momenttoclock(E56,5)&\"  =  \"&momenttoclock(E56,6)","v":" 5 hours 27 minutes 11 parts  =  5 hours 497 parts"}]
["CC",null,"Molad Hebrew Date",null,{"$f":"FixedToHebrewString(E55)","v":"Yom Shlishi, 1 Tishrei, 5782"}]
[7,1,"Molad weekday number (Sun=1 ... Sat=7)",null,{"$f":"FixedToWeekdayNum(E55)+1","v":3}]
[7,1,"Disallowed weekday? (Sun=1, Wed=4, Fri=6)","לא אד\"ו ראשׁ",{"$f":"modulus((MoladWeekdayNum-1)*3,7)<3","v":false},{"$f":"IF(E59,\"Postpone one day\",\"\")","v":""}]
[7,2,"\"Old\" Molad (on or after noon = 18th hour)?","מולד זקן",{"$f":"E56>=0.75","v":false},{"$f":"IF(E60,\"Postpone one day\",\"\")","v":""}]
[7,3,"Disallowed weekday after old molad?","לא אד\"ו ראשׁ",{"$f":"AND(E60,modulus((MoladWeekdayNum)*3,7)<3)","v":false},{"$f":"IF(E61,\"Postpone another day\",\"\")","v":""}]
["mine","Logically it is more efficient to check for Molad Zakein before checking for a disallowed weekday, to avoid a second check for disallowed weekday after applying the Zakein postponement."]
["mine","The logic can be simplified further by always adding 1/4 day to the moment of the molad of Tishrei, which eliminates the need for the molad zakein rule altogether."]
["mine","and it can be simplified even further still by a one-time adjustment of +1/4 day to the molad epoch, which would forever eliminate all molad zakein adjustments."]
[7,4,{"$f":"\"Tishrei Molad \"&hYear&\" on Tuesday and year non-leap?\"","v":"Tishrei Molad 5782 on Tuesday and year non-leap?"},null,{"$f":"AND(MoladWeekdayNum=3,NOT(isHebrewLeapYear(hYear)))","v":false}]
[7,4,"Tuesday postponement cutoff time",null,{"$f":"9/24+204/25920","v":0.38287037037037036},{"$f":"\" \"&momenttodc(E66,5)&\"  =  \"&momenttodc(E66,6)&\"  =  \"&momenttodc(E66,9)","v":" 9 hours 11 minutes 6 parts  =  9 hours 204 parts  =  9924 parts"}]
[7,4,"Postpone Tuesday to Thursday?",null,{"$f":"AND(E65,E56>=E66)","v":false},{"$f":"IF(E67,\"Postpone two days\",\"\")","v":""}]
["mine",null,{"$f":"\"Months Elapsed from Epoch to Tishrei \"&hYear+1","v":"Months Elapsed from Epoch to Tishrei 5783"},null,{"$f":"ElapsedMonths(hYear+1,7)","v":71514}]
["mine",null,{"$f":"\"Molad of Tishrei for Hebrew year \"&hYear+1","v":"Molad of Tishrei for Hebrew year 5783"},null,{"$f":"TraditionalMolad(E68)","v":738424.1252314812}]
["mine",null,"Fractional Portion of Molad Moment (time)",null,{"$f":"MomentToTimeOfDay(E69)","v":0.12523148127365857},{"$f":"\" \"&momenttoclock(E70,5)&\"  =  \"&momenttoclock(E70,6)","v":" 3 hours 6 parts  =  3 hours 6 parts"}]
["mine",null,"Molad Hebrew Date",null,{"$f":"FixedToHebrewString(E69)","v":"Yom Sheini, 1 Tishrei, 5783"}]
["mine",null,{"$f":"\"Tishrei Molad \"&hYear+1&\" on or after noon?\"","v":"Tishrei Molad 5783 on or after noon?"},null,{"$f":"E70>=0.75","v":false},{"$f":"IF(AND(E65,E72),\"Postpone two days\",\"\")","v":""}]
[7,5,{"$f":"\"Tishrei Molad \"&hYear&\" on Monday and year \"&hYear-1&\" leap?\"","v":"Tishrei Molad 5782 on Monday and year 5781 leap?"},null,{"$f":"AND(MoladWeekdayNum=2,isHebrewLeapYear(hYear-1))","v":false}]
[7,5,"Monday postponement cutoff time",null,{"$f":"1/2+3/24+589/25920","v":0.6477237654320988},{"$f":"\" \"&momenttodc(E74,5)&\"  =  \"&momenttodc(E74,6)&\"  =  \"&momenttodc(E74,9)","v":" 15 hours 32 minutes 13 parts  =  15 hours 589 parts  =  16789 parts"}]
[7,5,"Postpone Monday to Tuesday?",null,{"$f":"AND(E73,E56>=E74)","v":false},{"$f":"IF(E75,\"Postpone one day\",\"\")","v":""}]
["mine",null,{"$f":"\"Months Elapsed from Epoch to Tishrei \"&hYear-1","v":"Months Elapsed from Epoch to Tishrei 5781"},null,{"$f":"ElapsedMonths(hYear-1,7)","v":71489}]
["mine",null,{"$f":"\"Molad of Tishrei for Hebrew year \"&hYear-1","v":"Molad of Tishrei for Hebrew year 5781"},null,{"$f":"TraditionalMolad(E76)","v":737685.8603780861}]
["mine",null,"Fractional Portion of Molad Moment (time)",null,{"$f":"MomentToTimeOfDay(E77)","v":0.8603780861012638},{"$f":"\" \"&momenttoclock(E78,5)&\"  =  \"&momenttoclock(E78,6)","v":" 20 hours 38 minutes 17 parts  =  20 hours 701 parts"}]
["mine",null,"Molad Hebrew Date",null,{"$f":"FixedToHebrewString(E77)","v":"Yom Chamishi, 28 Elul, 5780"}]
["mine",null,{"$f":"\"Tishrei Molad \"&hYear-1&\" on or after noon?\"","v":"Tishrei Molad 5781 on or after noon?"},null,{"$f":"E78>=0.75","v":true},{"$f":"IF(AND(E73,E80),\"Postpone one day\",\"\")","v":""}]
[null,null,"Total Rosh HaShannah Postponement Days","דְחִיות ראש השנה",{"$f":"IF(E59,1,0)+IF(E60,1,0)+IF(E61,1,0)+IF(AND(E65,E72),2,0)+IF(AND(E73,E80),1,0)","v":0}]
[null,null,{"$f":"\"Actual day of Rosh HaShannah \"&hYear","v":"Actual day of Rosh HaShannah 5782"},null,{"$f":"INT(E55)+E81","v":738040},{"$f":"FixedToHebrewString(E82)","v":"Yom Shlishi, 1 Tishrei, 5782"}]
[8,7,{"$f":"\"Length of Hebrew Year \"&hYear","v":"Length of Hebrew Year 5782"},null,{"$f":"HebrewToFixed(hYear+1,7,1)-E82","v":384},"days"]
[8,7,{"$f":"\"Length Type of Hebrew Year \"&hYear","v":"Length Type of Hebrew Year 5782"},null,{"$f":"IF(OR(hYearLength=353,hYearLength=383),\"Deficient\",IF(OR(hYearLength=355,hYearLength=385),\"Perfect\",\"Normal\"))","v":"Normal"},"Deficient = 353 or 383;  Normal = 354 or 384;  Perfect = 355 or 385"]
[8,6,{"$f":"\"Length of Cheshvan \"&hYear","v":"Length of Cheshvan 5782"},null,{"$f":"IF(LengthType=\"Perfect\",30,29)","v":29},"days"]
[8,6,{"$f":"\"Length of Kislev \"&hYear","v":"Length of Kislev 5782"},null,{"$f":"IF(LengthType=\"Deficient\",29,30)","v":30},"days"]
[]
[9,null,"Tekufat Shmuel","תְקוּפָת שמואל"]
[null,null,"First Tekufat Nisan (epoch)","תְקוּפָת ניסן",{"$f":"RMBM_TekufatShmuel(1,0)","v":{"v":-1373257,"d":"-1373257.0000"}},{"$f":"\" \"&FixedToHebrewString(E89)&\" at \"&momenttoclock(E89,7)&\" after mean sunset\"","v":" Yom Rivii, 22 Adar, 1 at 0 hours after mean sunset"}]
[null,null,"Molad Nisan in year one","מולד ניסן",{"$f":"TraditionalMolad(ElapsedMonths(1,1))","v":{"v":-1373249.6002314817,"d":"-1373249.6002"}},{"$f":"\" \"&FixedToHebrewString(E90)&\" at \"&momenttoclock(E90,7)&\" after mean sunset\"","v":" Yom Rivii, 29 Adar, 1 at 9 hours 642 parts after mean sunset"}]
[null,null,{"$f":"\"tekufah \"&IF(E89<E90,\"before\",\"after\")&\" molad\"","v":"tekufah before molad"},null,{"$f":"ABS(E90-E89)","v":{"v":7.399768518283963,"d":"7.3998"}},{"$f":"\" \"&momenttodc(E91,6)","v":" 7 days 9 hours 642 parts"}]
[9,1,"Assumed Length of Solar Year",null,{"$f":"365+1/4","v":365.25},{"$f":"\" \"&momenttodc(E92,5)","v":" 365 days 6 hours"}]
[9,2,"19 solar years minus 235 lunar months",null,{"$f":"19*E92-235*MoladInterval","v":0.06037808641940501},{"$f":"\" \"&momenttodc(E93,5)&\"  =  \"&momenttodc(E93,6)&\"  =  \"&momenttodc(E93,9)","v":" 1 hour 26 minutes 17 parts  =  1 hour 485 parts  =  1565 parts"}]
[9,2,"Season Length (=Solar Year / 4)",null,{"$f":"E92/4","v":91.3125},{"$f":"\" \"&momenttodc(E94,5)","v":" 91 days 7 hours 30 minutes"}]
[null,null,{"$f":"\"Season remainder in excess of \"&INT(E94)/7&\" weeks\"","v":"Season remainder in excess of 13 weeks"},null,{"$f":"modulus(E94,7)","v":0.3125},{"$f":"\" \"&momenttodc(E95,5)","v":" 7 hours 30 minutes"}]
[9,4,"solar  year remainder in excess of 12 lunar months",null,{"$f":"E92-12*MoladInterval","v":{"v":10.88287037037037,"d":"10.8829"}},{"$f":"\" \"&momenttodc(E96,6)","v":" 10 days 21 hours 204 parts"}]
[]
[null,null,"autumn (180°)","תְקוּפָת תשרי",{"$f":"RMBM_TekufatShmuel(hYear,180)","v":{"v":738070.625,"d":"738070.6250"}},{"$f":"\" \"&FixedToHebrewString(E98)&\" at \"&momenttoclock(E98,7)&\" after mean sunset\"","v":" Yom Chamishi, 1 Cheshvan, 5782 at 15 hours after mean sunset"}]
[{"$nulls":3},"מולד תשרי",{"$f":"TraditionalMolad(ElapsedMonths(hYear,7))","v":{"v":738040.227507716,"d":"738040.2275"}}]
[null,null,{"$f":"\"tekufah \"&IF(E98<E99,\"before\",\"after\")&\" molad\"","v":"tekufah after molad"},null,{"$f":"ABS(E99-E98)","v":{"v":30.397492283955216,"d":"30.3975"}},{"$f":"\" \"&momenttodc(E100,6)","v":" 30 days 9 hours 583 parts"}]
[null,null,"winter (270°)","תְקוּפָת טבת",{"$f":"RMBM_TekufatShmuel(hYear,270)","v":738161.9375},{"$f":"\" \"&FixedToHebrewString(E101)&\" at \"&momenttoclock(E101,7)&\" after mean sunset\"","v":" Yom Chamishi, 4 Shevat, 5782 at 22 hours 540 parts after mean sunset"}]
[{"$nulls":3},"מולד טבת",{"$f":"TraditionalMolad(ElapsedMonths(hYear,10))","v":{"v":738128.8192901234,"d":"738128.8193"}}]
[null,null,{"$f":"\"tekufah \"&IF(E101<E102,\"before\",\"after\")&\" molad\"","v":"tekufah after molad"},null,{"$f":"ABS(E102-E101)","v":{"v":33.11820987658575,"d":"33.1182"}},{"$f":"\" \"&momenttodc(E103,6)","v":" 33 days 2 hours 904 parts"}]
[null,null,"spring (0°)","תְקוּפָת ניסן",{"$f":"RMBM_TekufatShmuel(hYear,0)","v":{"v":738253.25,"d":"738253.2500"}},{"$f":"\" \"&FixedToHebrewString(E104)&\" at \"&momenttoclock(E104,7)&\" after mean sunset\"","v":" Yom Shishi, 7 Nisan, 5782 at 6 hours after mean sunset"}]
[{"$nulls":3},"מולד ניסן",{"$f":"TraditionalMolad(ElapsedMonths(hYear,1))","v":{"v":738246.9416666664,"d":"738246.9417"}}]
[null,null,{"$f":"\"tekufah \"&IF(E104<E105,\"before\",\"after\")&\" molad\"","v":"tekufah after molad"},null,{"$f":"ABS(E105-E104)","v":{"v":6.308333333581686,"d":"6.3083"}},{"$f":"\" \"&momenttodc(E106,6)","v":" 6 days 7 hours 432 parts"}]
[null,null,"summer (90°)","תְקוּפָת תמוז",{"$f":"RMBM_TekufatShmuel(hYear,90)","v":738344.5625},{"$f":"\" \"&FixedToHebrewString(E107)&\" at \"&momenttoclock(E107,7)&\" after mean sunset\"","v":" Yom Shishi, 9 Tammuz, 5782 at 13 hours 540 parts after mean sunset"}]
[{"$nulls":3},"מולד תמוז",{"$f":"TraditionalMolad(ElapsedMonths(hYear,4))","v":{"v":738335.5334490738,"d":"738335.5334"}}]
[null,null,{"$f":"\"tekufah \"&IF(E107<E108,\"before\",\"after\")&\" molad\"","v":"tekufah after molad"},null,{"$f":"ABS(E108-E107)","v":{"v":9.029050926212221,"d":"9.0291"}},{"$f":"\" \"&momenttodc(E109,6)","v":" 9 days 0 hours 753 parts"}]
