¬·ACCEL BAS (AZMUTH BAS ÐcBIN BAS –…BINOM-4 BAS) #BINOMIALBAS3 ±BINOMIALCOM<q’LBINOMIALDOC­ ³#BINSTAR BAS¶BÐBLAKHOLEBASºJ”COMPRESSBASÐÕCRAMERS3BASÑÜCRAMERS3COMàN¡´CRAMERS3DOC.zXCRAMERS3PRNFò‹CUMPROBSBAS[FIBON BAS`ÃHOLECALCBASbô'HOLECALCCOM}_¥<HOLECALCDOCÜ%vQHOLECALCPRN spHYPERBOLBAS!›{LSTBIN BAS)½ELSTBIN2 BAS0|LSTPOIS BAS5”NORMAL BAS:æ4PARABOLABAS>´PARABOLADOCE ~™POIS BASN ÝPOISSON BASYúŽPOISSON COM_W=_POISSON DOC¶ «ÎPOSITIONBAS¿„�POSITIONDOCÎ… QUADRATSBASረQUADROOTBASéñ³QUADROOTCOMÿW‘mQUADROOTPRNV(0RISE-SETBASr G”RISE-SETDOC ŒSRISETIMEBAS‰|ÓRISING BASšbŽROOTS BAS¡VSPHERIC BAS©«ŸSTARFIX BAS°6*STARFIX COMæ¥õKTIME BAS‹•QTIME FINœÑTRANSIT BAS²;ÕUNIFMOT BASÃ^=ÿÿ 10 REM THIS PROGRAM CALCULATES THE ENERGIES AND WIRE LENGTH FACTORS FOR 20 REM A TUNED LINEAR ACCELERATOR. WRITTEN BY MIKE FINERTY 4-10-84 30 REM IN NEVADA BASIC 12 DIGIT PRECISSION 40 INPUT "STARTING ENERGY",S1 50 INPUT "ENDING ENERGY",S2 60 INPUT "NUMBER OF ACCELERATING STEPS",N 70 PRINT "AVERAGE ACCELERATING ENERGY ";(S2-S1)/N;" ELECTRON VOLTS" 80 FOR E=S1 TO S2 STEP (S2-S1)/N 90 LET C=2.99792458E8 100 LET E0=5.110041E5 110 LET B=4*(E/E0)^2*C^2 120 LET D=4*(E/E0)^2*C^4 130 LET A=1 140 LET V2=-B/2+(B^2+4*D)^.5/2 150 LET V=V2^.5 160 LPRINT "ENERGY","ELECTRON VELOCITY","V/C%" 170 LPRINT E,V,TAB(42);V/C*100 180 IF V=0 THEN 210 190 LPRINT "DELTA = ";C/V-INT(C/V) 200 LPRINT 210 NEXT %" 170 LPRINT E,V,TAB(42);V/C*100 180 IF V=0 THEN 210 190 LPRINT "DELTA = ";C/V-INT(C/V) 200 LPRINT ÿb � *** THIS IS PROGRAM FIXER.BAS A MBASIC PROGRAM TO CAULCULATE ***Xb� ****************** ALTITUDE AND AZMUTH *************************›b� *** FROM LATITUDE, RIGHT ASCENTION, DECLINATION SIDERIAL ***âb(� ****************************TIME********************************%c2� *********ALL UNITS IN DECIMAL DEGREES OR HOURS *************lc<� *** BY MIKE FINERTY ***********************22 AUGUST 1985 ******³cF� %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ÆcPPI ð U–hÚI‚ÜcZC1 ð U–hÚI‚õ´êcdC2 ð õC1dn… "LATITUDE IS: ", LATdxLAT ð LATôC16d‚ … "RIGHT ASCENTION = ", RALdŒRA ð RA ô  ô C1hd–… "DECLINATION = ", DEC{d DEC ð DEC ô C1ždª… "SIDEARIAL TIME = ", SIDTIME¾d´SIDTIME ð SIDTIME ô  ô C1Õd¾LHA ð SIDTIME ó RA eÈALTSIN ð ÿ‰(LAT)ôÿ‰(DEC) ò ÿŒ(LAT)ôÿŒ(DEC)ôÿŒ(LHA),eÒALTCOS ð (óALTSINö)ö€HeÜALT ð ÿŽ(ALTSINõALTCOS)^eæALTITUDE ð ALTôC2–eðAZCOS ð (ÿ‰(DEC)óÿ‰(ALT)ôÿ‰(LAT))õ(ÿŒ(ALT)ôÿŒ(LAT))ºeúAZSIN ð ÿŒ(DEC)ôÿ‰(LHA)õÿŒ(ALT)ÓeAZ ð ÿŽ(AZSINõAZCOS)êeAZMUTH ð ÿ†(AZôC2)f"‹ AZSIN ñ ÷ AZCOS ñ Ï AZMUTH ð ´ ó AZMUTHLf,‹ AZSIN ï ÷ AZCOS ñ Ï AZMUTH ð ´ ò AZMUTH~f1‹ AZSIN ï ÷ AZCOS ï Ï AZMUTH ð h ó AZMUTH›f@‘ "ALTITUDE = ";ALTITUDEµfJ‘ "AZMUTH = "; AZMUTHâfT‹ ALTITUDE ñ Ï ‘ "OBJECT BELOW HORIZON" g^‘ "DO YOU WANT ANOTHER OBJECT? Y/N? "gh… A$*gr‹ A$ ð "Y" Ï ‚ AZMUTHâfT‹ ALTITUDE ñ Ï 10 LPRINT 20 LPRINT "PROGRAM BINPROBS: SINGLE TERMS OF THE BINOMIAL DISTRIBUTION" 30 REM N IS NUMBER OF TRIES 40 INPUT "N=",N 50 PRINT 60 LPRINT "N =";N 70 REM R IS NUMBER OF SUCCESSES 80 INPUT "R=",R 90 PRINT 100 LPRINT "R =";R 110 PRINT "RUNTIME =";.23*R;"seconds" 120 PRINT 130 REM THETA IS PROBABILITY OF SUCCESS PER TRY 140 INPUT "THETA =",T 150 LPRINT "THETA =";T 160 PRINT 170 PRINT "CALCULATIONS IN PROGRESS" 180 FOR X=1 TO R 190 LET Y=Y+LOG10(X) 200 NEXT X 210 LET M=N-R+1 220 FOR Z=M TO N 230 LET P=P+LOG10(Z) 240 NEXT Z 250 LET C=P-Y 260 LET S=1-T 270 LET Q=R*LOG10(T) 280 LET U=(N-R)*LOG10(S) 290 LET L=C+Q+U 300 PRINT "LOGPROB =";L 310 LPRINT "LOGPROB =";L 320 PRINT "probability =";10^(L-INT(L)+1);"ten";INT(L)-1 330 LPRINT "PROBABILITY =";10^(L-INT(L)+1);"TEN";INT(L)-1 340 LET G2=10-INT(LOG10(ABS(Y+Q+U)))-INT(LOG10(1.25*R)) 350 PRINT "CALCULATIONS GOOD TO ";G2;" DIGITS" 360 LPRINT "CALCULATIONS GOOD TO ";G2;" DIGITS" 370 PRINT "--oo000oo--" 380 LPRINT "--oo000oo--" 390 PRINT 400 LPRINT 410 END ATIONS GOOD TO ";G2;" DIGITS" 370 PRINT "--oo000oo--" 380 LPRINT "--oo000oo--" 390 PRINT 400 LPRINT 410 END 10 REM: NEVADA BASIC 12 DIGIT PRECISSION PROGRAM 20 LPRINT "PROGRAM BINPROBS: SINGLE TERMS OF THE BINOMIAL DISTRIBUTION" 30 REM N IS NUMBER OF TRIES 40 INPUT "N=",N 50 PRINT 60 LPRINT "N =";N 70 REM R IS NUMBER OF SUCCESSES 80 INPUT "R=",R 90 PRINT 100 LPRINT "R =";R 110 PRINT "RUNTIME =";.23*R;"seconds" 120 PRINT 130 REM THETA IS PROBABILITY OF SUCCESS PER TRY 140 INPUT "THETA =",T 150 LPRINT "THETA =";T 160 PRINT 170 PRINT "CALCULATIONS IN PROGRESS" 180 FOR X=1 TO R 190 LET Y=Y+LOG10(X) 200 NEXT X 210 LET M=N-R+1 220 FOR Z=M TO N 230 LET P=P+LOG10(Z) 240 NEXT Z 250 LET C=P-Y 260 LET S=1-T 270 LET Q=R*LOG10(T) 280 LET U=(N-R)*LOG10(S) 290 LET L=C+Q+U 300 PRINT "LOGPROB =";L,"H = ";-L/N/LOG10(4) 310 LPRINT "LOGPROB =";L,"H = ";-L/N/LOG10(4) 320 PRINT "probability =";10^(L-INT(L)+1);"ten";INT(L)-1 330 LPRINT "PROBABILITY =";10^(L-INT(L)+1);"TEN";INT(L)-1 340 LET G2=10-INT(LOG10(ABS(L)))-INT(LOG10(1.25*R)) 350 PRINT "CALCULATIONS GOOD TO ";G2;" DIGITS" 360 LPRINT "CALCULATIONS GOOD TO ";G2;" DIGITS" 370 PRINT "--oo000oo--" 380 LPRINT "--oo000oo--" 390 PRINT 400 LPRINT 410 END ATIONS GOOD TO ";G2;" DIGITS" 370 PRINT "--oo010 VAR A,B,LOGPROB,LOG_NCR,N,R,T,X,M,Z,P,Y,Q,U,S =REAL.DOUBLE 15 VAR C$ = STRING 20 INPUT "N = ";N 30 LPRINTER 40 PRINT "N = ";N 45 CONSOLE 50 INPUT "R = ";R 60 LPRINTER 70 PRINT "R = ";R 80 CONSOLE 90 PRINT "RUNTIME = "; 0.4*R;"SECONDS" 100 INPUT "THETA =";T 110 LPRINTER 120 PRINT "THETA =";T 130 CONSOLE 140 PRINT "CALCULATIONS IN PROGRESS" 150 FOR X = 1 TO R 160 Y = Y + LOG(X)/LOG(10) 170 NEXT X 180 M = N - R + 1 190 FOR Z = M TO N 200 P = P + LOG(Z)/LOG(10) 210 NEXT Z 220 LOG_NCR = P - Y 230 S = 1 - T 240 Q = R*LOG(T)/LOG(10) 250 U = (N - R)*LOG(S)/LOG(10) 260 LOGPROB = LOG_NCR + Q + U 270 PRINT 280 LPRINTER 290 PRINT 295 PRINT "LOGPROB =";LOGPROB 300 CONSOLE 310 PRINT 315 PRINT "LOGPROB=";LOGPROB 320 A = 10^(LOGPROB - INT(LOGPROB)) 330 B = INT(LOGPROB) 340 C$= "PROBABILITY = #.