[]
[10,null,"Tekufat Rav Adda","תְקוּפָת רַב אדא",null,"each part = chelek = minute / 18 or hour / 1080, each moment = regah = chelek / 76"]
[10,1,"Assumed Length of Solar Year",null,{"$f":"MoladInterval*235/19","v":{"v":365.24682220597794,"d":"365.246822206"}},{"$f":"\" \"&momenttodc(E112,5)","v":" 365 days 5 hours 55 minutes 7 parts 48 moments"}]
[10,2,"Season Length (=Solar Year / 4)",null,{"$f":"E112/4","v":{"v":91.31170555149448,"d":"91.3117055515"}},{"$f":"\" \"&momenttodc(E113,5)","v":" 91 days 7 hours 28 minutes 15 parts 31 moments"}]
[null,null,{"$f":"\"Season remainder in excess of \"&INT(E113)/7&\" weeks\"","v":"Season remainder in excess of 13 weeks"},null,{"$f":"modulus(E113,7)","v":{"v":0.31170555149448376,"d":"0.3117"}},{"$f":"\" \"&momenttodc(E114,5)","v":" 7 hours 28 minutes 15 parts 31 moments"}]
[]
[null,null,"autumn (180°)","תְקוּפָת תשרי",{"$f":"RMBM_TekufatAdda(hYear,180)","v":{"v":738059.2557616553,"d":"738059.255762"}},{"$f":"\" \"&FixedToHebrewString(E116)&\" at \"&momenttoclock(E116,7)&\" after mean sunset\"","v":" Yom Rishon, 20 Tishrei, 5782 at 6 hours 149 parts 26 moments after mean sunset"}]
[null,null,"winter (270°)","תְקוּפָת טבת",{"$f":"RMBM_TekufatAdda(hYear,270)","v":{"v":738150.5674672064,"d":"738150.567467"}},{"$f":"\" \"&FixedToHebrewString(E117)&\" at \"&momenttoclock(E117,7)&\" after mean sunset\"","v":" Yom Rishon, 22 Tevet, 5782 at 13 hours 668 parts 57 moments after mean sunset"}]
[null,null,"spring (0°)","תְקוּפָת ניסן",{"$f":"RMBM_TekufatAdda(hYear,0)","v":{"v":738241.879172758,"d":"738241.879173"}},{"$f":"\" \"&FixedToHebrewString(E118)&\" at \"&momenttoclock(E118,7)&\" after mean sunset\"","v":" Yom Rishon, 24 Adar Sheini, 5782 at 21 hours 108 parts 12 moments after mean sunset"}]
[null,null,"summer (90°)","תְקוּפָת תמוז",{"$f":"RMBM_TekufatAdda(hYear,90)","v":{"v":738333.1908783095,"d":"738333.190878"}},{"$f":"\" \"&FixedToHebrewString(E119)&\" at \"&momenttoclock(E119,7)&\" after mean sunset\"","v":" Yom Sheini, 28 Sivan, 5782 at 4 hours 627 parts 43 moments after mean sunset"}]
[]
[12,null,"Solar Position","מָקוֹם הַשֶׁמֶשׁ"]
[null,null,"Solar Longitude at Rambam Epoch","מָקוֹם הַשֶׁמֶשׁ בְּעִקָר",{"$f":"DMStoDegrees(7,3,32)","v":7.058888888888888},{"$f":"DegreesToDMS(E122)","v":"7° 3' 32\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E122))","v":"Aries 7° 3' 32\""}]
[12,1,"Solar Mean Motion per Day","מַהֲלָך אֶמצַע הַשֶׁמֶשׁ יוֹמִי",{"$f":"(RMBM_SolarMeanLongitude(RMBMepoch+100)-RMBM_SolarMeanLongitude(RMBMepoch))/100","v":0.985647222222222},{"$f":"DegreesToDMSTF(E123)","v":"0° 59' 8\" 19\"' 48\"\""},"based on 100 days"]
[null,null,{"v":10,"d":"10 "},null,{"$f":"C124*SolarMotionPerDay","v":9.85647222222222},{"$f":"DegreesToDMSTF(E124)","v":"9° 51' 23\" 18\"'"}]
[null,null,{"v":29,"d":"29 "},null,28.58376944444444,{"$f":"DegreesToDMST(E125)","v":"28° 35' 1\" 34\"'"}]
[null,null,{"v":100,"d":"100 "},null,98.5647222222222,{"$f":"DegreesToDMS(E126)","v":"98° 33' 53\""}]
[null,null,{"v":354,"d":"354 "},null,348.9191166666666,{"$f":"DegreesToDMS(E127)","v":"348° 55' 9\""}]
[null,null,{"v":1000,"d":"1000 "},null,985.647222222222,{"$f":"DegreesToDMS(E128)","v":"265° 38' 50\""}]
[null,null,{"v":10000,"d":"10000 "},null,9856.47222222222,{"$f":"DegreesToDMS(E129)","v":"136° 28' 20\""}]
[null,null,"Solar Mean Ecliptic Longitude","מָקוֹם אֶמצַע הַשֶׁמֶשׁ",{"$f":"RMBM_SolarMeanLongitude(moment)","v":167.287583622674},{"$f":"DegreesToDMS(E130)","v":"167° 17' 15\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E130))","v":"Virgo 17° 17' 15\""}]
[]
[null,null,"Aphelion at Rambam Epoch","מָקוֹם גוֹבַה הַשֶׁמֶשׁ בְּעִקָר",{"$f":"DMStoDegrees(86,45,8)","v":86.75222222222222},{"$f":"DegreesToDMS(E132)","v":"86° 45' 8\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E132))","v":"Gemini 26° 45' 8\""}]
[12,2,"Aphelion Mean Motion per Day","מַהֲלָך גוֹבַה הַשֶׁמֶשׁ יוֹמִי",{"$f":"(RMBM_ApogeeLongitude(RMBMepoch+100)-RMBM_ApogeeLongitude(RMBMepoch))/100","v":{"v":4.1666666666628772E-5,"d":"0.000041667"}},{"$f":"DegreesToDMSTF(E133)","v":"0° 0' 0\" 9\"'"},"based on motion in 10 days"]
[null,null,{"v":10,"d":"10 "},null,{"$f":"C134*AphelionPerDay","v":4.1666666666628771E-4},{"$f":"DegreesToDMSTF(E134)","v":"0° 0' 1\" 30\"'"}]
[null,null,{"v":29,"d":"29 "},null,1.2083333333322344E-3,{"$f":"DegreesToDMST(E135)","v":"0° 0' 4\" 21\"'"}]
[null,null,{"v":100,"d":"100 "},null,0.004166666666662877,{"$f":"DegreesToDMS(E136)","v":"0° 0' 15\""}]
[null,null,{"v":354,"d":"354 "},null,0.014749999999986585,{"$f":"DegreesToDMS(E137)","v":"0° 0' 53\""}]
[null,null,{"v":1000,"d":"1000 "},null,0.04166666666662877,{"$f":"DegreesToDMS(E138)","v":"0° 2' 30\""}]
[null,null,{"v":10000,"d":"10000 "},null,0.4166666666662877,{"$f":"DegreesToDMS(E139)","v":"0° 25'"}]
[null,null,"Aphelion Ecliptic Longitude","מָקוֹם גוֹבַה הַשֶׁמֶשׁ",{"$f":"RMBM_ApogeeLongitude(moment)","v":99.58812934027777},{"$f":"DegreesToDMS(E140)","v":"99° 35' 17\""}]
[]
[13,1,"Solar Mean Course","מַסלוּל הַשֶׁמֶשׁ",{"$f":"modulus(SolarMeanLongitude-AphelionLongitude, 360)","v":67.69945428239622},{"$f":"DegreesToDMS(E142)","v":"67° 41' 58\""},"(Solar Mean Longitude - Aphelion Longitude) MOD 360"]
[13,4,"Solar Longitude Adjust","מְנָת מַסלוּל הַשֶׁמֶשׁ",{"$f":"RMBM_SolarLongitudeAdjust(SolarMeanCourse)","v":1.8116575713732703},{"$f":"DegreesToDMS(E143)","v":"1° 48' 42\""},"Subtract from Solar Mean Longitude = Solar True Longitude"]
[null,null,"Solar True Ecliptic Longitude","מָקוֹם הַשֶׁמֶשׁ הַאֲמִתִי",{"$f":"RMBM_SolarTrueLongitude(moment)","v":165.47592605130072},{"$f":"DegreesToDMS(E144)","v":"165° 28' 33\""},{"$f":"RMBM_DegreesInConstellation(RoundArcMinutes(E144))","v":"Virgo 15° 29'"}]
[]
[13,11,"Tekufat Rambam (based on an iterative converging binary search using Rambam's true solar longitude method from chapters 12 and 13)"]
[null,null,"The following moladot are merely employed as approximate starting points for equinox or solstice searching, known to be <1 year before target."]
[null,null,"molad for Nisan of Previous Year",null,{"$f":"TraditionalMolad(ElapsedMonths(hYear-1,1))","v":{"v":737863.0439429013,"d":"737863.043943"}},{"$f":"\" \"&FixedToHebrewString(E148)&\" at \"&momenttoclock(E148,6)&\" after mean sunset\"","v":" Yom Rishon, 1 Nisan, 5781 at 1 hour 59 parts after mean sunset"}]
[null,null,"molad for Tishrei of Target Year",null,{"$f":"TraditionalMolad(ElapsedMonths(hYear,7))","v":{"v":738040.227507716,"d":"738040.227508"}},{"$f":"\" \"&FixedToHebrewString(E149)&\" at \"&momenttoclock(E149,6)&\" after mean sunset\"","v":" Yom Shlishi, 1 Tishrei, 5782 at 5 hours 497 parts after mean sunset"}]
[null,null,"Assumed Length of Mean Solar Year",null,{"$f":"360/E123","v":{"v":365.2422407160552,"d":"365.242240716"}},{"$f":"\" \"&momenttodc(E150,13)","v":" 365 days 5h 48m 49.6s"}]
[]
[null,null,"autumn (180°)","תְקוּפָת תשרי",{"$f":"RMBM_SolarLongitudeAfter(MoladNisanPreviousYear,180)","v":{"v":738055.6547724518,"d":"738055.654772"}},{"$f":"\" \"&FixedToHebrewString(E152)&\" at \"&momenttoclock(E152,1)&\" after mean sunset\"","v":" Yom Rivii, 16 Tishrei, 5782 at 15h 42m 52s after mean sunset"}]
[null,null,"winter (270°)","תְקוּפָת טבת",{"$f":"RMBM_SolarLongitudeAfter(MoladNisanPreviousYear,270)","v":{"v":738145.3080326354,"d":"738145.308033"}},{"$f":"\" \"&FixedToHebrewString(E153)&\" at \"&momenttoclock(E153,1)&\" after mean sunset\"","v":" Yom Shlishi, 17 Tevet, 5782 at 7h 23m 34s after mean sunset"}]
[null,null,"spring (0°)","תְקוּפָת ניסן",{"$f":"RMBM_SolarLongitudeAfter(MoladTishreiTargetYear,0)","v":{"v":738234.3072850923,"d":"738234.307285"}},{"$f":"\" \"&FixedToHebrewString(E154)&\" at \"&momenttoclock(E154,1)&\" after mean sunset\"","v":" Yom Rishon, 17 Adar Sheini, 5782 at 7h 22m 29s after mean sunset"}]
[null,null,"summer (90°)","תְקוּפָת תמוז",{"$f":"RMBM_SolarLongitudeAfter(MoladTishreiTargetYear,90)","v":{"v":738327.2641881448,"d":"738327.264188"}},{"$f":"\" \"&FixedToHebrewString(E155)&\" at \"&momenttoclock(E155,1)&\" after mean sunset\"","v":" Yom Shlishi, 22 Sivan, 5782 at 6h 20m 26s after mean sunset"}]
[]
[14,null,"Lunar Position","מָקוֹם הַיָרֵחַ"]
[14,4,"Lunar Mean Longitude at Rambam Epoch","מָקוֹם אֶמצַע הַיָרֵחַ בְּעִקָר",{"$f":"DMStoDegrees(31,14,43)","v":31.24527777777778},{"$f":"DegreesToDMS(E158)","v":"31° 14' 43\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E158))","v":"Taurus 1° 14' 43\""}]
[14,2,"Lunar Mean Motion per Day","מַהֲלָך אֶמצַע הַיָרֵחַ יוֹמִי",13.1763972222222,{"$f":"DegreesToDMSTF(E159)","v":"13° 10' 35\" 1\"' 48\"\""},"based on 100 days"]
[null,null,{"v":10,"d":"10 "},null,{"$f":"C160*LunarMeanPerDay","v":131.76397222222198},{"$f":"DegreesToDMSTF(E160)","v":"131° 45' 50\" 18\"'"}]
[null,null,{"v":29,"d":"29 "},null,382.1155194444438,{"$f":"DegreesToDMST(E161)","v":"22° 6' 55\" 52\"'"}]
[null,null,{"v":100,"d":"100 "},null,1317.63972222222,{"$f":"DegreesToDMS(E162)","v":"237° 38' 23\""}]
[null,null,{"v":354,"d":"354 "},null,4664.4446166666585,"344° 26' 41\""]
[null,null,{"v":1000,"d":"1000 "},null,13176.3972222222,"216° 23' 50\""]
[null,null,{"v":10000,"d":"10000 "},null,131763.972222222,"3° 58' 20\""]
[14,5,"Lunar Position Adjustment",null,{"$f":"LunarMeanLongitude-modulus(E158+LunarMeanPerDay*(moment-RMBMepoch),360)","v":6.51925802230835e-09},"0°"]
[14,6,"Lunar Mean Ecliptic Longitude","מָקוֹם אֶמצַע הַיָרֵחַ",{"$f":"RMBM_LunarMeanLongitude(moment)","v":175.5067589697428},"175° 30' 24\"",{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E167))","v":"Virgo 25° 30' 24\""}]
[null,null,"Lunar Mean Elongation","מֶרְחָק הַיָרֵחַ",{"$f":"modulus(LunarMeanLongitude-SolarMeanLongitude,360)","v":8.219175347068813},{"$f":"DegreesToDMS(E168)","v":"8° 13' 9\""},"Always a small positive number on the eve of first lunar crescent sighting."]