## TEN +#####" 350 PRINT USING C$,A,B 360 LPRINTER 370 PRINT USING C$,A,B 380 PRINT "--ooO0Ooo--" 390 PRINT 400 PRINT 410 CONSOLE 420 PRINT "--ooO0Ooo--" 430 PRINT 440 PRINT 450 END A,B,LOGPROB,LOG_NCR,N,R,T,X,M,Z,P,Y,Q,U,S =REAL.DOUBLE 15 VAR C$ = STRING 20 INPUT "N = ";N 30 LPRINTER 40 PRINT "N =ÃÃ%‹g9g9*ùÍ´>Í1>Í1>Í1>Í1>Í1>Í1ÅÍ32ÍB2Íï.N = ÍB2ÍC/ÍB2yÍb-!É8Í=%ÍB2yÍc2>Í1>Í1>Í1>Í1ÅÍ32ÚN = !•åÍé+ÍÐ6É8Í‚ÍB2Íc2>Í1>Í1>Í1>Í1ÅÍ32ÍB2Íï.R = ÍB2ÍC/ÍB2yÍb-!Ð8Í=%ÍB2yÍc2>Í1>Í1>Í1 >Í1 ÅÍ32Ã!R = !åÍé+ÍÐ6Ð8Í‚ÍB2Íc2>Í1>Í1>Í1>Í1ÅÍ32Ãf RUNTIME = ![åÍé+ÃtÿÌÌÌÍ¿6pÍÐ6Ð8Í®Í!"Í1Ã’SECONDS!ŠåÍé+ÍB2Íc2>Í1>Í1ÅÍ32ÍB2Íï.THETA =ÍB2ÍC/ÍB2yÍb-!×8Í=%ÍB2yÍc2>Í1>Í1>Í1>Í1ÅÍ32à THETA =!åÍé+ÍÐ6×8Í‚ÍB2Íc2>Í1>Í1>Í1>Í1ÅÍ32Ã\CALCULATIONS IN PROGRESS!CåÍé+ÍB2Íc2>Í1>Í1Ã�€ÍÐ6z>!Þ8Í2Íë6Í'2åÍÐ6Ð8ä€!�>Íž6>Í1>Í1ÃÁ ÍÐ6ú8ÍÐ6Þ8Í®ÍÉ Í€Í¿6½ÍÉ Í€Í*Íl'>!ú8Íë6>Í1>Í1!¬Í% >Í1 >Í1 ÀÍÐ6É8ÍÐ6Ð8Íq'ÍÐ6Íl'>!å8Íë6>Í1!>Í1!ÍÐ6å8>!ì8Í2Íë6Í'2åÍÐ6É8Ãg€!`>Íž6>Í1">Í1"Ä ÍÐ6ó8ÍÐ6ì8Í®ÍÉ Í€Í¿6€ÍÉ Í€Í*Íl'>!ó8Íë6>Í1#>Í1#!oÍ% >Í1$>Í1$ÍÐ6ó8ÍÐ6ú8Íq'>!Â8Íë6>Í1%>Í1%Ãÿ€ÍÐ6øÍÐ6×8Íq'>!9Íë6>Í1&>Í1&Ã) ÍÐ6Ð8ÍÐ6×8Í®ÍÉ Í€ͤ(Í¿6%ÍÉ Í€Í*>!9Íë6>Í1'>Í1'Ãj ÍÐ6É8ÍÐ6Ð8Íq'ÍÐ69Í®ÍÉ Í€ͤ(Í¿6fÍÉ Í€Í*>!9Íë6>Í1(>Í1(ÍÐ6Â8ÍÐ69Íl'ÍÐ69Íl'>!»8Íë6>Í1)>Í1)ÅÍ32ÍB2Íc2>Í10>Í10>Í11>Í11ÅÍ32ÍB2Íc2>Í12>Í12ÅÍ32Ã, LOGPROB =!"åÍé+ÍÐ6»8Í‚ÍB2Íc2>Í13>Í13>Í14>Í14ÅÍ32ÍB2Íc2>Í15>Í15ÅÍ32ÉLOGPROB=!€åÍé+ÍÐ6»8Í‚ÍB2Íc2>Í16>Í16ö ÍÐ6¯ÍÐ6»8ÍÐ6»8Í®Í{Í€Íq'Ͱ >!­8Íë6>Í17>Í17ÍÐ6»8Í®Í{Í€>!´8Íë6>Í18>Í18Ã/PROBABILITY = #.## TEN +#####!å!9Íæ2>Í19>Í19!9å>ÿÍK/ÅÍ32ÍÐ6­8Í‚ÍÍÐ6´8Í‚Í>ÍK/ÍB2Íc2>Í1@>Í1@>Í1A>Í1A!9å>ÿÍK/ÅÍ32ÍÐ6­8Í‚ÍÍÐ6´8Í‚Í>ÍK/ÍB2Íc2>Í1B>Í1BÅÍ32Ãæ --ooO0Ooo--!ÚåÍé+ÍB2Íc2>Í1C>Í1CÅÍ32ÍB2Íc2>Í1D>Í1DÅÍ32ÍB2Íc2>Í1E>Í1E>Í1F>Í1FÅÍ32ÃX --ooO0Ooo--!LåÍé+ÍB2Íc2>Í1G>Í1GÅÍ32ÍB2Íc2>Í1H>Í1HÅÍ32ÍB2Íc2>Í1I>Í1IÃ>Í1QÃÉCopyright (C) 1979, By Topaz programming. All rights reserved. From here on protected by End User License.  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MAX IS 25µå2‡3!‹3"ˆ3¯2Š3á^#Vë"â.>!�.å*â.å*ˆ3É*ˆ3~þ ʰ.þÊË.#"ˆ3:Š3Æ2Š3Ò.!ä.ÃÚ0>!¾.å*â.å*ˆ3É*ˆ36!‹3"ˆ3ñÉ#"ˆ3:Š3Æ2Š3Ò¾.>ÿ2Š3þ.-ASCII FILÅá~·Êý.#åÍ™4Ãï.#~#åþÈþõyÌc2ñÈÍG2É2B/~·Ê2/2A/#~·Ê2/åÍ™4Ñ!A/5Ê2/ëÃ/:B/þÊG2þyÊc2É!I/Ã2? 2¹/á"s/þÊv/Íy32¼/!¼/Íæ2!½/"º/!¼/Í¿0:Ž4!é*º/o/Õ~·Èþ#Èþ.Èþ,Èþ-Èþ$Èþ*Èþ^Èþ+Èþ/Èþ&Èþ!Èþ\ª/#~·ÈÑå:Ž4O~Í™4á#Ãy/N#å 6á~·ÊÒ0#ÃÈ0È6#ÃÒ0^ë"ë#:ÿ0þÿÊ÷0͘1:’4Íc2Ã*ù*1é2o1á~2“4#~2”4#å:o1!p1®þÊF1:’4O>[Í™4ÍÉ1>]Í™4> Í™4:q1=2q1ÂF1>2q1yÍc2Í7·ÈæþÊþÂa1:p1/2p1ÉþÀÍ7þÂd1É^ë"ë#͘1!‹1Í2:’4Íc2É WARNING ONLÙ:’4OåÍc2áÍ2!º1Í2:”4þÿÈ!À1Í2ÍÉ1É ERROÒ IN LINE *“4|æðÆ0åÍ™4á|æÆ0åÍ™4á}æðÆ0åÍ™4á}æÆ0Í™4!‘4>†wÉ~·ú2åÍ™4!‘44á#Ã2æÍ™4Éë* s#r#" ëÉ* +V+^" ëÉáÁy2Ž4åþ ØÿÃ7:Ž4OÉ!ó4 ~ÖÒN2Æõ> Í™4ñ<þÂU2ÉO> Í™4> Í™4¯2‘4Éá"­2Ͱ2:Š3!‹3Íž6:ˆ3þ“2:Š3õ!å:Š3!‹3Íž6:ˆ3þ¬2:Š3õ!å!éá"Ï22ˆ3þÊÒ2!á2O  ~2Š3!‹3Íë6!éÍy32Š3!Š3Íæ2ÃÎ2ã"`3áÑz³Ê3OFx·Ê13y·Â3#6Ã13#w·Ê13Ê13 Â3#6Ã13ñO~¹Ú73Ê,3å #6á#yÍë6å*`3ãÉ"^3Š3|ºÂK3}»ÂK3qÃ3!‹3y2Š3Íë6*^3Íb3Ã13FŠ3O #È6 Èw·ÈÃj3áÑz³Êƒ3ÕéñõÕéÿÿÿÿþ Ê´4þ Ê´4!ó4 4þ ÂÀ46ÃÀ4!5 4þ ÊÀ46õy2ñ4>Í55þÊÓ4ñÃ7ñ2ò4^#V!é4å!ò4>ÕÉ:ñ4O:ò4É·ÊS5!A ÂA5l5å#~#^#VáÉáN#å!A Â_5l5ëá~#Âl5é·Èëá"7ë^#=ʺ6V#=Õ¦6*7éÕ*7éá^#V#ëN#F#ÅN#FÅëéá^#V#ëN#F#ÅN#F#ÅN#F#ÅNÅëé·Èëá"7ë__{ÑÒ7s+=Ê7Ñr+=Ê7s+=Â7!éK7Ã7i7Åõå> ¹Ú27!D ãÉ!87ÃÚ0%BAD CHANNEL NUMBEÒÓ7ÃK8ÃK8ÃÇ7ÃÞ7ÃÏ7ÃK8ÃK8ÃK8ÃP8Ê7Ã98ÃB8ÃK8ÃK8ÃK8ÃK8ÃK8ÃK8ÃK8ÃK8ñ_ÍÁÉñÍ#8|µÂ¬7*¨7ÕéÁæÉ:"8·Â¾7ÿͷʳ7õ¯2"8ñè7ñÍÁÉñÁ!Ù7åÅÃß7ÈÅÔ7ñ:"8·Âú7Í#8|µÂ8*ú7ÕéÁ·7È>ÿÉ|þÊ8ÿÍ2"8Ãú7¯2"8þÍÃú7*78|¥þÿÀ! Í"78Éÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:›8·Âm8\Íþÿ!œ8ÊÚ0>ÿ2›8:š8þ€ÂŒ8€Í\Í!œ8·ÂÚ0_<2š8!€~ÁÉ€&INPUT FILE REAÄPÚ<ýtBinomial.* is an S-Baisc program which computes the Binomial Distribution probability of N tries, R successes with a probablity of success of Theta per try. It is good for the extended range. The number of good digits is 5 - #of numerals in the characteristic of Logprob - #of digits in R. It works by adding and subtracting logarithms and thus is good beyond the normal range of the S-Basic language. For instance if we start with 134 tries with 23 successes with a probability of success per try of .00512, we receive a logprob of -27.29354453793 and a probability of 5.09E-28. Using other methods the computer would signal an overflow. The precission of this program can be extended by using a double precission log function. The same result can be obtained by using Nevada Basic with 12 digit precission. This Program was written by: Michael P Finerty 2358 E Parkside Drive Tucson Ariz.,85713 A Nevada Basic 12 digit version appears on this disk under the name of BINPROBS.BAS.es the Binomial Distribution probability of N tries, R successes with a probablit10 DIM T(1002),S(1000),V(1000),A(1000) 20 INPUT "P = ";P 30 INPUT "ECCENTRICITY =";R 40 FOR N = 0 TO 1000 50 T(N) = N/10 60 NEXT N 70 FOR N = 1 TO 1000 80 S(N)=P/(1+R*((COS(T(N))-R)/(1-R*COS(T(N))))) 90 V(N) = (S(N)-S(N-1))/(T(N)-T(N-1)) 100 A(N) = (V(N)-V(N-1))/(T(N)-T(N-1)) 110 M = M + 1 120 NEXT N 130 FOR N = 1 TO M 140 PRINT "N =";N;TAB(20)"S =";S(N) 150 PRINT TAB(40);"V =";V(N) 160 PRINT TAB(60);"A =";A(N) 170 FOR PAUSE = 1 TO 100 180 NEXT PAUSE 190 NEXT N )"S =";S(N) 150 PRINT TAB10 REM THIS IS PROGRAM BLAKHOLE.BAS, A PROGRAM THAT ASSESSES 20 REM THE PROPERTIES OF NEWTONIAN BLACKHOLES 30 REM YOU ARE REQUIRED TO INPUT ONE OF THE PROPERTIES: 40 REM MASS, RADIUS OR DENSITY; THE PROGRAM WILL RETURN THE OTHERS. 50 REM THIS PROGRAM WAS WRITTEN BY MIKE FINERTY, 5 NOVEMBER 1984 60 REM ************************************************************* 70 DIM A$(4) 80 LET L = 2.3052585# 90 LET K = 3.22E+27 100 PRINT "PROGRAM RETURNS THE CRITICAL VALUES OF R, D & M, GIVEN ONE OF THEM 110 PRINT "PLEASE SELECT ONE:" 120 PRINT 130 PRINT "R ..... RADIUS IN CENTIMETERS" 140 PRINT 150 PRINT "D ..... DENSITY IN GRAMS/CUBIC CENTIMETER" 160 PRINT 170 PRINT "M ..... MASS IN GRAMS" 180 PRINT 190 PRINT "MLOG .. LOGARITHM OF MASS IN GRAMS" 200 PRINT 210 INPUT "SELECT ONE HERE:";A$ 220 INPUT "WHAT VALUE FOR THIS VARIABLE?";QUANT 230 IF ABS(LOG(QUANT)/L)>34 THEN PRINT "OUT OF RANGE OF MBASIC" 240 IF ABS(LOG(QUANT)/L)>34 THEN GOTO 600 250 IF A$ = "R" THEN GOTO 300 260 IF A$ = "D" THEN GOTO 370 270 IF A$ = "M" THEN GOTO 450 280 IF A$ = "MLOG" THEN GOTO 530 290 REM GIVEN RADIUS WE CALCULATE THE FOLLOWING: 300 DLOG = LOG(K)/L - 2*LOG(QUANT)/L 310 MLOG = .622089 + LOG(K)/L + LOG(QUANT)/L 320 SOLS = MLOG - 33.2989 330 PRINT "DENSITY =";10^(DLOG - INT(DLOG));"TEN";INT(DLOG);" GRAMS/CC" 340 PRINT "MASS =";10^(MLOG-INT(MLOG));"TEN";INT(MLOG);" GRAMS" 350 PRINT "SOLAR MASSES =";10^(SOLS - INT(SOLS));"TEN";INT(SOLS);"SOLS" 360 GOTO 600 370 REM GIVEN DENSITY WE CALCULATE THE FOLLOWING: 380 RLOG = .5*(LOG(K)/L-LOG(QUANT)/L) 390 MLOG = .622089 + .5*(3*LOG(K)/L-LOG(QUANT)/L) 400 SOLS = MLOG - 33.2989 410 PRINT "RADIUS = ";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);"CENTIMETERS" 420 PRINT "MASS = ";10^(MLOG - INT(MLOG));"TEN";INT(MLOG);"GRAMS" 430 PRINT "SOLAR MASSES =";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);"SOLS" 440 GOTO 600 450 REM GIVEN MASS IN GRAMS WE CALCULATE THE FOLLOWING: 460 SOLS = LOG(QUANT)/L - 33.2989 470 DLOG = 1.24418 + 3*LOG(K)/L - 2*LOG(QUANT)/L 480 RLOG = -.622089 + LOG(QUANT)/L - LOG(K)/L 490 PRINT "SOLAR MASSES = "10^(SOLS-INT(SOLS));"TEN";INT(SOLS);"SOLS" 500 PRINT "DENSITY = "; 10^(DLOG-INT(DLOG));"TEN";INT(DLOG);"GM/CC" 510 PRINT "RADUIS =";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);"CM" 520 GOTO 600 530 REM GIVEN COMMON LOG (BASE 10) OF MASS, WE CALCULATE: 540 SOLS = QUANT - 33.2989 550 DLOG = 1.24418 + 3*LOG(K)/L - 2*QUANT 560 RLOG = -.622089 + QUANT - LOG(K)/L 570 PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);"SOLS" 580 PRINT "DENSITY = ";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);"GM/CC" 590 PRINT "RADIUS = ";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);"CM" 600 PRINT "--ooO0Ooo--" 610 PRINT "DO YOU WANT ANOTHER OBJECT? Y/N?" 620 INPUT ANS$ 630 IF ANS$ = "Y" OR ANS$="y" THEN GOTO 80 640 END ooO0Ooo--" 610 PRINT "ÿÞa ž ÿ–();ÿ–(Q)äaŽêa�REM this is Program CRAMERS3.BAS, A program to calculate the REM solutions to 3 simultaneous linear equations in 3 unknowns REM using Cramer's Rule of substitution to form 3X3 Determinates REM REM THIS PROGRAM WAS WRITEN BY MICHAEL P. FINERTY 10/18/84 REM ************************************************************ 10 REM REM A(N)*X1 + B(N)*X2 + C(N)*X3 = D IS AN EQUATION IN 3 UNKNOWNS VAR DET, DET0, DET1, DET2, DET3 = REAL.DOUBLE VAR A$ = STRING VAR N = INTEGER REM DIM COM REAL.DOUBLE A(3) B(3) C(3) D(3) X(3) Y(3) Z(3) REM REM READ IN VALUES OF A,B,C&D FOR EACH OF THE EQUATIONS REM FOR N = 1 TO 3 PRINT "PLEASE INPUT A(";N;")" INPUT A(N) PRINT "PLEASE INPUT B(";N;")" INPUT B(N) PRINT "PLEASE INPUT C(";N;")" INPUT C(N) PRINT "PLEASE INPUT D(";N;")" INPUT D(N) NEXT N FOR N = 1 TO 3 X(N) = A(N) Y(N) = B(N) Z(N) = C(N) NEXT N REM GOSUB 100 REM DET0 = DET IF DET0 = 0 THEN PRINT "INCONSISTANT EQUATIONS, NO SOLUTION" IF DET0 = 0 THEN 200 FOR N = 1 TO 3 X(N) = D(N) Y(N) = B(N) Z(N) = C(N) NEXT N REM GOSUB 100 REM DET1 = DET PRINT "X1 = "; DET1/DET0 REM FOR N = 1 TO 3 X(N) = A(N) Y(N) = D(N) Z(N) = C(N) NEXT N REM GOSUB 100 REM DET2 = DET PRINT "X2 =";DET2/DET0 REM FOR N = 1 TO 3 X(N) = A(N) Y(N) = B(N) Z(N) = D(N) NEXT N REM GOSUB 100 REM DET3 = DET REM PRINT "X3 = ";DET3/DET0 REM 200 REM PRINT "DO YOU WISH TO SOLVE ANOTHER SET OF EQUATIONS? Y/N?" INPUT A$ IF A$ = "y" OR A$ = "Y" THEN 10 END 100 REM SUBROUTINE TO CALCULATE DETERMINATES FROM X(N),Y(N) AND REM Z(N) REM DET = X(1)*Y(2)*Z(3) + X(2)*Y(3)*Z(1) + X(3)*Y(1)*Z(2) DET = DET - X(3)*Y(2)*Z(1) - X(1)*Y(3)*Z(2) - X(2)*Y(1)*Z(3) RETURN  X(N) = A(N) Y(N) = ÃÃ%‹Î'Î'*ùÍÝ >͹>͹>͹>͹>͹>͹>͹>͹>͹>͹ >͹>͹>͹>͹!"!="6!`"Y!ƒ"|!¦"Ÿ!É"Â!ì"å>͹>͹>͹>͹ü*ºå>!Ì'ÍÑÍ–%ÍÞåÃÔ*ÒåÃÝ!Û>ÍZ%>͹ÅÍêÃPLEASE INPUT A(!õåÍú*Ì'åÍ3Ã)!åÍúÍùÍ >͹ÅÍê*Ì'å!ÍWÍÑÍùÍúÍùyÍ;ÍÞÍŽÍùyÍ >͹ ÅÍêÃyPLEASE INPUT B(!iåÍú*Ì'åÍ3ÃŒ)!ŠåÍúÍùÍ >͹!ÅÍê*Ì'å!6ÍWÍÑÍùÍúÍùyÍ;ÍÞÍŽÍùyÍ >͹"ÅÍêÃíPLEASE INPUT C(!ÝåÍú*Ì'åÍ3Ã)!þåÍúÍùÍ >͹#ÅÍê*Ì'å!YÍWÍÑÍùÍúÍùyÍ;ÍÞÍŽÍùyÍ >͹$ÅÍêÃaPLEASE INPUT D(!QåÍú*Ì'åÍ3Ãt)!råÍúÍùÍ >͹%ÅÍê*Ì'å!|ÍWÍÑÍùÍúÍùyÍ;ÍÞÍŽÍùyÍ >͹&!åÍ’ >͹'ÃÎ*Ìå>!Ì'ÍÑÍ–%ÍÞåÃæ*äåÃï!í>ÍZ%>͹(*Ì'å!ŸÍWÍÑ*Ì'å!Í:ÍÞ>Í–%>͹)*Ì'å!ÂÍWÍÑ*Ì'å!6Í:ÍÞ>Í–%>͹0*Ì'å!åÍWÍÑ*Ì'å!YÍ:ÍÞ>Í–%>͹1!÷Í’ >͹2>͹3ÍR >͹4>͹5Í{%X'>!_'Í–%>͹6óÍ{%_'Í{%¬Í Í!Ê>͹6ÅÍêÃú#INCONSISTANT EQUATIONS, NO SOLUTION!ÖåÍúÍùÍ >͹7ÃÍ{%_'Í{%Í Í!Ê.É >͹8Ã:*8å>!Ì'ÍÑÍ–%ÍÞåÃR*PåÃ[!Y>ÍZ%>͹9*Ì'å!ŸÍWÍÑ*Ì'å!|Í:ÍÞ>Í–%>͹@*Ì'å!ÂÍWÍÑ*Ì'å!6Í:ÍÞ>Í–%>͹A*Ì'å!åÍWÍÑ*Ì'å!YÍ:ÍÞ>Í–%>͹B!cÍ’ >͹C>͹DÍR >͹E>͹FÍ{%X'>!f'Í–%>͹GÅÍêÃ$X1 = !åÍúÍ{%f'Í{%_'ÍUÍ^ ÍùÍ >͹H>͹IÃT*Rå>!Ì'ÍÑÍ–%ÍÞåÃl*jåÃu!s>ÍZ%>͹P*Ì'å!ŸÍWÍÑ*Ì'å!Í:ÍÞ>Í–%>͹Q*Ì'å!ÂÍWÍÑ*Ì'å!|Í:ÍÞ>Í–%>͹R*Ì'å!åÍWÍÑ*Ì'å!YÍ:ÍÞ>Í–%>͹S!}Í’ >͹T>͹UÍR >͹V>͹WÍ{%X'>!m'Í–%>͹XÅÍêÃ=X2 =!8åÍúÍ{%m'Í{%_'ÍUÍ^ ÍùÍ >͹Y>͹`Ãm*kå>!Ì'ÍÑÍ–%ÍÞåÃ…*ƒåÃŽ!Œ>ÍZ%>͹a*Ì'å!