[15,1,"Double Elongation","מֶרְחָק הַכָּפוּל",{"$f":"2*LunarMeanElongation","v":16.438350694137625},{"$f":"DegreesToDMS(E169)","v":"16° 26' 18\""}]
[]
[14,4,"Path Mean Longitude at Rambam Epoch","מָקוֹם אֶמצַע הַמַסלוּל בְּעִקָר",{"$f":"DMStoDegrees(84,28,42)","v":84.47833333333334},{"$f":"DegreesToDMS(E171)","v":"84° 28' 42\""}]
[14,3,"Lunar Path Mean Motion per Day","מַהֲלָך אֶמצַע הַמַסלוּל יוֹמִי",{"$f":"DMStoDegrees(13,3,53,55,48)","v":13.064980555555556},{"$f":"DegreesToDMSTF(E172)","v":"13° 3' 53\" 55\"' 48\"\""},"based on 100 days"]
[null,null,{"v":10,"d":"10 "},null,{"$f":"C173*LunarPathMeanPerDay","v":130.64980555555556},{"$f":"DegreesToDMSTF(E173)","v":"130° 38' 59\" 18\"'"}]
[null,null,{"v":29,"d":"29 "},null,378.8844361111111,{"$f":"DegreesToDMST(E174)","v":"18° 53' 3\" 58\"'"}]
[null,null,{"v":100,"d":"100 "},null,1306.4980555555555,{"$f":"DegreesToDMS(E175)","v":"226° 29' 53\""}]
[null,null,{"v":354,"d":"354 "},null,4625.003116666667,"305° 0' 11\""]
[null,null,{"v":1000,"d":"1000 "},null,13064.980555555556,"104° 58' 50\""]
[null,null,{"v":10000,"d":"10000 "},null,130649.80555555556,"329° 48' 20\""]
[14,3,"Lunar Path Mean Longitude","מָקוֹם אֶמצַע הַמַסלוּל",{"$f":"RMBM_LunarPathMeanLongitude(moment)","v":105.52418084582314},{"$f":"DegreesToDMS(E179)","v":"105° 31' 27\""}]
[15,3,"Amount to Add to Path Mean",null,{"$f":"RMBM_AddToMeanPath(DoubleElongation)","v":2},"2°","Based on double elongation to double its resolution"]
[15,"3 end","Correct Course","מַסלוּל הַנָכוֹן",{"$f":"modulus(LunarPathMeanLongitude+AddToPathMean,360)","v":107.52418084582314},"107° 31' 27\""]
[15,"5-6","Lunar Angle of Course","מְנָת מַסלוּל הַיָרֵחַ",{"$f":"RMBM_LunarAngleOfCourse(CorrectCourse)","v":-5.020470620645987},"-(5° 1' 14\")"]
[null,null,"Lunar True Ecliptic Longitude","מָקוֹם הַיָרֵחַ הַאֲמִתִי",{"$f":"LunarMeanLongitude+LunarAngleOfCourse","v":170.4862883490968},{"$f":"DegreesToDM(E183)","v":"170° 29'"},{"$f":"RMBM_DegreesInConstellation(RoundArcMinutes(E183))","v":"Virgo 20° 29'"}]
[]
[16,null,"Ascending & Descending Lunar Orbital Nodes","הַראשׁ וְהַזָנָב"]
[16,"end 2","Lunar Rosh Longitude at Rambam Epoch","(מָקוֹם הַראשׁ בְּעִקָר (מִזְרָחָה",{"$f":"DMStoDegrees(180,57,28)","v":180.95777777777778},{"$f":"DegreesToDMS(E186)","v":"180° 57' 28\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E186))&\" (epoch position east of equinox)\"","v":"Libra 0° 57' 28\" (epoch position east of equinox)"}]
[16,"end 5","360° - above because motion east to west","(מָקוֹם הַראשׁ בְּעִקָר (מערבה",{"$f":"360-E186","v":179.04222222222222},{"$f":"DegreesToDMS(E187)","v":"179° 2' 32\""},{"$f":"RMBM_DegreesInConstellation(RoundArcSeconds(E187))&\" (epoch position west of equinox)\"","v":"Virgo 29° 2' 32\" (epoch position west of equinox)"}]
[16,2,"Lunar Ascending Node Motion per Day","מַהֲלָך הַראשׁ יוֹמִי",{"$f":"(RMBM_LunarRoshLongitude(RMBMepoch)-RMBM_LunarRoshLongitude(RMBMepoch+100))/100","v":0.05295277777777784},{"$f":"DegreesToDMSTF(E188)","v":"0° 3' 10\" 37\"' 48\"\""},"east to west (retrograde, opposite to direction of lunar orbital motion)"]
[null,null,{"v":10,"d":"10 "},null,{"$f":"C189*RoshPerDay","v":0.5295277777777784},{"$f":"DegreesToDMSTF(E189)","v":"0° 31' 46\" 18\"'"}]
[null,null,{"v":29,"d":"29 "},null,{"$f":"C190*RoshPerDay","v":1.5356305555555574},{"$f":"DegreesToDMST(E190)","v":"1° 32' 8\" 16\"'"}]
[null,null,{"v":100,"d":"100 "},null,{"$f":"C191*RoshPerDay","v":5.295277777777784},{"$f":"DegreesToDMS(E191)","v":"5° 17' 43\""}]
[null,null,{"v":354,"d":"354 "},null,{"$f":"C192*RoshPerDay","v":18.745283333333354},"18° 44' 43\""]
[null,null,{"v":1000,"d":"1000 "},null,52.95277777777784,"52° 57' 10\""]
[null,null,{"v":10000,"d":"10000 "},null,529.5277777777784,"169° 31' 40\""]
[16,3,"Motion per Day times Elapsed Days",null,{"$f":"RoshPerDay*ElapsedDays","v":16312.726492766225},"112° 43' 35\""]
[16,3,"Add position of ascending node at Rambam epoch","תוסיף מָקוֹם הַראשׁ (מִזְרָחָה)",{"$f":"modulus(E195+E186,360)","v":293.6842705440031},"293° 41' 3\"","MOD 360°"]
[16,3,"Take from 360° = Longitude of ascending node","(מָקוֹם הַראשׁ (מערבה",{"$f":"360-E196","v":66.31572945599692},"66° 18' 57\"",{"$f":"RMBM_DegreesInConstellation(RoundArcMinutes(E197))","v":"Gemini 6° 19'"}]
["mine",null,"Simpler: epoch west minus total motion, MOD 360°","(מָקוֹם הַראשׁ (מערבה",{"$f":"modulus(E187-E195,360)","v":66.31572945599692},{"$f":"DegreesToDMS(E198)","v":"66° 18' 57\""},{"$f":"RMBM_DegreesInConstellation(RoundArcMinutes(E198))","v":"Gemini 6° 19'"}]
[16,6,"Longitude of descending node (= ascending+180°)","מָקוֹם הַזָנָב",{"$f":"modulus(LunarAscNodeLongitude+180,360)","v":246.31572945599692},"246° 18' 57\"",{"$f":"RMBM_DegreesInConstellation(RoundArcMinutes(E199))","v":"Sagittarius 6° 19'"}]
[]
[16,10,"Course of Lunar Latitude","מַסלוּל הַרוֹחַב ",{"$f":"modulus(LunarTrueLongitude-LunarAscNodeLongitude,360)","v":104.1705588930999},{"$f":"DegreesToDM(E201)","v":"104° 10'"},"(Lunar True Longitude - Lunar Rosh Longitude) MOD 360"]
[null,null,"Course converted to 0-90° range",null,{"$f":"IF(CourseLunarLat>270,360-CourseLunarLat,IF(CourseLunarLat>180,CourseLunarLat-180,IF(CourseLunarLat>90,180-CourseLunarLat)))","v":75.8294411069001},"75° 50'","0-90° range to match the text, but not used further herein"]
[16,"11-18","Table entry above course",{"$f":"CEILING(E202/10,1)*10","v":80},{"$f":"VLOOKUP(D203,'Lunar Latitude'!A1:D38,4,TRUE)","v":4.916666666666667},"4° 55'"]
[null,null,"Table entry below course",{"$f":"INT(E202/10)*10","v":70},{"$f":"VLOOKUP(D204,'Lunar Latitude'!A1:D38,4,TRUE)","v":4.7},"4° 42'"]
[16,"11-18","Table entry above course",{"$f":"CEILING(CourseLunarLat/10,1)*10","v":110},{"$f":"VLOOKUP(D205,'Lunar Latitude'!A1:D38,4,TRUE)","v":4.7},{"$f":"DegreesToDM(E205)","v":"4° 42'"}]
[null,null,"Table entry below course",{"$f":"INT(CourseLunarLat/10)*10","v":100},{"$f":"VLOOKUP(D206,'Lunar Latitude'!A1:D38,4,TRUE)","v":4.916666666666667},"4° 55'","positive = north, negative = south of the ecliptic"]
[null,null,"Difference",{"$f":"D205-D206","v":10},{"$f":"E205-E206","v":-0.21666666666666679},"-(0° 13')"]
[null,null,"Average change per degree from Ascending Node",1,{"$f":"(E205-E206)/D207","v":-0.021666666666666678},{"$f":"DegreesToDMS(E208)","v":"-(0° 1' 18\")"}]
[null,null,"Degrees beyond table entry below course",null,{"$f":"E201-D206","v":4.170558893099894},{"$f":"DegreesToDM(E209)","v":"4° 10'"}]
[16,"12-15","Amount to add to table entry below course","מְנָת הַמַסלוּל הַרוֹחַב ",{"$f":"E209*E208","v":-0.09036210935049775},"-(0° 5')"]
[null,null,"Lunar Latitude (linear interpolation)","רוֹחַב הַיָרֵחַ",{"$f":"E206+E210","v":4.82630455731617},{"$f":"DegreesToDM(ABS(E211))&IF(E211<0,\" South\",\" North\")","v":"4° 50' North"},"use sine interpolation (below) instead of this linear interpolation"]
["mine",null,"Lunar Latitude (sine interpolation)","רוֹחַב הַיָרֵחַ",{"$f":"5*SIN(RADIANS(E201))","v":4.847856358476611},{"$f":"DegreesToDM(ABS(E212))&IF(E212<0,\" South\",\" North\")","v":"4° 51' North"}]
[]
[17,null,"Visibility of the First Lunar Crescent","תצפיות של הירח"]
[{"$f":"A$214","v":17},1,"First Longitude (Moon - Sun along the ecliptic)","אוֹרֶך רִאשׁוֹן",{"$f":"modulus(LunarTrueLongitude-SolarTrueLongitude,360)","v":5.010362297796092},{"$f":"DegreesToDM(E215)","v":"5° 1'"},"On the eve of first lunar crescent sighting Moon is always <60° east of Sun"]
[null,null,"Within First Quarter",null,{"$f":"FirstLongitude<=90","v":true},null,"suppress crescent visibility prediction if beyond first quarter"]
[{"$f":"A$214","v":17},2,"First Latitude (=Lunar Ecliptic Latitude)","רוֹחַב רִאשׁוֹן",{"$f":"LunarLatitude","v":4.847856358476611},{"$f":"DegreesToDM(ABS(E217))&IF(E217<0,\" South\",\" North\")","v":"4° 51' North"}]
[{"$f":"A$214","v":17},4,"Lunar True Longitude Capricorn to Gemini?",null,{"$f":"OR(LunarTrueLongitude>=270,LunarTrueLongitude<90)","v":false}]
[17,3,"TRUE: First check (First Longitude 9-15°)","winter and spring",{"$f":"IF(CapricornToGemini,IF(FirstLongitude>90,\"Beyond first quarter\",IF(FirstLongitude<=9,\"Impossible to see crescent\",IF(FirstLongitude>15,\"Crescent will be visible\",\"Crescent might be visible\"))&\" in Israel\"),\"not applicable\")","v":"not applicable"},null,"Capricorn (G'di) = 270°, Gemini (T'omim) ends at 90°"]