ŸÍWÍÑ*Ì'å!Í:ÍÞ>Í–%>͹b*Ì'å!ÂÍWÍÑ*Ì'å!6Í:ÍÞ>Í–%>͹c*Ì'å!åÍWÍÑ*Ì'å!|Í:ÍÞ>Í–%>͹d!–Í’ >͹e>͹fÍR >͹g>͹hÍ{%X'>!t'Í–%>͹i>͹pÅÍêÃ^ X3 = !X åÍúÍ{%t'Í{%_'ÍUÍ^ ÍùÍ >͹q>͹r>͹r>͹sÅÍêÃÔ 3DO YOU WISH TO SOLVE ANOTHER SET OF EQUATIONS? Y/N?!  åÍúÍùÍ >͹tÅÍêÍùÍúÍùyÍ;!{'Í!ÍùyÍ >͹uà yà Y!{'å! åÍ: Í !{'å! åÍ: Í Íÿ Í<ÊA Ã@>͹vÃ>͹w>͹w>͹x>͹y>͹€Ãs Ãx Ã}  Ç ÃŒ Ñ Ö Û *q å!ŸÍ:*v å!ÂÍ:Íõ*{ å!åÍ:Íõ*€ å!ŸÍ:*… å!ÂÍ:Íõ*Š å!åÍ:Íõͽ*� å!ŸÍ:*” å!ÂÍ:Íõ*™ å!åÍ:Íõͽ>!X'Í–%>͹�Ã! Ã& Ã+ Ã0 Ã5 Ã: Ã? ÃD ÃI Í{%X'* å!ŸÍ:*$ å!ÂÍ:Íõ*) å!åÍ:ÍõÍÂ*. å!ŸÍ:*3 å!ÂÍ:Íõ*8 å!åÍ:ÍõÍÂ*= å!ŸÍ:*B å!ÂÍ:Íõ*G å!åÍ:ÍõÍÂ>!X'Í–%>͹‚É>͹„ÃÉCopyright (C) 1979, By Topaz programming. All rights reserved. From here on protected by End User License.  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MAX IS 25µå2>!!B!"?!¯2A!á^#Vë"»>!få*»å*?!É*?!~þ ʉþʤ#"?!:A!Æ2A!ÒX!½Ñ>!—å*»å*?!É*?!6!B!"?!ñÉ#"?!:A!Æ2A!Ò—>ÿ2A!×-ASCII FILÅ2ù~·Êé2ø#~·ÊéåÍU#Ñ!ø5ÊéëÃÓ:ùþÊþþyÊ É!ù? 2pá"*þÊ-Í0!2s!sÍ� !t"q!sÍv:E"!é*q&Õ~·Èþ#Èþ.Èþ,Èþ-Èþ$Èþ*Èþ^Èþ+Èþ/Èþ&Èþ!Èþ\Âa#~·ÈÑå:E"O~ÍU#á#Ã0N#å 6á~·Ê‰#ÃÈ6#É^ë"ë#:¶þÿÊ®ÍO:N#Í Ã*ù*·é2&á~2O##~2P##å:&!'®þÊý:N#O>[ÍU#Í€>]ÍU#> ÍU#:(=2(Âý>2(yÍ ÍÁ%·ÈæþÊþÂ:'/2'ÉþÀÍÁ%þÂÉ^ë"ë#ÍO!B͹:N#Í É WARNING ONLÙ:N#OåÍ á͹!q͹:P#þÿÈ!w͹Í€É ERROÒ IN LINE *O#|æðÆ0åÍU#á|æÆ0åÍU#á}æðÆ0åÍU#á}æÆ0ÍU#!M#>†wÉ~·úËåÍU#!M#4á#ùæÍU#Éë* s#r#" ëÉ* +V+^" ëÉáÁy2E"åþ ØÿÃÇ%:E"OÉ!¯# ~ÖÒ Æõ> ÍU#ñ<þ ÉO> ÍU#> ÍU#¯2M#Éá"d Íg :A!!B!ÍZ%:?!þÂJ :A!õ!å:A!!B!ÍZ%:?!þÂc :A!õ!å!éá"† 2?!þʉ !˜ O  ~2A!!B!Í–%!éÍ0!2A!!A!Í� Ã… ã"!áÑz³ÊÑ OFx·Êè y·Â» #6Ãè #w·Êè Êè » #6Ãè ñO~¹Úî Êã å #6á#yÍ–%å*!ãÉ"!A!|ºÂ!}»Â!qÃÓ !B!y2A!Í–%*!Í!Ãè FA!O #È6 Èw·ÈÃ!!áÑz³Ê:!ÕéñõÕéÿÿÿÿþ Êp#þ Êp#!¯# 4þ Â|#6Ã|#!Ð# 4þ Ê|#6õy2­#>Íñ#þÊ�#ñÃÇ%ñ2®#^#V!¥#å!®#>ÕÉ:­#O:®#É·Ê$!A Âý#($å#~#^#VáÉáN#å!A Â$($ëá~#Â($é·Èëá"¾%ë^#=Êv%V#=ÕÂb%*¾%éÕ*¾%éá^#V#ëN#F#ÅN#F#ÅN#F#ÅNÅëé·Èëá"¾%ë__{ÑÒ±%s+=ʽ%Ñr+=ʽ%s+=°%!éö%ÃÊ%&Åõå> ¹ÚÝ%!D ãÉ!ã%Ñ%BAD CHANNEL NUMBEÒÃ>&Ãö&Ãö&Ãr&É&Ãz&Ãö&Ãö&Ãö&Ãû&Ã5&Ãä&Ãí&Ãö&Ãö&Ãö&Ãö&Ãö&Ãö&Ãö&Ãö&ñ_ÍÁÉñÍÎ&|µÂW&*S&ÕéÁæÉ:Í&·Âi&ÿÍ·Ê^&õ¯2Í&ñÃS&ñÍÁÉñÁ!„&åÅÊ&ÈÅÃ?&ñ:Í&·Â¥&ÍÎ&|µÂ¬&*¥&ÕéÁ·7È>ÿÉ|þÊ¿&ÿÍ2Í&Ã¥&¯2Í&þÍÃ¥&*â&|¥þÿÀ! Í"â&Éÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:F'·Â'\Íþÿ!G'Ê‘>ÿ2F':E'þ€Â7'€Í\Í!G'·Â‘_<2E'!€~ÁÉ€&INPUT FILE REAÄPÚ<ýt CRAMERS3.DOC ****************************************************************** CRAMERS3.COM IS AN S-BASIC PROGRAM USED TO FIND THE SOLUTION SET TO 3 LINEAR EQUATIONS IN 3 UNKNOWNS. IT MAKES USE OF CRAMER'S RULE FROM ALGEBRA. IT WAS WRITTEN BY MIKE FINERTY 10/18/84 TO ALLEVIATE FRUSTRATION ARISING IN THE WRITING OF ANOTHER PROGRAM. IT IS IN THE PUBLIC DOMAIN FOR NON COMERCIAL USE ****************************************************************** DURING THE SUMMER OF 1984, I WROTE A CRAMER'S RULE PROGRAM IN FORTRAN FOR A CLASS IN FORTRAN 77. THE PROGRAM MADE USE OF 4 SUBROUTINES AND TWO COMMON BLOCK STATEMENTS. LAST NIGHT IT OCCURED TO ME THAT THERE WAS A SIMPLER SOLUTION USING ONE SUBROUTINE AND ONE COMMON BLOCK. CRAMERS3.COM IS THE RESULT. THE PROGRAM REQUIRES THE INPUT OF 9 COEFFICIENTS AND 3 CONSTANTS AS THEY ARE READ IN A LINE OFF THE PAGE. THE GENERAL FORM OF THE EQUATIONS IS: A(N)*X1 + B(N)*X2 + C(N)*X3 = D(N) ; N = {1,2,3} THE A'S, B'S AND C'S FORM A MATRIX AS FOLLOWS: | A(1) B(1) C(1) | | | | A(2) B(2) C(2) | = MAT0 | | | A(3) B(3) C(3) | THE DETERMINATE OF THE A,B&C'S IS CALLED DET0 AND IS EVALUATED BY SUBROUTINE 100 (BOTTOM OF .PRN AND .BAS FILES). BY SUBSTITUTING D(N) FOR A(N),B(N) OR C(N) A NEW MATRIX IS CREATED, WHICH CONFORMS TO THE REQUIREMENT OF CRAMER'S RULE. RESPECTIVELY: THE DETERMINATE SOLUTION TO THESE SINGLE SUBSTITUTIONS ARE DET1, DET2, AND DET3, OBTAINED BY SENDING THE MATRIX FORMED BY X(N),Y(N) AND Z(N) TO THE DETERMINATE SOLVER, SUBROUTINE 100. WHEN X(N) = D(N), DET1 IS RETURNED. WHEN Y(N) = D(N), DET2 IS RETURNED AND WHEN Z(N) = D(N), DET3 IS RETURNED. THESE ARE RETURNED IN THE FORM OF THE VARIABLE "DET" AND ALL FOUR DETERMINATE SOULUTIONS ARE STORED IN THE HOLDING VARIABLES DET0, DET1, DET2 AND DET3, RESPECTIVELY. THE SOLUTION SET IS GIVEN BY THE FOLLOWING RELATIONS: X1 = DET1/DET0 X2 = DET2/DET0 X3 = DET3/DET0 THESE ARE RETURNED AS DOUBLE PRECISSION VALUES BY THE PROGRAM. THE PROGRAM HAS BEEN CHECKED OUT BY SOLVING THE PROBLEM SET IN SECTION 46 OF BRINK'S @U(A FIRST YEAR OF COLLEGE MATHEMATICS) FROM WHICH THE ALGORITHM WAS TAKEN. I HOPE THE PROGRAM IS OF USE TO STUDENTS CHECKING THEIR HOMEWORK BY COMPUTER, & OTHERS WHO NEED THE SOLUTION AND ARE NOT PARTICUALARLY INTERESTED IN THE METHOD (MORE GENERAL TYPES OF SOLUTIONS EXIST USING INVERSE MATRICIES). I ADVISE STUDENTS WHO ARE STUDYING LINEAR EQUATIONS IN 3 UNKNOWNS TO DO THE PROBLEM OUT BY HAND FIRST. I GUARANTEE THAT YOU WILL NOT BE EXAMINED ON MY ABILITY TO PROGRAM A COMPUTER. USE IT TO CHECK YOUR HOMEWORK; BUT DO THAT HOMEWORK TOO. MIKE FINERTY 2358 E PARKSIDE DR TUCSON, ARIZONA 85713OLDING VARIABLES DET0, DET1, DET2 AND DET3, RESPECTIVELY. THE SOLUTION SET IS GIVEN B0001:00 REM this is Program CRAMERS3.BAS, A program to calculate the 0002:00 REM solutions to 3 simultaneous linear equations in 3 unknowns 0003:00 REM using Cramer's Rule of substitution to form 3X3 Determinates 0004:00 REM 0005:00 REM THIS PROGRAM WAS WRITEN BY MICHAEL P. FINERTY 10/18/84 0006:00 REM ************************************************************ 0007:00 10 REM 0008:00 REM A(N)*X1 + B(N)*X2 + C(N)*X3 = D IS AN EQUATION IN 3 UNKNOWNS 0009:00 VAR DET, DET0, DET1, DET2, DET3 = REAL.DOUBLE 0010:00 VAR A$ = STRING 0011:00 VAR N = INTEGER 0012:00 REM 0013:00 DIM COM REAL.DOUBLE A(3) B(3) C(3) D(3) X(3) Y(3) Z(3) 0014:00 REM 0015:00 REM READ IN VALUES OF A,B,C&D FOR EACH OF THE EQUATIONS 0016:00 REM 0017:00 FOR N = 1 TO 3 0018:01 PRINT "PLEASE INPUT A(";N;")" 0019:01 INPUT A(N) 0020:01 PRINT "PLEASE INPUT B(";N;")" 0021:01 INPUT B(N) 0022:01 PRINT "PLEASE INPUT C(";N;")" 0023:01 INPUT C(N) 0024:01 PRINT "PLEASE INPUT D(";N;")" 0025:01 INPUT D(N) 0026:01 NEXT N 0027:00 FOR N = 1 TO 3 0028:01 X(N) = A(N) 0029:01 Y(N) = B(N) 0030:01 Z(N) = C(N) 0031:01 NEXT N 0032:00 REM 0033:00 GOSUB 100 0034:00 REM 0035:00 DET0 = DET 0036:00 IF DET0 = 0 THEN PRINT "INCONSISTANT EQUATIONS, NO SOLUTION" 0037:00 IF DET0 = 0 THEN 200 0038:00 FOR N = 1 TO 3 0039:01 X(N) = D(N) 0040:01 Y(N) = B(N) 0041:01 Z(N) = C(N) 0042:01 NEXT N 0043:00 REM 0044:00 GOSUB 100 0045:00 REM 0046:00 DET1 = DET 0047:00 PRINT "X1 = "; DET1/DET0 0048:00 REM 0049:00 FOR N = 1 TO 3 0050:01 X(N) = A(N) 0051:01 Y(N) = D(N) 0052:01 Z(N) = C(N) 0053:01 NEXT N 0054:00 REM 0055:00 GOSUB 100 0056:00 REM 0057:00 DET2 = DET 0058:00 PRINT "X2 =";DET2/DET0 0059:00 REM 0060:00 FOR N = 1 TO 3 0061:01 X(N) = A(N) 0062:01 Y(N) = B(N) 0063:01 Z(N) = D(N) 0064:01 NEXT N 0065:00 REM 0066:00 GOSUB 100 0067:00 REM 0068:00 DET3 = DET 0069:00 REM 0070:00 PRINT "X3 = ";DET3/DET0 0071:00 REM 0072:00 200 REM 0073:00 PRINT "DO YOU WISH TO SOLVE ANOTHER SET OF EQUATIONS? Y/N?" 0074:00 INPUT A$ 0075:00 IF A$ = "y" OR A$ = "Y" THEN 10 0076:00 END 0077:00 100 REM SUBROUTINE TO CALCULATE DETERMINATES FROM X(N),Y(N) AND 0078:00 REM Z(N) 0079:00 REM 0080:00 DET = X(1)*Y(2)*Z(3) + X(2)*Y(3)*Z(1) + X(3)*Y(1)*Z(2) 0081:00 DET = DET - X(3)*Y(2)*Z(1) - X(1)*Y(3)*Z(2) - X(2)*Y(1)*Z(3) 0082:00 RETURN 0083:00 0084:00 ****** End of program ****** 10 LPRINT "REM: THIS IS PROGRAM 'LSTPOIS', SINGLE TERMS OF POISSON DISTRIBUTION" 20 LPRINT 30 PRINT 40 INPUT "LAMBDA =", L 50 LPRINT "LAMBDA ="L; 60 FOR X = 0 TO 2*L 70 PRINT "CALCULATIONS IN PROGRESS" 80 Y = 0 90 FOR N = 1 TO X 100 Y = Y - LOG(N)/LOG(10) 110 NEXT N 120 Z = X*LOG(L)/LOG(10) 130 R = -L/LOG(10) 140 LOGPROB = Y + Z + R 150 CUMPROB = CUMPROB + 10^(LOGPROB) 160 LPRINT "LAMBDA = ";L, "X = ";X 170 LPRINT "LOGPROB:" LOGPROB 180 LPRINT "PROBABILITY =" 10^(LOGPROB-INT(LOGPROB)); "TEN" INT(LOGPROB) 190 LPRINT "CUMPROB =", CUMPROB 200 LPRINT 210 PRINT 220 NEXT X BABILITY =" 10^(LOGPROB-INT(LOGPROB)); "TEN10 REM FIBONACCI SEQUENCE TERMS 20 FOR X = 1 TO 100 30 Y = (((3.236067977#^X)-(-1.236067977#^X)))/((2^X)*(2.236067977#)) 35 IF Y < 32767 THEN Y = CINT(Y) 36 IF Y > 1E+10 THEN 60 40 LPRINT X;Y 50 NEXT X 60 PRINT "THAT'S ALL FOLKS" 36067977#)) 35 IREM REM THIS IS PROGRAM HOLECALC.BAS. IT CALCULATES THE PROPERTIES OF REM A NEWTONIAN BLACK HOLE (MASS DENSITY OR RADIUS) GIVEN ONE OF REM THOSE PROPERTIES.***THIS IS VERSION # 2*** REM IT CAN BE SHOWN THAT IF K = 3*C^2/(4*Pi*G) = 3.22 * TEN(27) GM/CC REM THAT R^2*D = K, WHERE C IS THE VELOCITY OF LIGHT, G IS REM NEWTON'S GRAVITATIONAL CONSTANT, PI = 3.1415926, R IS THE REM IS THE CRITICAL RADIUS AND D IS THE CRITICAL DENSITY AT THAT REM RADIUS. REM PREVIOUS ESTIMATES WERE BASED ON A MISTAKE BY THE REV MR REM MICHELL IN PROCEDINGS OF ROYAL ACADEMY (LONDON), WHO ASSUMED REM THAT IF THE ESCAPE VELOCITY WAS C, BODIES WOULD BE UNABLE TO REM LEAVE THE BLACK HOLE. IT IS PATENTLY OBVIOUS FROM CELESTIAL REM MECHANICS THAT SUBLUMINIAL VELOCITY OBJECTS WOULD BE ABLE TO REM ORBIT UNTIL THE ESCAPE VELOCITY REACHED 2^.5 * C, AT WHICH REM NOT EVEN LIGHT WOULD BE ABLE TO ORBIT. REM THIS PROGRAM WAS WRITTEN BY MIKE FINERTY, 11/25/84 IN S-BASIC REM 200 YEARS AFTER MR MICHELL'S MISTAKE. REVISED 4/23/85. REM ************************************************************* REM 10 VAR K,G,RLOG,DLOG,MLOG,QUANT,SOLS,L = REAL VAR ANS, RESPONSE = STRING:10 LET L = 2.302585 LET K = 3.22E+27 REM PRINT "PROGRAM RETURNS CRITICAL VALUE OF R,D&M IN CGS SYSTEM" PRINT "PLEASE SELECT INPUT" PRINT PRINT "R ....... RADIUS IN CM" PRINT PRINT "D ....... DENISTY IN GRAMS/CC" PRINT PRINT "M ....... MASS IN GRAMS" PRINT PRINT "MLOG .... LOGARITHM OF MASS IN GRAMS" PRINT REM INPUT "PLEASE INPUT LETTER OF CHOICE"; RESPONSE INPUT "PLEASE INPUT QUANTITY OF CHOICE"; QUANT IF ABS(LOG(QUANT)/L) > 34 THEN PRINT "OUT OF RANGE" IF ABS(LOG(QUANT)/L) > 34 THEN GOTO 20 PRINT RESPONSE;" = ";QUANT REM CASE RESPONSE OF "R": BEGIN DLOG = LOG(K)/L - (2*LOG(QUANT)/L)) MLOG = .6220886 + LOG(K)/L + LOG(QUANT)/L PRINT "DENSITY=";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" PRINT "MASS = ";10^(MLOG-INT(MLOG));"TEN";INT(MLOG);" GMS" SOLS = MLOG - 33.29885 PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" END "D": BEGIN RLOG = 0.5*(LOG(K)/L - LOG(QUANT)/L) MLOG = .6220886 + 0.5*(3*LOG(K)/L-LOG(QUANT)/L) SOLS = MLOG - 33.29885 PRINT "RADIUS =";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" PRINT "MASS =";10^(MLOG-INT(MLOG));"TEN";INT(MLOG);" GMS" PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" END "M": BEGIN DLOG = 1.244177 + 3*LOG(K)/L -2*LOG(QUANT)/L RLOG = -.6220886 +LOG(QUANT)/L-LOG(K)/L SOLS = LOG(QUANT)/L - 33.29885 PRINT "DENSITY = ";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" PRINT "RADUIS = ";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" END "MLOG": BEGIN SOLS = QUANT - 33.2989 DLOG = 1.24418 + 3*LOG(K)/L - 2*QUANT RLOG = -.622089 + QUANT - LOG(K)/L PRINT "SOLAR MASSES =";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" PRINT "DENSITY =";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" PRINT "RADIUS =";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" END END 20 PRINT "DO YOU WISH TO TRY ANOTHER VARIABLE OR VALUE? Y/N?" INPUT ANS IF ANS = "Y" OR ANS = "y" THEN GOTO 10 INT(RLOG);" CM" PRINT "MASS =";10^(MLOG-INT(MLOG));ÃÃ%‹00*ùÍé>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf' >Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf'>Íf' >Íf'!