[17,4,"FALSE: First check (First Longitude 10-24°)","summer and autumn",{"$f":"IF(NOT(CapricornToGemini),IF(FirstLongitude>90,\"Beyond first quarter\",IF(FirstLongitude<=10,\"Impossible to see Moon\",IF(FirstLongitude>24,\"Crescent will be visible\",\"Crescent might be visible\"))&\" in Israel\"),\"not applicable\")","v":"Impossible to see Moon in Israel"},null,"Cancer (Sartan) = 90°, Sagittarius (Keshet) ends at 270°"]
[17,5,"Longitude Sighting Adjustment","שִׁנוּי הַמַרְאֶה לאוֹרֶך",{"$f":"VLOOKUP(LunarTrueLongitude,Tables!A2:D13,4,TRUE)/60","v":0.6166666666666667},{"$f":"DegreesToDM(E221)","v":"0° 37'"},"geocentric to topocentric lunar parallax adjustment"]
[17,6,"Second Longitude","אוֹרֶך שֵׁנִי",{"$f":"FirstLongitude-E221","v":4.393695631129425},{"$f":"DegreesToDM(E222)","v":"4° 24'"},"Lunar longitude adjusted for observing from the surface"]
[17,8,"Latitude Sighting Adjustment","שִׁנוּי הַמַרְאֶה לרוֹחַב",{"$f":"VLOOKUP(LunarTrueLongitude,Tables!A2:E13,4,TRUE)/60","v":0.6166666666666667},{"$f":"DegreesToDM(E223)","v":"0° 37'"},"geocentric to topocentric lunar parallax adjustment"]
[17,"7,9","Second Latitude","רוֹחַב שֵׁנִי",{"$f":"FirstLatitude-E223","v":4.231189691809945},{"$f":"DegreesToDM(ABS(E224))&IF(E224<0,\" South\",\" North\")","v":"4° 14' North"},"Lunar latitude adjusted for observing from the surface"]
[17,10,"Proportion of Second Latitude to Separate",null,{"$f":"VLOOKUP(LunarTrueLongitude,Tables!A17:D46,4,TRUE)","v":0.4}]
[17,10,"Circuit of the Moon","מַעְגָל הַיָרֵחַ",{"$f":"ABS(E225*SecondLatitude)","v":1.692475876723978},{"$f":"DegreesToDM(E226)","v":"1° 42'"},"To correct for \"slight fluctuations in the lunar orbit\""]
[17,11,"Third Longitude","אוֹרֶך שְׁלִישִׁי",{"$f":"IF(CapricornToGemini,IF(LunarLatitude>0,SecondLongitude-CircuitOfTheMoon,SecondLongitude+CircuitOfTheMoon),IF(LunarLatitude>0,SecondLongitude+CircuitOfTheMoon,SecondLongitude-CircuitOfTheMoon))","v":6.086171507853403},{"$f":"DegreesToDM(E227)","v":"6° 5'"}]
[17,12,"Proportion of Third Longitude to Add",null,{"$f":"VLOOKUP(LunarTrueLongitude,Tables!B51:E62,4,TRUE)","v":-0.3333333333333333}]
[17,null,"Amount of Third Longitude to Add",null,{"$f":"E228*ThirdLongitude","v":-2.0287238359511344},{"$f":"DegreesToDM(E229)","v":"-(2° 2')"}]
[17,12,"Fourth Longitude","אוֹרֶך רְבִיעִי",{"$f":"ThirdLongitude+E228*ThirdLongitude","v":4.057447671902269},{"$f":"DegreesToDM(E230)","v":"4° 3'"}]
[17,12,"Geographic Latitude Correction","מְנָת גוֹבַה הַמְדִינָה",{"$f":"ABS(FirstLatitude)*2/3","v":3.2319042389844075},{"$f":"DegreesToDM(CorrectionLatitude)","v":"3° 14'"}]
[17,12,"Arc of Sighting","קֶשֶׁת הַרְאִיָה",{"$f":"IF(WithinFirstQuarter,IF(LunarLatitude>0,FourthLongitude+CorrectionLatitude,FourthLongitude-CorrectionLatitude),0)","v":7.289351910886676},{"$f":"DegreesToDM(ArcOfSighting)","v":"7° 17'"},"altitude of Moon - altitude of Sun, measured along the celestial equator"]
[{"$nulls":6},"divided by 4 = Moon set time lag (minutes) after Sun set"]
[17,15,"Visible? (<=9° impossible, >=14° easy)",null,{"$f":"IF(WithinFirstQuarter,IF(ArcOfSighting<=9,\"impossible\",IF(ArcOfSighting>=14,\"easy\",\"maybe\")),\"\")","v":"impossible"}]
[17,17,"Arc >=9° and 1st longitude >=13°?",null,{"$f":"IF(WithinFirstQuarter,AND(ArcOfSighting>=9,FirstLongitude>=13),\"\")","v":false}]
[17,18,"Arc >=10° and 1st longitude >=12°?",null,{"$f":"IF(WithinFirstQuarter,AND(ArcOfSighting>=10,FirstLongitude>=12),\"\")","v":false}]
[17,19,"Arc >=11° and 1st longitude >=11°?",null,{"$f":"IF(WithinFirstQuarter,AND(ArcOfSighting>=11,FirstLongitude>=11),\"\")","v":false}]
[17,20,"Arc >=12° and 1st longitude >=10°?",null,{"$f":"IF(WithinFirstQuarter,AND(ArcOfSighting>=12,FirstLongitude>=10),\"\")","v":false}]
[17,21,"Arc >=13° and 1st longitude >=9°?",null,{"$f":"IF(WithinFirstQuarter,AND(ArcOfSighting>=13,FirstLongitude>=9),\"\")","v":false}]
[null,null,"Visible? (any of the above = TRUE)",null,{"$f":"IF(WithinFirstQuarter,IF(OR(E235:E239),\"YES\",\"NO\"),\"\")","v":"NO"}]
["mine",null,"Arc >=9° and 1st longitude >= (22° – Arc)?",null,{"$f":"IF(AND(ArcOfSighting>=9,FirstLongitude>=22-ArcOfSighting),\"YES\",\"NO\")","v":"NO"},null,"Single expression equivalent to #15 through #21."]
[]
[19,null,"Direction and Orientation of the First Visible Lunar Crescent"]
[19,"5-9","Earth Axial Tilt (maximum declination)","נְטִיָה גַלגַל הַשֶׁמֶשׁ",23.5,{"$f":"DegreesToDM(AxialTilt)","v":"23° 30'"},"was about 23.5° in era of Rambam, declining, presently about 23.4°"]
[null,null,"Solar Declination","נְטִיָה הַשֶׁמֶשׁ",{"$f":"RMBM_Declination(E144,AxialTilt)","v":5.8934890530402075},{"$f":"DegreesToDM(ABS(E245))&IF(E245<0,\" South\",\" North\")","v":"5° 54' North"}]
[19,10,"Lunar Declination","נְטִיָה הַיָרֵחַ",{"$f":"RMBM_Declination(LunarTrueLongitude,AxialTilt)+LunarLatitude","v":8.73202172331434},{"$f":"DegreesToDM(ABS(E246))&IF(E246<0,\" South\",\" North\")","v":"8° 44' North"}]
[19,"12-14","Appearance of Lunar Crescent",null,{"$f":"IF(VisibleQ=\"YES\",\"Crescent \"&IF(ABS(LunarDeclination)<3,\"due W, curve to E\",IF(LunarDeclination<0,\"in SW, curve to NE\",\"in NW, curve to SE\")),\"\")","v":""}]
[]
[19,15,"How high in the sky will the new lunar crescent be?  Approximately equal to the Arc of Sighting."]

{"sheet":"Zodiac Start Mid","index":1,"n_rows":25,"n_cols":4,"rows_kept":25}
["Longitude","Classic","Hebrew","English"]
[0,{"$f":"DegreesInConstellationClassic($A2)","v":"Aries 0°"},{"$f":"DegreesInConstellationHebrew($A2)","v":"Taleh 0°"},{"$f":"DegreesInConstellationEnglish($A2)","v":"Lamb 0°"}]
[{"$f":"A2+15","v":15},"Aries 15°","Taleh 15°","Lamb 15°"]
[30,"Taurus 0°","Shor 0°","Bull 0°"]
[45,"Taurus 15°","Shor 15°","Bull 15°"]
[60,"Gemini 0°","T'omim 0°","Twins 0°"]
[75,"Gemini 15°","T'omim 15°","Twins 15°"]
[90,"Cancer 0°","Sartan 0°","Crab 0°"]
[105,"Cancer 15°","Sartan 15°","Crab 15°"]
[120,"Leo 0°","Aryeh 0°","Lion 0°"]
[135,"Leo 15°","Aryeh 15°","Lion 15°"]
[150,"Virgo 0°","Betulah 0°","Virgin 0°"]
[165,"Virgo 15°","Betulah 15°","Virgin 15°"]
[180,"Libra 0°","Moznaim 0°","Scales 0°"]
[195,"Libra 15°","Moznaim 15°","Scales 15°"]
[210,"Scorpio 0°","Akrav 0°","Scorpion 0°"]
[225,"Scorpio 15°","Akrav 15°","Scorpion 15°"]
[240,"Sagittarius 0°","Keshet 0°","Bow 0°"]
[255,"Sagittarius 15°","Keshet 15°","Bow 15°"]
[270,"Capricorn 0°","G'di 0°","Kid 0°"]
[285,"Capricorn 15°","G'di 15°","Kid 15°"]
[300,"Aquarius 0°","D'li 0°","Water Bucket 0°"]
[315,"Aquarius 15°","D'li 15°","Water Bucket 15°"]
[330,"Pisces 0°","Dagim 0°","Fish 0°"]
[345,"Pisces 15°","Dagim 15°","Fish 15°"]

{"sheet":"Zodiac Each Degree","index":2,"n_rows":181,"n_cols":8,"rows_kept":181}
["Longitude","Classic","Hebrew","English","Longitude","Classic","Hebrew","English"]
[0,{"$f":"DegreesInConstellationClassic($A2)","v":"Aries 0°"},{"$f":"DegreesInConstellationHebrew($A2)","v":"Taleh 0°"},{"$f":"DegreesInConstellationEnglish($A2)","v":"Lamb 0°"},{"$f":"A181+1","v":180},{"$f":"DegreesInConstellationClassic($E2)","v":"Libra 0°"},{"$f":"DegreesInConstellationHebrew($E2)","v":"Moznaim 0°"},{"$f":"DegreesInConstellationEnglish($E2)","v":"Scales 0°"}]
[{"$f":"A2+1","v":1},{"$f":"DegreesInConstellationClassic($A3)","v":"Aries 1°"},{"$f":"DegreesInConstellationHebrew($A3)","v":"Taleh 1°"},{"$f":"DegreesInConstellationEnglish($A3)","v":"Lamb 1°"},{"$f":"E2+1","v":181},"Libra 1°","Moznaim 1°","Scales 1°"]
[2,"Aries 2°","Taleh 2°","Lamb 2°",182,"Libra 2°","Moznaim 2°","Scales 2°"]
[3,"Aries 3°","Taleh 3°","Lamb 3°",183,"Libra 3°","Moznaim 3°","Scales 3°"]
[4,"Aries 4°","Taleh 4°","Lamb 4°",184,"Libra 4°","Moznaim 4°","Scales 4°"]
[5,"Aries 5°","Taleh 5°","Lamb 5°",185,"Libra 5°","Moznaim 5°","Scales 5°"]
[6,"Aries 6°","Taleh 6°","Lamb 6°",186,"Libra 6°","Moznaim 6°","Scales 6°"]
[7,"Aries 7°","Taleh 7°","Lamb 7°",187,"Libra 7°","Moznaim 7°","Scales 7°"]
[8,"Aries 8°","Taleh 8°","Lamb 8°",188,"Libra 8°","Moznaim 8°","Scales 8°"]
[9,"Aries 9°","Taleh 9°","Lamb 9°",189,"Libra 9°","Moznaim 9°","Scales 9°"]
[10,"Aries 10°","Taleh 10°","Lamb 10°",190,"Libra 10°","Moznaim 10°","Scales 10°"]
[11,"Aries 11°","Taleh 11°","Lamb 11°",191,"Libra 11°","Moznaim 11°","Scales 11°"]
[12,"Aries 12°","Taleh 12°","Lamb 12°",192,"Libra 12°","Moznaim 12°","Scales 12°"]
[13,"Aries 13°","Taleh 13°","Lamb 13°",193,"Libra 13°","Moznaim 13°","Scales 13°"]
[14,"Aries 14°","Taleh 14°","Lamb 14°",194,"Libra 14°","Moznaim 14°","Scales 14°"]
[15,"Aries 15°","Taleh 15°","Lamb 15°",195,"Libra 15°","Moznaim 15°","Scales 15°"]
[16,"Aries 16°","Taleh 16°","Lamb 16°",196,"Libra 16°","Moznaim 16°","Scales 16°"]
[17,"Aries 17°","Taleh 17°","Lamb 17°",197,"Libra 17°","Moznaim 17°","Scales 17°"]
[18,"Aries 18°","Taleh 18°","Lamb 18°",198,"Libra 18°","Moznaim 18°","Scales 18°"]
[19,"Aries 19°","Taleh 19°","Lamb 19°",199,"Libra 19°","Moznaim 19°","Scales 19°"]
[20,"Aries 20°","Taleh 20°","Lamb 20°",200,"Libra 20°","Moznaim 20°","Scales 20°"]
[21,"Aries 21°","Taleh 21°","Lamb 21°",201,"Libra 21°","Moznaim 21°","Scales 21°"]
[22,"Aries 22°","Taleh 22°","Lamb 22°",202,"Libra 22°","Moznaim 22°","Scales 22°"]
[23,"Aries 23°","Taleh 23°","Lamb 23°",203,"Libra 23°","Moznaim 23°","Scales 23°"]
[24,"Aries 24°","Taleh 24°","Lamb 24°",204,"Libra 24°","Moznaim 24°","Scales 24°"]
[25,"Aries 25°","Taleh 25°","Lamb 25°",205,"Libra 25°","Moznaim 25°","Scales 25°"]
[26,"Aries 26°","Taleh 26°","Lamb 26°",206,"Libra 26°","Moznaim 26°","Scales 26°"]
[27,"Aries 27°","Taleh 27°","Lamb 27°",207,"Libra 27°","Moznaim 27°","Scales 27°"]
[28,"Aries 28°","Taleh 28°","Lamb 28°",208,"Libra 28°","Moznaim 28°","Scales 28°"]
[29,"Aries 29°","Taleh 29°","Lamb 29°",209,"Libra 29°","Moznaim 29°","Scales 29°"]
[30,"Taurus 0°","Shor 0°","Bull 0°",210,"Scorpio 0°","Akrav 0°","Scorpion 0°"]
[31,"Taurus 1°","Shor 1°","Bull 1°",211,"Scorpio 1°","Akrav 1°","Scorpion 1°"]
[32,{"$f":"DegreesInConstellationClassic($A34)","v":"Taurus 2°"},{"$f":"DegreesInConstellationHebrew($A34)","v":"Shor 2°"},{"$f":"DegreesInConstellationEnglish($A34)","v":"Bull 2°"},212,{"$f":"DegreesInConstellationClassic($E34)","v":"Scorpio 2°"},{"$f":"DegreesInConstellationHebrew($E34)","v":"Akrav 2°"},{"$f":"DegreesInConstellationEnglish($E34)","v":"Scorpion 2°"}]
[{"$f":"A34+1","v":33},"Taurus 3°","Shor 3°","Bull 3°",{"$f":"E34+1","v":213},"Scorpio 3°","Akrav 3°","Scorpion 3°"]
[34,"Taurus 4°","Shor 4°","Bull 4°",214,"Scorpio 4°","Akrav 4°","Scorpion 4°"]
[35,"Taurus 5°","Shor 5°","Bull 5°",215,"Scorpio 5°","Akrav 5°","Scorpion 5°"]
[36,"Taurus 6°","Shor 6°","Bull 6°",216,"Scorpio 6°","Akrav 6°","Scorpion 6°"]
[37,"Taurus 7°","Shor 7°","Bull 7°",217,"Scorpio 7°","Akrav 7°","Scorpion 7°"]
[38,"Taurus 8°","Shor 8°","Bull 8°",218,"Scorpio 8°","Akrav 8°","Scorpion 8°"]
[39,"Taurus 9°","Shor 9°","Bull 9°",219,"Scorpio 9°","Akrav 9°","Scorpion 9°"]
[40,"Taurus 10°","Shor 10°","Bull 10°",220,"Scorpio 10°","Akrav 10°","Scorpion 10°"]
[41,"Taurus 11°","Shor 11°","Bull 11°",221,"Scorpio 11°","Akrav 11°","Scorpion 11°"]
[42,"Taurus 12°","Shor 12°","Bull 12°",222,"Scorpio 12°","Akrav 12°","Scorpion 12°"]
[43,"Taurus 13°","Shor 13°","Bull 13°",223,"Scorpio 13°","Akrav 13°","Scorpion 13°"]
[44,"Taurus 14°","Shor 14°","Bull 14°",224,"Scorpio 14°","Akrav 14°","Scorpion 14°"]
[45,"Taurus 15°","Shor 15°","Bull 15°",225,"Scorpio 15°","Akrav 15°","Scorpion 15°"]
[46,"Taurus 16°","Shor 16°","Bull 16°",226,"Scorpio 16°","Akrav 16°","Scorpion 16°"]
[47,"Taurus 17°","Shor 17°","Bull 17°",227,"Scorpio 17°","Akrav 17°","Scorpion 17°"]
[48,"Taurus 18°","Shor 18°","Bull 18°",228,"Scorpio 18°","Akrav 18°","Scorpion 18°"]
[49,"Taurus 19°","Shor 19°","Bull 19°",229,"Scorpio 19°","Akrav 19°","Scorpion 19°"]
[50,"Taurus 20°","Shor 20°","Bull 20°",230,"Scorpio 20°","Akrav 20°","Scorpion 20°"]
[51,"Taurus 21°","Shor 21°","Bull 21°",231,"Scorpio 21°","Akrav 21°","Scorpion 21°"]
[52,"Taurus 22°","Shor 22°","Bull 22°",232,"Scorpio 22°","Akrav 22°","Scorpion 22°"]
[53,"Taurus 23°","Shor 23°","Bull 23°",233,"Scorpio 23°","Akrav 23°","Scorpion 23°"]
[54,"Taurus 24°","Shor 24°","Bull 24°",234,"Scorpio 24°","Akrav 24°","Scorpion 24°"]
[55,"Taurus 25°","Shor 25°","Bull 25°",235,"Scorpio 25°","Akrav 25°","Scorpion 25°"]
[56,"Taurus 26°","Shor 26°","Bull 26°",236,"Scorpio 26°","Akrav 26°","Scorpion 26°"]
[57,"Taurus 27°","Shor 27°","Bull 27°",237,"Scorpio 27°","Akrav 27°","Scorpion 27°"]
[58,"Taurus 28°","Shor 28°","Bull 28°",238,"Scorpio 28°","Akrav 28°","Scorpion 28°"]
[59,"Taurus 29°","Shor 29°","Bull 29°",239,"Scorpio 29°","Akrav 29°","Scorpion 29°"]
[60,"Gemini 0°","T'omim 0°","Twins 0°",240,"Sagittarius 0°","Keshet 0°","Bow 0°"]
[61,"Gemini 1°","T'omim 1°","Twins 1°",241,"Sagittarius 1°","Keshet 1°","Bow 1°"]
[62,"Gemini 2°","T'omim 2°","Twins 2°",242,"Sagittarius 2°","Keshet 2°","Bow 2°"]
[63,"Gemini 3°","T'omim 3°","Twins 3°",243,"Sagittarius 3°","Keshet 3°","Bow 3°"]
[64,{"$f":"DegreesInConstellationClassic($A66)","v":"Gemini 4°"},{"$f":"DegreesInConstellationHebrew($A66)","v":"T'omim 4°"},{"$f":"DegreesInConstellationEnglish($A66)","v":"Twins 4°"},244,{"$f":"DegreesInConstellationClassic($E66)","v":"Sagittarius 4°"},{"$f":"DegreesInConstellationHebrew($E66)","v":"Keshet 4°"},{"$f":"DegreesInConstellationEnglish($E66)","v":"Bow 4°"}]
[{"$f":"A66+1","v":65},"Gemini 5°","T'omim 5°","Twins 5°",{"$f":"E66+1","v":245},"Sagittarius 5°","Keshet 5°","Bow 5°"]
[66,"Gemini 6°","T'omim 6°","Twins 6°",246,"Sagittarius 6°","Keshet 6°","Bow 6°"]
[67,"Gemini 7°","T'omim 7°","Twins 7°",247,"Sagittarius 7°","Keshet 7°","Bow 7°"]
[68,"Gemini 8°","T'omim 8°","Twins 8°",248,"Sagittarius 8°","Keshet 8°","Bow 8°"]
[69,"Gemini 9°","T'omim 9°","Twins 9°",249,"Sagittarius 9°","Keshet 9°","Bow 9°"]
[70,"Gemini 10°","T'omim 10°","Twins 10°",250,"Sagittarius 10°","Keshet 10°","Bow 10°"]
[71,"Gemini 11°","T'omim 11°","Twins 11°",251,"Sagittarius 11°","Keshet 11°","Bow 11°"]
[72,"Gemini 12°","T'omim 12°","Twins 12°",252,"Sagittarius 12°","Keshet 12°","Bow 12°"]
[73,"Gemini 13°","T'omim 13°","Twins 13°",253,"Sagittarius 13°","Keshet 13°","Bow 13°"]
[74,"Gemini 14°","T'omim 14°","Twins 14°",254,"Sagittarius 14°","Keshet 14°","Bow 14°"]
[75,"Gemini 15°","T'omim 15°","Twins 15°",255,"Sagittarius 15°","Keshet 15°","Bow 15°"]
[76,"Gemini 16°","T'omim 16°","Twins 16°",256,"Sagittarius 16°","Keshet 16°","Bow 16°"]
[77,"Gemini 17°","T'omim 17°","Twins 17°",257,"Sagittarius 17°","Keshet 17°","Bow 17°"]
[78,"Gemini 18°","T'omim 18°","Twins 18°",258,"Sagittarius 18°","Keshet 18°","Bow 18°"]
[79,"Gemini 19°","T'omim 19°","Twins 19°",259,"Sagittarius 19°","Keshet 19°","Bow 19°"]
[80,"Gemini 20°","T'omim 20°","Twins 20°",260,"Sagittarius 20°","Keshet 20°","Bow 20°"]
[81,"Gemini 21°","T'omim 21°","Twins 21°",261,"Sagittarius 21°","Keshet 21°","Bow 21°"]
[82,"Gemini 22°","T'omim 22°","Twins 22°",262,"Sagittarius 22°","Keshet 22°","Bow 22°"]
[83,"Gemini 23°","T'omim 23°","Twins 23°",263,"Sagittarius 23°","Keshet 23°","Bow 23°"]
[84,"Gemini 24°","T'omim 24°","Twins 24°",264,"Sagittarius 24°","Keshet 24°","Bow 24°"]
[85,"Gemini 25°","T'omim 25°","Twins 25°",265,"Sagittarius 25°","Keshet 25°","Bow 25°"]
[86,"Gemini 26°","T'omim 26°","Twins 26°",266,"Sagittarius 26°","Keshet 26°","Bow 26°"]
[87,"Gemini 27°","T'omim 27°","Twins 27°",267,"Sagittarius 27°","Keshet 27°","Bow 27°"]
[88,"Gemini 28°","T'omim 28°","Twins 28°",268,"Sagittarius 28°","Keshet 28°","Bow 28°"]
[89,"Gemini 29°","T'omim 29°","Twins 29°",269,"Sagittarius 29°","Keshet 29°","Bow 29°"]
[90,"Cancer 0°","Sartan 0°","Crab 0°",270,"Capricorn 0°","G'di 0°","Kid 0°"]
[91,"Cancer 1°","Sartan 1°","Crab 1°",271,"Capricorn 1°","G'di 1°","Kid 1°"]
[92,"Cancer 2°","Sartan 2°","Crab 2°",272,"Capricorn 2°","G'di 2°","Kid 2°"]
[93,"Cancer 3°","Sartan 3°","Crab 3°",273,"Capricorn 3°","G'di 3°","Kid 3°"]
[94,"Cancer 4°","Sartan 4°","Crab 4°",274,"Capricorn 4°","G'di 4°","Kid 4°"]
[95,"Cancer 5°","Sartan 5°","Crab 5°",275,"Capricorn 5°","G'di 5°","Kid 5°"]
[96,{"$f":"DegreesInConstellationClassic($A98)","v":"Cancer 6°"},{"$f":"DegreesInConstellationHebrew($A98)","v":"Sartan 6°"},{"$f":"DegreesInConstellationEnglish($A98)","v":"Crab 6°"},276,{"$f":"DegreesInConstellationClassic($E98)","v":"Capricorn 6°"},{"$f":"DegreesInConstellationHebrew($E98)","v":"G'di 6°"},{"$f":"DegreesInConstellationEnglish($E98)","v":"Kid 6°"}]
[{"$f":"A98+1","v":97},"Cancer 7°","Sartan 7°","Crab 7°",{"$f":"E98+1","v":277},"Capricorn 7°","G'di 7°","Kid 7°"]
[98,"Cancer 8°","Sartan 8°","Crab 8°",278,"Capricorn 8°","G'di 8°","Kid 8°"]
[99,"Cancer 9°","Sartan 9°","Crab 9°",279,"Capricorn 9°","G'di 9°","Kid 9°"]
[100,"Cancer 10°","Sartan 10°","Crab 10°",280,"Capricorn 10°","G'di 10°","Kid 10°"]
[101,"Cancer 11°","Sartan 11°","Crab 11°",281,"Capricorn 11°","G'di 11°","Kid 11°"]
[102,"Cancer 12°","Sartan 12°","Crab 12°",282,"Capricorn 12°","G'di 12°","Kid 12°"]
[103,"Cancer 13°","Sartan 13°","Crab 13°",283,"Capricorn 13°","G'di 13°","Kid 13°"]
[104,"Cancer 14°","Sartan 14°","Crab 14°",284,"Capricorn 14°","G'di 14°","Kid 14°"]