>Íf'!>Íf'">Íf'#ÃÉ“]ŒÍ.Å>!þ/Í .>Íf'$Ãä\¦xXÍ.à>!â/Í .>Íf'%>Íf'&ÅÍ~(Ã>5PROGRAM RETURNS CRITICAL VALUE OF R,D&M IN CGS SYSTEM!åͪ"Í�(Í®(>Íf''ÅÍ~(ÃoPLEASE SELECT INPUT![åͪ"Í�(Í®(>Íf'(ÅÍ~(Í�(Í®(>Íf')ÅÍ~(öR ....... RADIUS IN CM!Ÿåͪ"Í�(Í®(>Íf'0ÅÍ~(Í�(Í®(>Íf'1ÅÍ~(ÃD ....... DENISTY IN GRAMS/CC!æåͪ"Í�(Í®(>Íf'2ÅÍ~(Í�(Í®(>Íf'3ÅÍ~(ÃLM ....... MASS IN GRAMS!4åͪ"Í�(Í®(>Íf'4ÅÍ~(Í�(Í®(>Íf'5ÅÍ~(á$MLOG .... LOGARITHM OF MASS IN GRAMS!|åͪ"Í�(Í®(>Íf'6ÅÍ~(Í�(Í®(>Íf'7>Íf'8ÅÍ~(Í�(ÍS%PLEASE INPUT LETTER OF CHOICEÍ�(ͧ%Í�(yÍÆ#! 0Í­)Í�(yÍ®(>Íf'9ÅÍ~(Í�(ÍS%PLEASE INPUT QUANTITY OF CHOICEÍ�(ͧ%Í�(yÍÆ#!ö/Í1Í�(yÍ®(>Íf'@ÃpˆÍ.ö/Í‹Í.þ/ÍÞÍ—Í.lÍÑͿʻ>Íf'@ÅÍ~(î OUT OF RANGE!¡åͪ"Í�(Í®(>Íf'AÃɈÍ.ö/Í‹Í.þ/ÍÞÍ—Í.ÅÍÑÍ¿Êô>Íf'AÃ(>Íf'BÅÍ~(! 0åͪ"à = ! åͪ"Í.ö/Í>Í�(Í®(>Íf'C>Íf'D! 0å>;(Ã@R!>åÍ�ÂZ>Íf'E>Íf'FÃ_€Í.â/Í‹Í.þ/ÍÞÍ.[Í.ö/͓͋Í.þ/ÍÞÍh>!î/Í .>Íf'GàŸA2Í.œÍ.â/Í‹Í.þ/ÍÞÍcÍ.ö/Í‹Í.þ/ÍÞÍc>!ò/Í .>Íf'HÅÍ~(ÃìDENSITY=!ãåͪ"Ãú Í.öÍ.î/Í.î/ÍùÍhÍZÍ>ÃTEN!åͪ"Í.î/ÍùÍ>Ã9 GMS/CC!1åͪ"Í�(Í®(>Íf'IÅÍ~(Ã^MASS = !Våͪ"Ãl Í.hÍ.ò/Í.ò/ÍùÍhÍZÍ>ÃŽTEN!Šåͪ"Í.ò/ÍùÍ>è GMS!£åͪ"Í�(Í®(>Íf'PÃÃ…2Í.ò/Í.¿Íh>!ú/Í .>Íf'QÅÍ~(ÃøSOLAR MASSES = !èåͪ"àÍ.Í.ú/Í.ú/ÍùÍhÍZÍ>Ã(TEN!$åͪ"Í.ú/ÍùÍ>ÃC SOLS!=åͪ"Í�(Í®(>Íf'RÃ>;(ÃdD!båÍ�— >Íf'S>Íf'TÀÍ.Í.â/Í‹Í.þ/ÍÞÍ.ö/Í‹Í.þ/ÍÞÍhÍ“>!ê/Í .>Íf'UÃÄŸA2ÃË€ÃÒÀÍ.ÀÍ.ÇÍ.ÎÍ.â/͓͋Í.þ/ÍÞÍ.ö/Í‹Í.þ/ÍÞÍhÍ“Íc>!ò/Í .>Íf'VÃ#…2Í.ò/Í.Íh>!ú/Í .>Íf'WÅÍ~(ÃQRADIUS =!Håͪ"Ã_ Í.[Í.ê/Í.ê/ÍùÍhÍZÍ>Ã�TEN!}åͪ"Í.ê/ÍùÍ>Ú CM!–åͪ"Í�(Í®(>Íf'XÅÍ~(þMASS =!·åͪ"ÃÌ Í.ÈÍ.ò/Í.ò/ÍùÍhÍZÍ>ÃîTEN!êåͪ"Í.ò/ÍùÍ>à  GMS! åͪ"Í�(Í®(>Íf'YÅÍ~(Ã5 SOLAR MASSES = !% åͪ"ÃC  Í.? Í.ú/Í.ú/ÍùÍhÍZÍ>Ãe TEN!a åͪ"Í.ú/ÍùÍ>À  SOLS!z åͪ"Í�(Í®(>Íf'`Ã>;(á M!Ÿ åÍ�Âê >Íf'a>Íf'bÃÀ ŸA0ÃÇ ÀÃÎ €Í.¼ Í.à Í.â/͓͋Í.þ/ÍÞÍcÍ.Ê Í.ö/͓͋Í.þ/ÍÞÍh>!î/Í .>Íf'cà ŸA2Í. ÍúÍ.ö/Í‹Í.þ/ÍÞÍcÍ.â/Í‹Í.þ/ÍÞÍh>!ê/Í .>Íf'dÃc …2Í.ö/Í‹Í.þ/ÍÞÍ._ Íh>!ú/Í .>Íf'eÅÍ~(Þ DENSITY = !“ åͪ"ì  Í.¨ Í.î/Í.î/ÍùÍhÍZÍ>ÃÎ TEN!Ê åͪ"Í.î/ÍùÍ>Ãë  GMS/CC!ã åͪ"Í�(Í®(>Íf'fÅÍ~(à RADUIS = ! åͪ"à  Í. Í.ê/Í.ê/ÍùÍhÍZÍ>ÃB TEN!> åͪ"Í.ê/ÍùÍ>Ã[  CM!W åͪ"Í�(Í®(>Íf'gÅÍ~(È SOLAR MASSES = !x åͪ"Ö  Í.’ Í.ú/Í.ú/ÍùÍhÍZÍ>ø TEN!´ åͪ"Í.ú/ÍùÍ>ÃÓ  SOLS!Í åͪ"Í�(Í®(>Íf'hÃ>;(Ã÷ MLOG!ò åÍ�Â>Íf'i>Íf'pà …2Í.ö/Í. Íh>!ú/Í .>Íf'qÃ9 ŸAJÃ@ ÀÃG €Í.5 Í.< Í.â/͓͋Í.þ/ÍÞÍcÍ.C Í.ö/Í“Íh>!î/Í .>Íf'rÃ� ŸA8Í.‰ ÍúÍ.ö/ÍcÍ.â/Í‹Í.þ/ÍÞÍh>!ê/Í .>Íf'sÅÍ~(Ã× SOLAR MASSES =!È åͪ"Ãå  Í.á Í.ú/Í.ú/ÍùÍhÍZÍ>à TEN! åͪ"Í.ú/ÍùÍ>Ã"  SOLS! åͪ"Í�(Í®(>Íf'tÅÍ~(ÃI DENSITY =!? åͪ"ÃW  Í.S Í.î/Í.î/ÍùÍhÍZÍ>Ãy TEN!u åͪ"Í.î/ÍùÍ>Ö  GMS/CC!Ž åͪ"Í�(Í®(>Íf'uÅÍ~(ü RADIUS =!³ åͪ"ÃÊ  Í.Æ Í.ê/Í.ê/ÍùÍhÍZÍ>Ãì TEN!è åͪ"Í.ê/ÍùÍ>à CM!åͪ"Í�(Í®(>Íf'vÃ>Íû(>Íf'x>Íf'xÅÍ~(Ãk2DO YOU WISH TO TRY ANOTHER VARIABLE OR VALUE? Y/N?!8åͪ"Í�(Í®(>Íf'yÅÍ~(Í�(ͧ%Í�(yÍÆ#!0Í­)Í�(yÍ®(>Íf'€Ã«Yðy!0å!©åÍͪ!0å!®åÍͪÍ»ÍßÊß>Íf'€Ã­>Íf'�ÃÉCopyright (C) 1979, By Topaz programming. All rights reserved. From here on protected by End User License.  á"r!v>Í .!z>Í .:}æþ2}:yõ2†ñæþ2y!v>Íî-ÍrÍá"t!v>Íî-!v>Íî-Í/Íh!z>Íî-͓͋!~>Í .!~>Íî-!‚>Í .!~>Íî-!‡>Íî-Íc!~>Íî-!‚>Íî-ÍŸ*t|µÊL!‡>Íî-¯*t|g}o"tÒ+!z>Íî-Í“*t|µÊI!z>Íî-!z>Íî-Í“!z>Í .ÃÍ“:†·òn!v>Í .!‡>Íî-!v>Íî-ÍÞ*ré€á"!>Í .!":·òÿ: Úÿ!>Íî-!n>Íî-ÍíÚæ*#"!>Íî-!n>Íî-ÍÞ!>Í .ë*|µÂ)!>Íî-!j>Íî-ÍíÒ)*+"!>Íî-!n>Íî-Í“!>Í .Ãî!>Íî-ÍrÍÁ!üÿy=Â?B>Íî-!>Íî-!>Íî-Í/ÍÞ!j>Íî-Íh!>Í .!">Íî-!&>Íî-!*>Íî-!.>Íî-!2>Íî-!6>Íî-!:>Íî-!>>Íî->2!!>Íî-Í“Íc:!=¸!>Íî-Í“Íc*|µÊûåÍÎÍ !f>Íî-Í“Íc*é!Ã>'LOG <=0 OR A^X A<=°ÿÿÄÿÿï�ÿ©áŽþö‚íþ«­‚ýÃ<ü“цùÓxA±rŒŸR±rÎåX^ù”…’ŒŸR“]Ž€ á"–!™>Í .:œWæþ2œzæ2Ÿ!™>Íî-!éá"Ä!Ç>Í .:ÍæW:Êæþ²2Ê!Ç>Íî-!éá"á|2·òàåÍÆá)}lg"!>6#=Âì>/!wÍ>":·ò :ö2!>Íî-!éá"]!f>Í .*g}lg:f·ò?!åÃ\ÖÒ`·ÊTG|g}ox<ÃD:låÜÆ!é!ÿÃTá"Ñ!Ü>Í .!Ü>Íî-!à>Í .!Ü>Íî-!ñ>Íî-Ícø>2ðá"Ñ!à>Í .!Ü>Í .!Ô>Í .!ñ>Íî-!ä>Í .!õ>Íî-!ì>Í .!Ô>Íî-!Ø>Í .!äè~#Âø!ä>Íî-!ì>Íî-Í“!ä>Í .!Ü>Íî-!à>Íî-Í“!Ü>Í .!Ô>Íî-!Ü>Íî-!ñ>Íî-!ä>Íî-ÍÞÍ“Íc!Ô>Í .!Ô>Íî-!Ø>Íî-ÍíÊÈ!äè¾Âš#Â…:ð=ÊÈ2ð!Ô>Íî-!Ø>Í .!ì>Íî-!ñ>Íî-Íc!ì>Í .Ãð!Ô>Íî-!退á"!Ž>Í .:‘·ò;!Ž>Íî-!+>Íî-Íc!Ž>Í .Ã;ÿÿÿá"!Ž>Í .:‘2–:Ž·ú‚þÒb!Ž4·#~wÂT:ŽÃH!‘:–æG~æþ°w!ŽÍB!Ž>Íî-!é!’>Íî-*éá"´!·>Í .:ºæþ2º!·>Íî-!éáÁÑz°W{±_Õéáã|/g}/o#ãéá"÷Íí>ÊóÚó>ÿÃóá"÷Íí>ÿÂó>Í‹!éá"!Ö)>Í .:Ù)î2Ù)!Ö)>Íî-!éá";Í�>ÿÊ7Ã5á";Í�>ÿÂ7>Íl!é>2Žá"n¯2Ö)2l2q!t>Í .:u·ÊÖ:w2mæþ2w!t>Íî->;(!‚>Íî-ÍíÚš!~>Íî-ÍÞ!l4Ãu>;(!†>Íî-ÍíÒ¿!~>Íî-Í“!l5Ú:q·ÂØ/2q!Š>Íî-ÍcÃu!t>Í .!l~·òê/<þÒò^~“w>“2s{2r!xÍw#Âÿ+~þ0Ê:m·> ò">-2Ö):r·òA€òo:r=2l>2r>2s!x×):r·ÊY=2r~#ÃG>.:s·Ê–=2s~#Ã]!×)x:r/<6.#60=Â|:rG:s€G#wÂŒëë+~þ0Ê–þ.ʤ#6:l·ÊÖ6E#+ò¹/<-p#Ö ÚÆýÆ:Ox·ÊÒÆ0w#q#6!Ö)~·Âí60#6>2Õ)Ãø#~·Âíx2Õ):ŽþÿÊ:&þÿÊ:Ù*O>!Õ)Íu%*néåÅ!t>Íî-!~>Íî-Í“!t>Í .¯2p!t~·Ê^ú^=w!w·~w+ ÂL:p2pÃ9!tÍB:pÆ0ÁáÉ €ýÌÌÌì†7¼á"Â!Ý*6ÿÍ1)!Õ)6ÿÍ1)!Þ*Ö)ÿ~·ÊÚO·ÊŹÂÁ#«¯!é ~·ÊÀOz¹ÂÁ#ÂÇÃÀ ·ÊÀ¹ÂÁÂÜÃÀá"M!Ö)>Í .!Ú)>Í .!Ý):Ù)®Ò~öþÃL:Ù)Ú)!Ö)ÍPÊ&*Mé!Ù)Ý)~æýwæý!×)Û)Ò?ë¾ÂL#ÂA!éÒUë®òiO·òaë·yÀ?ɾÉá"|!€·Âz!…å!éTrueFalseá"Ÿ!¢·Â™!¦>Íî-!é€á"¼Íè!ÿÿº!å!é>ÃÆ>á"Ü!Ö)Í .:×)·>ÿúÚ/·!éáã|µÈ>ÿ·Éá" Ñ{²ÊøåÃÕ!Õ)6ÿÍ1)* å:Ö)Ãáã}þTÊ-þtÊ-þYÊ-þyÊ-þÿÊ->·É>ÿ·É"Z!\ͯ:bæW:_æþ²2_*Z\w#ÂQÉ>Ãj>€2—á"”!Ÿ>Í .!š>Í .¯2ž2£ͤ!š>Íî-!éÍ-!šÍh!ŸÍh*˜|­òÑ:˜·òË!žÍuÃÑ!£Íu!£ž¯Ž+ÂÚ*˜}¬}òú·òú!žÍu>ÿ2˜!�¯7ŽwÒ+Â:˜æG!�~æþ°w!šÍB:›·ø¯2�É!�~_æþw!¢~Wæþw:—ªWë"˜!šŸN¹ÈG©ò\©x¹ÒbëÍhÃJ4·#~wÂlÉå~/w+Âxá·~Æw+~ˆwР‰Éá"P!l>Í .!h>Í .:m·òS:i·òS!o~_æþw!k~Wæþwë"p:h2r!_ ¯w#ÂÕÃçÊÍ{ÍŠÒà·!ekŽw+ ÂöÃà:rG:lO€2_x©ú7:_©ò7x·úS*pë!z>ÿÍÍ!w>Íî-*PéÍ™*pë!b:`ÍÍ!_>Íî-!é!s>Íî-*Péÿÿÿ!k·~w+ Â�É!m·~w# Â�É!e¯7ŽwÒª+ž0!`~·ø+~=w!e·~w+¼ ¬¯2_Éõz«æW~æþ²wñ·ø¯wÉá"Ð!<>Í .!8>Í .:=·òß:9·òÓ!?~_æþw!;~Wæþwë"@:824ÍÃ3!7Í Ê^¯!;Í!?;·ž+Â<?Ú"!?;Ž+ÂQ·Ã":<o:4g•GÆ24|­ò”x­ú”x·òÓ*@ë!>ÿÍ#!