[105,"Cancer 15°","Sartan 15°","Crab 15°",285,"Capricorn 15°","G'di 15°","Kid 15°"]
[106,"Cancer 16°","Sartan 16°","Crab 16°",286,"Capricorn 16°","G'di 16°","Kid 16°"]
[107,"Cancer 17°","Sartan 17°","Crab 17°",287,"Capricorn 17°","G'di 17°","Kid 17°"]
[108,"Cancer 18°","Sartan 18°","Crab 18°",288,"Capricorn 18°","G'di 18°","Kid 18°"]
[109,"Cancer 19°","Sartan 19°","Crab 19°",289,"Capricorn 19°","G'di 19°","Kid 19°"]
[110,"Cancer 20°","Sartan 20°","Crab 20°",290,"Capricorn 20°","G'di 20°","Kid 20°"]
[111,"Cancer 21°","Sartan 21°","Crab 21°",291,"Capricorn 21°","G'di 21°","Kid 21°"]
[112,"Cancer 22°","Sartan 22°","Crab 22°",292,"Capricorn 22°","G'di 22°","Kid 22°"]
[113,"Cancer 23°","Sartan 23°","Crab 23°",293,"Capricorn 23°","G'di 23°","Kid 23°"]
[114,"Cancer 24°","Sartan 24°","Crab 24°",294,"Capricorn 24°","G'di 24°","Kid 24°"]
[115,"Cancer 25°","Sartan 25°","Crab 25°",295,"Capricorn 25°","G'di 25°","Kid 25°"]
[116,"Cancer 26°","Sartan 26°","Crab 26°",296,"Capricorn 26°","G'di 26°","Kid 26°"]
[117,"Cancer 27°","Sartan 27°","Crab 27°",297,"Capricorn 27°","G'di 27°","Kid 27°"]
[118,"Cancer 28°","Sartan 28°","Crab 28°",298,"Capricorn 28°","G'di 28°","Kid 28°"]
[119,"Cancer 29°","Sartan 29°","Crab 29°",299,"Capricorn 29°","G'di 29°","Kid 29°"]
[120,"Leo 0°","Aryeh 0°","Lion 0°",300,"Aquarius 0°","D'li 0°","Water Bucket 0°"]
[121,"Leo 1°","Aryeh 1°","Lion 1°",301,"Aquarius 1°","D'li 1°","Water Bucket 1°"]
[122,"Leo 2°","Aryeh 2°","Lion 2°",302,"Aquarius 2°","D'li 2°","Water Bucket 2°"]
[123,"Leo 3°","Aryeh 3°","Lion 3°",303,"Aquarius 3°","D'li 3°","Water Bucket 3°"]
[124,"Leo 4°","Aryeh 4°","Lion 4°",304,"Aquarius 4°","D'li 4°","Water Bucket 4°"]
[125,"Leo 5°","Aryeh 5°","Lion 5°",305,"Aquarius 5°","D'li 5°","Water Bucket 5°"]
[126,"Leo 6°","Aryeh 6°","Lion 6°",306,"Aquarius 6°","D'li 6°","Water Bucket 6°"]
[127,"Leo 7°","Aryeh 7°","Lion 7°",307,"Aquarius 7°","D'li 7°","Water Bucket 7°"]
[128,{"$f":"DegreesInConstellationClassic($A130)","v":"Leo 8°"},{"$f":"DegreesInConstellationHebrew($A130)","v":"Aryeh 8°"},{"$f":"DegreesInConstellationEnglish($A130)","v":"Lion 8°"},308,{"$f":"DegreesInConstellationClassic($E130)","v":"Aquarius 8°"},{"$f":"DegreesInConstellationHebrew($E130)","v":"D'li 8°"},{"$f":"DegreesInConstellationEnglish($E130)","v":"Water Bucket 8°"}]
[{"$f":"A130+1","v":129},"Leo 9°","Aryeh 9°","Lion 9°",{"$f":"E130+1","v":309},"Aquarius 9°","D'li 9°","Water Bucket 9°"]
[130,"Leo 10°","Aryeh 10°","Lion 10°",310,"Aquarius 10°","D'li 10°","Water Bucket 10°"]
[131,"Leo 11°","Aryeh 11°","Lion 11°",311,"Aquarius 11°","D'li 11°","Water Bucket 11°"]
[132,"Leo 12°","Aryeh 12°","Lion 12°",312,"Aquarius 12°","D'li 12°","Water Bucket 12°"]
[133,"Leo 13°","Aryeh 13°","Lion 13°",313,"Aquarius 13°","D'li 13°","Water Bucket 13°"]
[134,"Leo 14°","Aryeh 14°","Lion 14°",314,"Aquarius 14°","D'li 14°","Water Bucket 14°"]
[135,"Leo 15°","Aryeh 15°","Lion 15°",315,"Aquarius 15°","D'li 15°","Water Bucket 15°"]
[136,"Leo 16°","Aryeh 16°","Lion 16°",316,"Aquarius 16°","D'li 16°","Water Bucket 16°"]
[137,"Leo 17°","Aryeh 17°","Lion 17°",317,"Aquarius 17°","D'li 17°","Water Bucket 17°"]
[138,"Leo 18°","Aryeh 18°","Lion 18°",318,"Aquarius 18°","D'li 18°","Water Bucket 18°"]
[139,"Leo 19°","Aryeh 19°","Lion 19°",319,"Aquarius 19°","D'li 19°","Water Bucket 19°"]
[140,"Leo 20°","Aryeh 20°","Lion 20°",320,"Aquarius 20°","D'li 20°","Water Bucket 20°"]
[141,"Leo 21°","Aryeh 21°","Lion 21°",321,"Aquarius 21°","D'li 21°","Water Bucket 21°"]
[142,"Leo 22°","Aryeh 22°","Lion 22°",322,"Aquarius 22°","D'li 22°","Water Bucket 22°"]
[143,"Leo 23°","Aryeh 23°","Lion 23°",323,"Aquarius 23°","D'li 23°","Water Bucket 23°"]
[144,"Leo 24°","Aryeh 24°","Lion 24°",324,"Aquarius 24°","D'li 24°","Water Bucket 24°"]
[145,"Leo 25°","Aryeh 25°","Lion 25°",325,"Aquarius 25°","D'li 25°","Water Bucket 25°"]
[146,"Leo 26°","Aryeh 26°","Lion 26°",326,"Aquarius 26°","D'li 26°","Water Bucket 26°"]
[147,"Leo 27°","Aryeh 27°","Lion 27°",327,"Aquarius 27°","D'li 27°","Water Bucket 27°"]
[148,"Leo 28°","Aryeh 28°","Lion 28°",328,"Aquarius 28°","D'li 28°","Water Bucket 28°"]
[149,"Leo 29°","Aryeh 29°","Lion 29°",329,"Aquarius 29°","D'li 29°","Water Bucket 29°"]
[150,"Virgo 0°","Betulah 0°","Virgin 0°",330,"Pisces 0°","Dagim 0°","Fish 0°"]
[151,"Virgo 1°","Betulah 1°","Virgin 1°",331,"Pisces 1°","Dagim 1°","Fish 1°"]
[152,"Virgo 2°","Betulah 2°","Virgin 2°",332,"Pisces 2°","Dagim 2°","Fish 2°"]
[153,"Virgo 3°","Betulah 3°","Virgin 3°",333,"Pisces 3°","Dagim 3°","Fish 3°"]
[154,"Virgo 4°","Betulah 4°","Virgin 4°",334,"Pisces 4°","Dagim 4°","Fish 4°"]
[155,"Virgo 5°","Betulah 5°","Virgin 5°",335,"Pisces 5°","Dagim 5°","Fish 5°"]
[156,"Virgo 6°","Betulah 6°","Virgin 6°",336,"Pisces 6°","Dagim 6°","Fish 6°"]
[157,"Virgo 7°","Betulah 7°","Virgin 7°",337,"Pisces 7°","Dagim 7°","Fish 7°"]
[158,"Virgo 8°","Betulah 8°","Virgin 8°",338,"Pisces 8°","Dagim 8°","Fish 8°"]
[159,"Virgo 9°","Betulah 9°","Virgin 9°",339,"Pisces 9°","Dagim 9°","Fish 9°"]
[160,{"$f":"DegreesInConstellationClassic($A162)","v":"Virgo 10°"},{"$f":"DegreesInConstellationHebrew($A162)","v":"Betulah 10°"},{"$f":"DegreesInConstellationEnglish($A162)","v":"Virgin 10°"},340,{"$f":"DegreesInConstellationClassic($E162)","v":"Pisces 10°"},{"$f":"DegreesInConstellationHebrew($E162)","v":"Dagim 10°"},{"$f":"DegreesInConstellationEnglish($E162)","v":"Fish 10°"}]
[{"$f":"A162+1","v":161},"Virgo 11°","Betulah 11°","Virgin 11°",{"$f":"E162+1","v":341},"Pisces 11°","Dagim 11°","Fish 11°"]
[162,"Virgo 12°","Betulah 12°","Virgin 12°",342,"Pisces 12°","Dagim 12°","Fish 12°"]
[163,"Virgo 13°","Betulah 13°","Virgin 13°",343,"Pisces 13°","Dagim 13°","Fish 13°"]
[164,"Virgo 14°","Betulah 14°","Virgin 14°",344,"Pisces 14°","Dagim 14°","Fish 14°"]
[165,"Virgo 15°","Betulah 15°","Virgin 15°",345,"Pisces 15°","Dagim 15°","Fish 15°"]
[166,"Virgo 16°","Betulah 16°","Virgin 16°",346,"Pisces 16°","Dagim 16°","Fish 16°"]
[167,"Virgo 17°","Betulah 17°","Virgin 17°",347,"Pisces 17°","Dagim 17°","Fish 17°"]
[168,"Virgo 18°","Betulah 18°","Virgin 18°",348,"Pisces 18°","Dagim 18°","Fish 18°"]
[169,"Virgo 19°","Betulah 19°","Virgin 19°",349,"Pisces 19°","Dagim 19°","Fish 19°"]
[170,"Virgo 20°","Betulah 20°","Virgin 20°",350,"Pisces 20°","Dagim 20°","Fish 20°"]
[171,"Virgo 21°","Betulah 21°","Virgin 21°",351,"Pisces 21°","Dagim 21°","Fish 21°"]
[172,"Virgo 22°","Betulah 22°","Virgin 22°",352,"Pisces 22°","Dagim 22°","Fish 22°"]
[173,"Virgo 23°","Betulah 23°","Virgin 23°",353,"Pisces 23°","Dagim 23°","Fish 23°"]
[174,"Virgo 24°","Betulah 24°","Virgin 24°",354,"Pisces 24°","Dagim 24°","Fish 24°"]
[175,"Virgo 25°","Betulah 25°","Virgin 25°",355,"Pisces 25°","Dagim 25°","Fish 25°"]
[176,"Virgo 26°","Betulah 26°","Virgin 26°",356,"Pisces 26°","Dagim 26°","Fish 26°"]
[177,"Virgo 27°","Betulah 27°","Virgin 27°",357,"Pisces 27°","Dagim 27°","Fish 27°"]
[178,"Virgo 28°","Betulah 28°","Virgin 28°",358,"Pisces 28°","Dagim 28°","Fish 28°"]
[179,"Virgo 29°","Betulah 29°","Virgin 29°",359,"Pisces 29°","Dagim 29°","Fish 29°"]

{"sheet":"Tables","index":3,"n_rows":112,"n_cols":7,"rows_kept":112}
["Lunar Long","Constellation","Hebrew","Long Subtract","Lat Subtract"]
[0,{"$f":"RMBM_DegreesInConstellation(A2)","v":"Aries 0°"},{"$f":"DegreesInConstellationHebrew(A2)","v":"Taleh 0°"},59,9]
[30,{"$f":"RMBM_DegreesInConstellation(A3)","v":"Taurus 0°"},"Shor 0°",60,10]
[60,"Gemini 0°","T'omim 0°",58,16]
[90,"Cancer 0°","Sartan 0°",52,27]
[120,"Leo 0°","Aryeh 0°",43,38]
[150,"Virgo 0°","Betulah 0°",37,44]
[180,"Libra 0°","Moznaim 0°",34,46]
[210,"Scorpio 0°","Akrav 0°",34,45]
[240,"Sagittarius 0°","Keshet 0°",36,44]
[270,"Capricorn 0°","G'di 0°",44,36]
[300,"Aquarius 0°","D'li 0°",53,27]
[330,"Pisces 0°","Dagim 0°",58,12]
[]
["Second Latitude amount to set aside (chapter 17 #10)",{"$nulls":3},"Half Cosine","Hebrew","Hebrew"]
["From","To","Mid","Separate","Curve Fit","From","To"]
[0,20,{"$f":"AVERAGE(A17:B17)","v":10},{"$f":"2/5","v":0.4},{"$f":"ABS(COS(RADIANS(C17)))/2.5","v":0.3939231012048832},{"$f":"DegreesInConstellationHebrew(A17)","v":"Taleh 0°"},{"$f":"DegreesInConstellationHebrew(B17)","v":"Taleh 20°"}]
[20,40,{"$f":"AVERAGE(A18:B18)","v":30},{"$f":"1/3","v":0.3333333333333333},{"$f":"ABS(COS(RADIANS(C18)))/2.5","v":0.34641016151377546},{"$f":"DegreesInConstellationHebrew(A18)","v":"Taleh 20°"},{"$f":"DegreesInConstellationHebrew(B18)","v":"Shor 10°"}]
[40,50,45,{"$f":"1/4","v":0.25},0.282842712474619,{"$f":"DegreesInConstellationHebrew(A19)","v":"Shor 10°"},{"$f":"DegreesInConstellationHebrew(B19)","v":"Shor 20°"}]
[50,60,55,{"$f":"1/5","v":0.2},0.22943057454041846,{"$f":"DegreesInConstellationHebrew(A20)","v":"Shor 20°"},{"$f":"DegreesInConstellationHebrew(B20)","v":"T'omim 0°"}]
[60,70,65,{"$f":"1/6","v":0.16666666666666666},0.16904730469627977,{"$f":"DegreesInConstellationHebrew(A21)","v":"T'omim 0°"},{"$f":"DegreesInConstellationHebrew(B21)","v":"T'omim 10°"}]
[70,80,75,{"$f":"1/12","v":0.08333333333333333},0.1035276180410083,{"$f":"DegreesInConstellationHebrew(A22)","v":"T'omim 10°"},{"$f":"DegreesInConstellationHebrew(B22)","v":"T'omim 20°"}]
[80,85,82.5,{"$f":"1/24","v":0.041666666666666664},0.052210476888020683,{"$f":"DegreesInConstellationHebrew(A23)","v":"T'omim 20°"},{"$f":"DegreesInConstellationHebrew(B23)","v":"T'omim 25°"}]
[85,95,90,0,2.45029690981724E-17,{"$f":"DegreesInConstellationHebrew(A24)","v":"T'omim 25°"},{"$f":"DegreesInConstellationHebrew(B24)","v":"Sartan 5°"}]
[95,100,97.5,{"$f":"1/24","v":0.041666666666666664},0.05221047688802064,{"$f":"DegreesInConstellationHebrew(A25)","v":"Sartan 5°"},{"$f":"DegreesInConstellationHebrew(B25)","v":"Sartan 10°"}]
[100,110,105,{"$f":"1/12","v":0.08333333333333333},0.10352761804100834,{"$f":"DegreesInConstellationHebrew(A26)","v":"Sartan 10°"},{"$f":"DegreesInConstellationHebrew(B26)","v":"Sartan 20°"}]
[110,120,115,{"$f":"1/6","v":0.16666666666666666},0.16904730469627974,{"$f":"DegreesInConstellationHebrew(A27)","v":"Sartan 20°"},{"$f":"DegreesInConstellationHebrew(B27)","v":"Aryeh 0°"}]
[120,130,125,{"$f":"1/5","v":0.2},0.22943057454041846,{"$f":"DegreesInConstellationHebrew(A28)","v":"Aryeh 0°"},{"$f":"DegreesInConstellationHebrew(B28)","v":"Aryeh 10°"}]
[130,140,135,{"$f":"1/4","v":0.25},0.282842712474619,{"$f":"DegreesInConstellationHebrew(A29)","v":"Aryeh 10°"},{"$f":"DegreesInConstellationHebrew(B29)","v":"Aryeh 20°"}]
[140,160,150,{"$f":"1/3","v":0.3333333333333333},0.34641016151377546,{"$f":"DegreesInConstellationHebrew(A30)","v":"Aryeh 20°"},{"$f":"DegreesInConstellationHebrew(B30)","v":"Betulah 10°"}]
[160,180,170,{"$f":"2/5","v":0.4},0.3939231012048832,{"$f":"DegreesInConstellationHebrew(A31)","v":"Betulah 10°"},{"$f":"DegreesInConstellationHebrew(B31)","v":"Moznaim 0°"}]
[180,200,190,{"$f":"2/5","v":0.4},0.3939231012048832,{"$f":"DegreesInConstellationHebrew(A32)","v":"Moznaim 0°"},{"$f":"DegreesInConstellationHebrew(B32)","v":"Moznaim 20°"}]
[200,220,210,{"$f":"1/3","v":0.3333333333333333},0.34641016151377546,{"$f":"DegreesInConstellationHebrew(A33)","v":"Moznaim 20°"},{"$f":"DegreesInConstellationHebrew(B33)","v":"Akrav 10°"}]
[220,230,225,{"$f":"1/4","v":0.25},0.28284271247461906,{"$f":"DegreesInConstellationHebrew(A34)","v":"Akrav 10°"},{"$f":"DegreesInConstellationHebrew(B34)","v":"Akrav 20°"}]
[230,240,235,{"$f":"1/5","v":0.2},0.22943057454041854,{"$f":"DegreesInConstellationHebrew(A35)","v":"Akrav 20°"},{"$f":"DegreesInConstellationHebrew(B35)","v":"Keshet 0°"}]
[240,250,245,{"$f":"1/6","v":0.16666666666666666},0.16904730469627965,{"$f":"DegreesInConstellationHebrew(A36)","v":"Keshet 0°"},{"$f":"DegreesInConstellationHebrew(B36)","v":"Keshet 10°"}]
[250,260,255,{"$f":"1/12","v":0.08333333333333333},0.10352761804100825,{"$f":"DegreesInConstellationHebrew(A37)","v":"Keshet 10°"},{"$f":"DegreesInConstellationHebrew(B37)","v":"Keshet 20°"}]
[260,265,262.5,{"$f":"1/24","v":0.041666666666666664},0.05221047688802065,{"$f":"DegreesInConstellationHebrew(A38)","v":"Keshet 20°"},{"$f":"DegreesInConstellationHebrew(B38)","v":"Keshet 25°"}]
[265,275,270,0,7.35089072945172e-17,{"$f":"DegreesInConstellationHebrew(A39)","v":"Keshet 25°"},{"$f":"DegreesInConstellationHebrew(B39)","v":"G'di 5°"}]
[275,280,277.5,{"$f":"1/24","v":0.041666666666666664},0.05221047688802051,{"$f":"DegreesInConstellationHebrew(A40)","v":"G'di 5°"},{"$f":"DegreesInConstellationHebrew(B40)","v":"G'di 10°"}]
[280,290,{"$f":"AVERAGE(A41:B41)","v":285},{"$f":"1/12","v":0.08333333333333333},0.10352761804100812,{"$f":"DegreesInConstellationHebrew(A41)","v":"G'di 10°"},{"$f":"DegreesInConstellationHebrew(B41)","v":"G'di 20°"}]
[290,300,{"$f":"AVERAGE(A42:B42)","v":295},{"$f":"1/6","v":0.16666666666666666},0.16904730469627985,{"$f":"DegreesInConstellationHebrew(A42)","v":"G'di 20°"},{"$f":"DegreesInConstellationHebrew(B42)","v":"D'li 0°"}]
[300,310,{"$f":"AVERAGE(A43:B43)","v":305},{"$f":"1/5","v":0.2},0.22943057454041843,{"$f":"DegreesInConstellationHebrew(A43)","v":"D'li 0°"},{"$f":"DegreesInConstellationHebrew(B43)","v":"D'li 10°"}]
[310,320,{"$f":"AVERAGE(A44:B44)","v":315},{"$f":"1/4","v":0.25},0.28284271247461895,{"$f":"DegreesInConstellationHebrew(A44)","v":"D'li 10°"},{"$f":"DegreesInConstellationHebrew(B44)","v":"D'li 20°"}]
[320,340,{"$f":"AVERAGE(A45:B45)","v":330},{"$f":"1/3","v":0.3333333333333333},0.34641016151377535,{"$f":"DegreesInConstellationHebrew(A45)","v":"D'li 20°"},{"$f":"DegreesInConstellationHebrew(B45)","v":"Dagim 10°"}]
[340,360,350,{"$f":"2/5","v":0.4},0.3939231012048832,{"$f":"DegreesInConstellationHebrew(A46)","v":"Dagim 10°"},{"$f":"DegreesInConstellationHebrew(B46)","v":" 0°"}]
[]
[]
["Third Longitude Adjustment (chapter 17 #12)"]
["Sign","From","To","Mid","Adjust"]
["Aries",0,30,{"$f":"AVERAGE(B51:C51)","v":15},{"$f":"1/6","v":0.16666666666666666}]
["Taurus",30,60,{"$f":"AVERAGE(B52:C52)","v":45},{"$f":"1/5","v":0.2}]
["Gemini",60,90,{"$f":"AVERAGE(B53:C53)","v":75},{"$f":"1/6","v":0.16666666666666666}]
["Cancer",90,120,{"$f":"AVERAGE(B54:C54)","v":105},0]
["Leo",120,150,135,{"$f":"-1/5","v":-0.2}]
["Virgo",150,180,165,{"$f":"-1/3","v":-0.3333333333333333}]
["Libra",180,210,195,{"$f":"-1/3","v":-0.3333333333333333}]
["Scorpio",210,240,225,{"$f":"-1/5","v":-0.2}]
["Sagittarius",240,270,255,0]
["Capricorn",270,300,285,{"$f":"1/6","v":0.16666666666666666}]
["Aquarius",300,330,315,{"$f":"1/5","v":0.2}]
["Pisces",330,360,345,{"$f":"1/6","v":0.16666666666666666}]
[]
[]
["Declination of the Ecliptic (chapter 19 #7, #8, #9)"]
[]
["Point At","Declination","Sine Fit"]
[0,0,{"$f":"SinDegrees(A68)*AxialTilt","v":0}]
[10,4,4.080732175172863]
[20,8,8.037473368153217]
[30,11.5,11.75]
[40,15,15.105508827633676]
[50,18,18.002044413295987]
[60,20,20.35159698893431]
[70,22,22.08277658846885]
[80,23,23.142982195786892]
[90,23.5,23.5]
[100,23,23.14298219578689]
[110,22,22.082776588468843]
[120,20,20.351596988934308]
[130,18,18.002044413295977]
[140,15,15.10550882763367]
[150,11.5,11.74999999999999]
[160,8,8.037473368153208]
[170,4,4.080732175172851]
[180,0,-1.7994272884956664E-14]
[190,{"$f":"-B69","v":-4},-4.0807321751728765]
[200,{"$f":"-B70","v":-8},-8.037473368153233]
[210,-11.5,-11.750000000000012]
[220,-15,-15.10550882763369]
[230,-18,-18.00204441329599]
[240,-20,-20.35159698893431]
[250,-22,-22.082776588468857]
[260,-23,-23.142982195786892]
[270,-23.5,-23.5]
[280,-23,-23.14298219578689]
[290,-22,-22.08277658846884]
[300,-20,-20.351596988934297]
[310,-18,-18.002044413295973]
[320,-15,-15.105508827633665]
[330,-11.5,-11.749999999999973]
[340,-8,-8.037473368153192]
[350,-4,-4.080732175172844]
[360,0,0]
[]
[]
["Arc of Sight","1st Longitude"]
[9,13]
[10,12]
[11,11]
[12,10]
[13,9]

{"sheet":"Lunar Latitude","index":4,"n_rows":38,"n_cols":8,"rows_kept":38}
["Course","Deg","Min","Degrees","Deg Min","Minutes","Sine Fit","Rate"]
[0,0,0,{"$f":"B2+C2/60","v":0},{"$f":"DegreesToDMS(D2)","v":"0°"},{"$f":"B2*60+C2","v":0},{"$f":"5*SIN(RADIANS(A2))","v":0},{"$f":"5*COS(RADIANS(A2))","v":5}]
[10,0,52,0.8666666666666667,{"$f":"DegreesToDMS(D3)","v":"0° 52'"},52,{"$f":"5*SIN(RADIANS(A3))","v":0.8682408883346516},{"$f":"5*COS(RADIANS(A3))","v":4.92403876506104}]
[20,1,43,1.7166666666666668,"1° 43'",103,1.7101007166283435,4.698463103929543]
[30,2,30,2.5,"2° 30'",150,2.4999999999999996,4.330127018922194]
[40,3,13,3.216666666666667,"3° 13'",193,3.2139380484326963,3.83022221559489]
[50,3,50,3.8333333333333335,"3° 50'",230,3.83022221559489,3.2139380484326967]
[60,4,20,4.333333333333333,"4° 20'",260,4.330127018922193,2.5000000000000004]
[70,4,42,4.7,"4° 42'",282,4.698463103929542,1.7101007166283442]
[80,4,55,4.916666666666667,"4° 55'",295,4.92403876506104,0.8682408883346521]
[90,5,0,5,"5°",300,5,3.06287113727155E-16]
[100,4,55,4.916666666666667,"4° 55'",295,4.92403876506104,-0.8682408883346515]