ÿ>Íî-*Ðé!7¯7ŽwÒ´+™!5Í !44#>€¶w!4ÍB*@ë!7:5Í#!4>Íî-!é!û>Íî-*Ðé!åÃ>' DIVISION BY ZERÏÿÿÿ!=Í !9·~w# ÂÉ~w+ÂÉõz«æW~æþ²wñ·ø¯wÉ~2‚#~·úo+~=w~õæþwñ~w+Â` ÂH6É:‚·ð+~·ø6# ÂzÉɯ>Žw+>Â�Ð~+2® #"¯ >+2± ~#·Ê4þ Ê4þ Ê4þEÂö~þ+Êþ-Ê+>+2± #~·Ê4{‡‡ƒ‡_~Í› ƒ_#Ã+6E:± þ+{ÊB/<2Æ ÍÑx//2² !² Í>":® þ+Ên:¸ ö2¸ :Æ ·Ê£!× òƒ/<2Æ !É "Ç >Íî-:Æ =Ê«2Æ *Ç >Íî-ÍÞ Ã‹!Ð >Íî-!² >Íî-ÍÞ *æ+>Í .*æ+Í"*æ+~æýw¯É¯2­ G!³ >6#=ÂÝ*¯ ~þEÊ{ #"¯ þ.Âþ>ÿ2­ ÃäõÅ!³ ¹ ~# Á!¸ ¸ ÍŒ !¸ ¸ ÍŒ !¸ ¾ ÍŒ !¸ ¸ ÍŒ ñÍ› 2¾ !½ >6+=ÂA !¸ ¾ ÍŒ :­ ·ÊY  Âä:­ ·Â{ *¯ ë!Æ þEÊ{ þ.Ê{ 4Ãk :³ ·ú© !¸ ¸ ÍŒ ɯÅŽw+Â� ÁÉÖ0Ú£ þ ØÑÑ>ÿ7Éѯ7ÉýÌÌÌÌÌÌ€ á"›!!Ã!>Í .!¼!>Í .:Ä!·òž!:½!·òž!!É!~_æþw!Â!~Wæþwë"Ê!:¼!2Ì!!ª!¯w# !0Ã2!ÊM!ÍÛ!Íê!Ò+!·!¶!Â! 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Í"l/Éÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:Ð/·Â¢/\Íþÿ!Ñ/Ê>'>ÿ2Ð/:Ï/þ€ÂÁ/€Í\Í!Ñ/·Â>'_<2Ï/!€~ÁÉ€&INPUT FILE REAÄ Ú<ýt HOLECALC.DOC HOLECALC.COM IS A COMPILED S-BASIC PROGRAM THAT CALCULATES THE PROPERTIES OF A BLACK HOLE GIVEN RADIUS, DENSITY OR MASS. HOLECALC.BAS IS THE SOURCE CODE FOR HOLECALC.COM AND HOLECALC.PRN HOLECALC.PRN IS THE PRINT FILE OF THE COMPILED PROGRAM HOLECALC.BAS TO HOLECALC.COM. WE ARE NOW IN VERSION 2 BECAUSE I DISCOVERED THAT MICRO C'S ZCPR NEW VERSION DOESN'T LIKE TO CHANGE MODES FOR PERFECT WRITER. WE NEED NORMAL MODE FOR THE HOLECALC.BAS PROGRAM. ***************************************************************** HOLECALC.* IS AN SBASIC PROGRAM CORRECTING PREVIOUS EFFORTS AT ASSESSING THE CHARACTERISTICS OF BLACK HOLES. BLACK HOLES WERE ORIGINALLY PREDICTED BY REV MR. JOHN MICHELL IN 1784 (SEE SKY AND TELESCOPE, OCTOBER 1984, P 313) MR MICHELL'S PAPER APPEARED IN THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY (LONDON, 1784). HE COUCHED HIS ARGUEMENT IN GEOMETRIC TERMS, AND IT IS FROM THIS DOCUMENT THAT THE MISCONCEPTION OF A BLACK HOLE IS DERIVED. MR MICHELL'S ARGUEMENT IS THAT THERE IS A MAXIMUM SIZE TO LUMINOUS STARS, BASED ON THEIR ESCAPE VELOCITY. IF THE ESCAPE VELOCITY IS THE VELOCITY OF LIGHT (SIC), THE BODY WILL BE INVISIBLE. THUS HE PREDICTED BLACK HOLES 200 YEARS AGO; HOWEVER, THERE IS A MISTAKE IN HIS REASONING: ESCAPE VELOCITY FROM EARTH'S GRAVITY IS APPROXIMATELY 25,000 MPH. WE ARE ALL WITNESSES TO THE FACT THAT SUB ESCAPE VELOCITY PACKAGES CAN ORBIT THE EARTH WITH NO TROUBLE. ORBITAL VELOCITY IS APPROXIMATELY 17,670 MPH UP TO ESCAPE VELOCITY. SO IT IS THAT OBJECTS MAY ORBIT A MASS AT WHOSE SURFACE THE ESCAPE VELOCITY IS THE VELOCITY OF LIGHT, (THAT IS OBJECTS TRAVELING AT SUBLUMINAL VELOCITIES.) LAPLACE MADE THE SAME MISTAKE (OR MORE PROBABLY SIMPLY FOLLOWED MICHELL IN HIS). THE VELOCITY OF ESCAPE THAT THEY WERE LOOKING FOR IS APPROXIMATELY 4.24264 X TEN TO THE 10TH POWER CM/SEC. THIS IS THE ROOT OF 2 TIMES 3 X TEN TO THE 10TH POWER, THE LATTER OF WHICH (3E10) IS THE VELOCITY OF LIGHT IN VACUUM IN CENTEMETERS PER SECOND. THE SCHWARTZCHILD RADIUS OF BLACK HOLES IS ALSO IN ERROR, BEING CALCULATED FROM LEPLACE'S EQUATIONS. CORRECT VALUES ARE GIVEN BY THE PROGRAM, BEING EXACTLY ONE HALF THE RADIUS PREVIOUSLY PREDICTED. AT THE HEART OF IT ALL LIE TWO FUNCTIONAL RELATIONSHIPS D*R^2 = K = 3.22E+27 GRAMS/CC*CM^2 = 3.22E+27 GRAMS/CM AND M = (4*Pi*R^3/3)*D (A) WITH THESE TWO RELATIONSHIPS, ALL OF THE OTHER RELATIONSHIPS CAN BE CALCULATED. THE CONSTANT, "K," IS SIMPLY THE RESULT OF SOLVING THE EQUATION: 2*C^2 = 2*G*M/R, SUBSTITUTING RELATION (A) FOR M AND SOLVING FOR THE PAIR (D*R^2). THE VALUE OF K IS APPROXIMATELY: K = 3.22127 TEN(27) GM/CM IT IS A CRITICAL VALUE: GIVEN ONE CONSTANT SAY DENSITY, THERE IS ONE RADIUS THAT A SPHERE WITH THAT AVERAGE DENSITY BECOMES A BLACK HOLE. ANY BODY LARGER THAN THAT AT THAT DENSITY OR ANY BODY DENSER THAN THAT AT THAT RADIUS WILL BE A BLACK HOLE. THE CRITICAL MASS FOR THAT DENSITY AND RADIUS IS ALSO CALCULATED. IT IS ALSO A CRITICAL VALUE. AT THAT RADIUS ANY MASS GREATER THAN M OR AT THAT AVERAGE DENSITY ANY MASS GREATER THAN M WILL COLLAPSE INTO A NEWTONIAN BLACK HOLE. THIS DOES NOT NECESSARILY MEAN THAT THE OBJECT WILL COLLAPSE INTO SINGUARITY, THAT DEPENDS ON TEMPERATURE AND DENSITY. THE REMAINDER OF PROPERTIES, DRAWN FROM GENERAL RELATIVITY, I AM NOT PREPARED TO DISCUSS A THIS TIME. THERE ARE PLENTY OF ARGUEMENTS IN THE MAGAZINES AS TO WHETHER OR NOT SUPERMASSIVE BALCK HOLES EXIST. I SUSPECT THAT THEY DO AND THAT OUR X-RAY SOURCES, PARTICUALRLY X-RAY BURSTERS, ARE SUPERMASSIVE BLACK HOLES (QUASARS TOO). THIS PROGRAM WAS WRITTEN FOR PEOPLE WHO WANT TO EXPLORE THOSE POSSIBILITIES. SORRY BUT THE LARGEST MASS ALLOWED BY S-BASIC IS 1E34 GMS. IF YOU WANT TO GET BIGGER, REPROGRAM WITH INPUTTING MLOG/L (THE LOGARITHM BASE 10 OF THE MASS) AND WORK OUT THE RELATIONSHIPS FOR THAT (QUANT = MLOG/L). IT IS SIMPLEST TO DO THIS ON A SCIENTIFIC HAND CALCULATOR, JUST USE THE LOG FUNCTION ON THE SCIENTIFIC NUMBER OF THE MASS IN GRAMS. THE UNIVERSE AS WE KNOW IT IS APPROXIMATELY 14 BILLION LIGHT YEARS (BEVALYS) = 1.325 TEN(28) CM IN RADIUS. YOU CAN CALCULATE ITS MAXIMUM MASS USING THE PROGRAM. USING THE REALTIONSHIP #OF MASSIVE PARTICLES = 2*REST MASS*6.23 TEN(23) YOU CAN CALCULATE THE MAXIMUM NUMBER OF PROTONS, ELECTRONS AND NEUTRONS IN THE VISIBLE UNIVERSE. IT SHOULD BE SOMEWHERE AROUND TEN (81) PARTICLES. AND THAT'S ALL THERE IS! MIKE FINERTY 2358 E PARKSIDE DR TUCSON, ARIZONA 85713 COMMENTS APPRECIATED!LRLY X-RAY BURSTERS, ARE SUPERMASSIVE BLACK HOLES (QUASARS TOO). THIS PROGRAM WAS 0001:00 REM 0002:00 REM THIS IS PROGRAM HOLECALC.BAS. IT CALCULATES THE PROPERTIES OF 0003:00 REM A NEWTONIAN BLACK HOLE (MASS DENSITY OR RADIUS) GIVEN ONE OF 0004:00 REM THOSE PROPERTIES.