[110,4,42,4.7,"4° 42'",282,4.698463103929543,-1.7101007166283435]
[120,4,20,4.333333333333333,"4° 20'",260,4.330127018922194,-2.499999999999999]
[130,3,50,3.8333333333333335,"3° 50'",230,3.83022221559489,-3.2139380484326967]
[140,3,13,3.216666666666667,"3° 13'",193,3.2139380484326976,-3.8302222155948895]
[150,2,30,2.5,"2° 30'",150,2.4999999999999996,-4.330127018922194]
[160,1,43,1.7166666666666668,"1° 43'",103,1.7101007166283444,-4.698463103929542]
[170,0,52,0.8666666666666667,"0° 52'",52,0.8682408883346514,-4.92403876506104]
[180,0,0,0,"0°",0,6.1257422745431e-16,-5]
[190,0,52,{"$f":"-(B21+C21/60)","v":-0.8666666666666667},"-(0° 52')",{"$f":"-(B21*60+C21)","v":-52},-0.8682408883346524,-4.92403876506104]
[200,1,43,{"$f":"-(B22+C22/60)","v":-1.7166666666666668},"-(1° 43')",{"$f":"-(B22*60+C22)","v":-103},-1.7101007166283433,-4.698463103929543]
[210,2,30,-2.5,"-(2° 30')",-150,-2.5000000000000004,-4.330127018922193]
[220,3,13,-3.216666666666667,"-(3° 13')",-193,-3.2139380484326963,-3.83022221559489]
[230,3,50,-3.8333333333333335,"-(3° 50')",-230,-3.8302222155948895,-3.2139380484326976]
[240,4,20,-4.333333333333333,"-(4° 20')",-260,-4.330127018922192,-2.500000000000002]
[250,4,42,-4.7,"-(4° 42')",-282,-4.698463103929543,-1.7101007166283426]
[260,4,55,-4.916666666666667,"-(4° 55')",-295,-4.92403876506104,-0.8682408883346516]
[270,5,0,-5,"-(5°)",-300,-5,-9.18861341181465e-16]
[280,4,55,-4.916666666666667,"-(4° 55')",-295,-4.924038765061041,0.8682408883346499]
[290,4,42,-4.7,"-(4° 42')",-282,-4.698463103929542,1.7101007166283448]
[300,4,20,-4.333333333333333,"-(4° 20')",-260,-4.330127018922193,2.5000000000000004]
[310,3,50,-3.8333333333333335,"-(3° 50')",-230,-3.8302222155948904,3.2139380484326963]
[320,3,13,-3.216666666666667,"-(3° 13')",-193,-3.213938048432698,3.830222215594889]
[330,2,30,-2.5,"-(2° 30')",-150,-2.500000000000002,4.330127018922192]
[340,1,43,-1.7166666666666668,"-(1° 43')",-103,-1.710100716628343,4.698463103929543]
[350,0,52,-0.8666666666666667,"-(0° 52')",-52,-0.868240888334652,4.92403876506104]
[360,0,0,0,"0°",0,-1.22514845490862E-15,5]

{"sheet":"Angle of Course","index":5,"n_rows":20,"n_cols":7,"rows_kept":20}
["True Path","Deg","Min","Angle of Course","Minutes","Poly Fit","Sine Fit"]
[0,0,0,{"$f":"B2+C2/60","v":0},{"$f":"B2*60+C2","v":0},{"$f":"0.0000009213993*A2^4-0.000383319*A2^3+0.01325515*A2^2+4.642596*A2+1.508217","v":1.508217},{"$f":"305*SIN(RADIANS(A2))","v":0}]
[10,0,50,0.8333333333333334,50,48.885586993000004,52.96269418841375]
[20,1,38,1.6333333333333333,98,96.74306888800001,104.31614371432896]
[30,2,24,2.4,144,143.11245243300002,152.49999999999997]
[40,3,6,3.1,186,186.24666320800003,196.05022095439446]
[50,3,44,3.7333333333333334,224,224.61976262500002,233.6435551512883]
[60,4,16,4.266666666666667,256,256.926947928,264.13774815425376]
[70,4,41,4.683333333333334,281,282.084552193,286.60624933970206]
[80,5,0,5,300,299.230044328,300.36636466872346]
[90,5,5,5.083333333333333,305,307.722029073,305]
[100,5,8,5.133333333333334,308,307.140247,300.36636466872346]
[110,4,59,4.983333333333333,299,297.285574513,286.60624933970206]
[120,4,40,4.666666666666667,280,278.1800238480001,264.1377481542538]
[130,4,11,4.183333333333334,251,250.06674307299994,233.6435551512883]
[140,3,33,3.55,213,213.4100160879999,196.05022095439455]
[150,2,48,2.8,168,168.89526262499993,152.49999999999997]
[160,1,56,1.9333333333333333,116,117.42903824800004,104.316143714329]
[170,0,59,0.9833333333333333,59,60.139034352999886,52.962694188413735]
[180,0,0,0,0,-1.6259218319998487,3.736702787471291E-14]

{"sheet":"Moon Mean Adj","index":6,"n_rows":62,"n_cols":12,"rows_kept":62}
[{"$nulls":5},"Solar","Course","Moon",null,"Math","Math Quad","Polynomial"]
[{"$nulls":5},"Longitude",null,"Mean Adj"]
["From","Mazal","To","Mazal","Diff","degrees","radians","minutes","Sine Fit","Sine Fit","Sine Fit","Fit"]
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[15,"Taleh 15°",60,"T'omim 0°",45,{"$f":"A5+(C5-A5)/2","v":37.5},0.6544984694978736,15,18.26284287026162,71.68297759977482,71.72525195162254,70.75258087656641]
[60,"T'omim 0°",120,"Aryeh 0°",60,90,1.5707963267948966,30,30,119.15211124699238,119.11183542333443,119.05020889904002]
[120,"Aryeh 0°",165,"Betulah 15°",45,142.5,2.4870941840919194,15,18.262842870261625,73.39613572126594,73.43840984344871,74.50865930897515]
[165,"Betulah 15°",195,"Moznaim 15°",30,180,3.141592653589793,0,3.67544536472586E-15,1.4795324939847467,1.41137721176231,-0.34345651335997457]
[195,"Moznaim 15°",240,"Keshet 0°",45,217.5,3.796091123087667,-15,-18.26284287026162,-70.43707073329644,-71.25242969074625,-74.86476420209362]
[240,"Keshet 0°",300,"D'li 0°",60,270,4.71238898038469,-30,-30,-116.1930462590229,-119.95690079974548,-74.3153090437599]
[300,"D'li 0°",345,"Dagim 15°",45,322.5,5.6286868376817125,-15,-18.262842870261625,-68.72391261180537,-78.09751799876997,241.36492946192584]
[345,"Dagim 15°",15,"Taleh 15°",30,360,6.283185307179586,0,-7.35089072945172e-15,4.4163749879694345,-10.323059887706929,812.55141672824]
[]
[]
[{"$nulls":5},"Solar","Course","Moon"]
[{"$nulls":5},"Longitude",null,"Mean Adj",{"$nulls":3},30]
["From","Mazal","minutes"]
[0,{"$f":"DegreesInConstellationHebrew(A18)","v":"Taleh 0°"},0]
[15,"Taleh 15°",0]
[15,"Taleh 15°",15]
[60,"T'omim 0°",15]
[60,"T'omim 0°",30]
[120,"Aryeh 0°",30]
[120,"Aryeh 0°",15]
[165,"Betulah 15°",15]
[165,"Betulah 15°",0]
[195,"Moznaim 15°",0]
[195,"Moznaim 15°",-15]
[240,"Keshet 0°",-15]
[240,"Keshet 0°",-30]
[300,"D'li 0°",-30]
[300,"D'li 0°",-15]
[345,"Dagim 15°",-15]
[345,"Dagim 15°",0]
[360," 0°",0]
[]
[]
[0,{"$f":"L$16*SIN(RADIANS(A38))","v":0}]
[{"$f":"A38+15","v":15},7.764571353075622]
[30,14.999999999999998]
[45,21.213203435596423]
[60,25.980762113533157]
[75,28.97777478867205]
[90,30]
[105,28.97777478867205]
[120,25.98076211353316]
[135,21.213203435596427]
[150,14.999999999999998]
[165,7.76457135307563]
[180,3.67544536472586E-15]
[195,-7.764571353075624]
[210,-15.000000000000004]
[225,-21.213203435596423]
[240,-25.980762113533153]
[255,-28.97777478867205]
[270,-30]
[285,-28.977774788672054]
[300,-25.980762113533157]
[315,-21.21320343559643]
[330,-15.000000000000014]
[345,-7.76457135307562]
[360,-7.35089072945172e-15]

{"sheet":"Course of Sun","index":7,"n_rows":21,"n_cols":7,"rows_kept":21}
["Course","Course","Adjust",null,"Math","Math Quad","Poly"]
["degrees","radians","minutes","Sine Fit","Sine Fit","Sine Fit","Fit"]
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[10,0.17453292519943295,20,20.664133142364708,19.394465451748232,19.397591282583576,19.92226616464]
[20,0.3490658503988659,40,40.70039705575458,39.61762772862846,39.65628155342588,39.350624344239996]
[30,0.5235987755982988,58,59.49999999999999,58.60266374899745,58.65033230905375,57.868565933839996]
[40,0.6981317007977318,{"$f":"60+15","v":75},76.49172555269817,75.77768027099391,75.81651950390793,74.80557163384]
[50,0.8726646259971648,{"$f":"60+29","v":89},91.15928873115838,90.62578057930058,90.64578193945108,89.58743389600001]
[60,1.0471975511965976,{"$f":"60+41","v":101},103.05702305034819,102.70077013027672,102.6986888310879,101.73625692344]
[70,1.2217304763960306,{"$f":"60+51","v":111},111.82342187352309,111.6407139473813,111.61879169019255,110.87045667063998]
[80,1.3962634015954636,{"$f":"60+57","v":117},117.19212260845275,117.17893383228736,117.14345483106365,116.70476084344]
[90,1.5707963267948966,{"$f":"60+59","v":119},119,119.15211124699238,119.11183542333443,119.05020889904002]
[100,1.7453292519943295,{"$f":"60+58","v":118},117.19212260845275,117.50524966495233,117.46977061998292,117.81415204600003]
[110,1.9198621771937625,113,111.8234218735231,112.29334561271125,112.2714232680311,113.00025324423999]
[120,2.0943951023931953,105,103.0570230503482,103.67971762827165,103.67763619784573,104.70848720503997]
[130,2.2689280275926285,93,91.15928873115838,91.93104390996047,91.95104509512814,93.13514039103998]
[140,2.443460952792061,79,76.4917255526982,77.40925943431878,77.4480984485043,78.57281101623994]
[150,2.6179938779914944,61,59.49999999999999,60.560558744987276,60.60822704256935,61.41040904599998]
[160,2.792526803190927,42,40.7003970557546,41.90183855728328,41.94049207586076,42.133156197040016]
[170,2.9670597283903604,21,20.664133142364705,22.00499211306799,22.008117593937705,21.32258593744006]
[180,3.141592653589793,0,1.4579266613412578E-14,1.4795324939847467,1.41137721176231,-0.34345651335997457]