***THIS IS VERSION # 2*** 0005:00 REM IT CAN BE SHOWN THAT IF K = 3*C^2/(4*Pi*G) = 3.22 * TEN(27) GM/CC 0006:00 REM THAT R^2*D = K, WHERE C IS THE VELOCITY OF LIGHT, G IS 0007:00 REM NEWTON'S GRAVITATIONAL CONSTANT, PI = 3.1415926, R IS THE 0008:00 REM IS THE CRITICAL RADIUS AND D IS THE CRITICAL DENSITY AT THAT 0009:00 REM RADIUS. 0010:00 REM PREVIOUS ESTIMATES WERE BASED ON A MISTAKE BY THE REV MR 0011:00 REM MICHELL IN PROCEDINGS OF ROYAL ACADEMY (LONDON), WHO ASSUMED 0012:00 REM THAT IF THE ESCAPE VELOCITY WAS C, BODIES WOULD BE UNABLE TO 0013:00 REM LEAVE THE BLACK HOLE. IT IS PATENTLY OBVIOUS FROM CELESTIAL 0014:00 REM MECHANICS THAT SUBLUMINIAL VELOCITY OBJECTS WOULD BE ABLE TO 0015:00 REM ORBIT UNTIL THE ESCAPE VELOCITY REACHED 2^.5 * C, AT WHICH 0016:00 REM NOT EVEN LIGHT WOULD BE ABLE TO ORBIT. 0017:00 REM THIS PROGRAM WAS WRITTEN BY MIKE FINERTY, 11/25/84 IN S-BASIC 0018:00 REM 200 YEARS AFTER MR MICHELL'S MISTAKE. REVISED 4/23/85. 0019:00 REM ************************************************************* 0020:00 REM 0021:00 10 VAR K,G,RLOG,DLOG,MLOG,QUANT,SOLS,L = REAL 0022:00 VAR ANS, RESPONSE = STRING:10 0023:00 LET L = 2.302585 0024:00 LET K = 3.22E+27 0025:00 REM 0026:00 PRINT "PROGRAM RETURNS CRITICAL VALUE OF R,D&M IN CGS SYSTEM" 0027:00 PRINT "PLEASE SELECT INPUT" 0028:00 PRINT 0029:00 PRINT "R ....... RADIUS IN CM" 0030:00 PRINT 0031:00 PRINT "D ....... DENISTY IN GRAMS/CC" 0032:00 PRINT 0033:00 PRINT "M ....... MASS IN GRAMS" 0034:00 PRINT 0035:00 PRINT "MLOG .... LOGARITHM OF MASS IN GRAMS" 0036:00 PRINT 0037:00 REM 0038:00 INPUT "PLEASE INPUT LETTER OF CHOICE"; RESPONSE 0039:00 INPUT "PLEASE INPUT QUANTITY OF CHOICE"; QUANT 0040:00 IF ABS(LOG(QUANT)/L) > 34 THEN PRINT "OUT OF RANGE" 0041:00 IF ABS(LOG(QUANT)/L) > 34 THEN GOTO 20 0042:00 PRINT RESPONSE;" = ";QUANT 0043:00 REM 0044:00 CASE RESPONSE OF 0045:00 "R": BEGIN 0046:01 DLOG = LOG(K)/L - (2*LOG(QUANT)/L)) 0047:01 MLOG = .6220886 + LOG(K)/L + LOG(QUANT)/L 0048:01 PRINT "DENSITY=";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" 0049:01 PRINT "MASS = ";10^(MLOG-INT(MLOG));"TEN";INT(MLOG);" GMS" 0050:01 SOLS = MLOG - 33.29885 0051:01 PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" 0052:01 END 0053:00 "D": BEGIN 0054:01 RLOG = 0.5*(LOG(K)/L - LOG(QUANT)/L) 0055:01 MLOG = .6220886 + 0.5*(3*LOG(K)/L-LOG(QUANT)/L) 0056:01 SOLS = MLOG - 33.29885 0057:01 PRINT "RADIUS =";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" 0058:01 PRINT "MASS =";10^(MLOG-INT(MLOG));"TEN";INT(MLOG);" GMS" 0059:01 PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" 0060:01 END 0061:00 "M": BEGIN 0062:01 DLOG = 1.244177 + 3*LOG(K)/L -2*LOG(QUANT)/L 0063:01 RLOG = -.6220886 +LOG(QUANT)/L-LOG(K)/L 0064:01 SOLS = LOG(QUANT)/L - 33.29885 0065:01 PRINT "DENSITY = ";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" 0066:01 PRINT "RADUIS = ";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" 0067:01 PRINT "SOLAR MASSES = ";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" 0068:01 END 0069:00 "MLOG": BEGIN 0070:01 SOLS = QUANT - 33.2989 0071:01 DLOG = 1.24418 + 3*LOG(K)/L - 2*QUANT 0072:01 RLOG = -.622089 + QUANT - LOG(K)/L 0073:01 PRINT "SOLAR MASSES =";10^(SOLS-INT(SOLS));"TEN";INT(SOLS);" SOLS" 0074:01 PRINT "DENSITY =";10^(DLOG-INT(DLOG));"TEN";INT(DLOG);" GMS/CC" 0075:01 PRINT "RADIUS =";10^(RLOG-INT(RLOG));"TEN";INT(RLOG);" CM" 0076:01 END 0077:00 END 0078:00 20 PRINT "DO YOU WISH TO TRY ANOTHER VARIABLE OR VALUE? Y/N?" 0079:00 INPUT ANS 0080:00 IF ANS = "Y" OR ANS = "y" THEN GOTO 10 0081:00 ****** End of program ****** 1 REM A IS SEMI-MAJ AXIS, B IS SEMI-MIN AXIS 2 REM FI IS ANGLE OF INCIDENCE IN DEGREEES 10 INPUT "A=";A 11 INPUT "B=";B 20 INPUT "FI:";FI 30 FI = FI*.0174532 40 REM FI IS NOW IN RADIANS 50 FOR Z = -10 TO 10 60 N = Z 70 GOSUB 260 80 MZ = MA 90 BZ = BA 100 FOR R = (Z+1) TO 10 110 N = R 120 GOSUB 260 130 MR = MA 140 BR = BA 150 AB = (BZ-BR)/(MR-MZ) 160 REM AB IS ABSISSA OF INTERSECTING RAYS 170 OD = MR*AB + BR 180 PRINT "Z:";Z, "R:";R 190 PRINT "MZ;"; MZ, "BZ:";BZ 200 PRINT "MR:";MR,"BR:";BR 210 PRINT "ABSISSA=";AB, "ORDINATE=";OD 220 PRINT 230 NEXT R 240 NEXT Z 250 STOP 260 REM THE FOLLOWING COMPUTES MA AND BA GIVEN 'N' 270 X = A*(((1+((N^2)/(B^2)))^.5)-1) 280 MO = -N*A/(B^2)/((1+((N^2)/(B^2)))^.5) 290 TH = ATN(MO) 300 IF N > 0 THEN 360 310 IF TH < = FI THEN 340 320 KA = TH + ABS(TH - FI) 330 GOTO 370 340 KA = TH - ABS(TH - FI) 350 GOTO 370 360 KA = 2*TH - FI 370 MA = TAN (KA) 380 BA = N - MA*X 390 RETURN  330 GOTO 370 340 KA = TH - ABS(TH - FI) 350 GOTO 370 360 K10 LPRINT 20 LPRINT "REM: THIS IS 'LSTBIN', SINGLE TERMS OF THE BINOMIAL DISTRIBUTION" 30 DEFDBL L 40 PRINT 50 LPRINT 60 INPUT; "N:"; N 70 PRINT 80 LPRINT "N=";N 90 INPUT; "R:";R 100 PRINT 110 LPRINT "R=";R 120 PRINT "RUNTIME =" .0908*R "SECONDS" 130 PRINT 140 INPUT; "THETA"; T 150 LPRINT "THETA="; T 160 PRINT 170 PRINT "CALCULATIONS IN PROGRESS" 180 FOR X = 1 TO R 190 Y = Y + LOG(X)/LOG(10) 200 NEXT 210 M = N - R + 1 220 FOR Z = M TO N 230 P = P + LOG(Z)/LOG(10) 240 NEXT Z 250 NCR = P - Y 260 S = 1 - T 270 Q = R*LOG(T)/LOG(10) 280 U = (N-R)*LOG(S)/LOG(10) 290 LOGPROB = NCR + Q + U 300 LPRINT 310 LPRINT 320 LPRINT "LOGPROB =" LOGPROB 330 LPRINT "PROBABILITY =" 10^(LOGPROB-INT(LOGPROB)), "TEN"INT(LOGPROB) 340 LPRINT 350 END  320 LPRINT "LOGPROB =" LOGPROB 330 LPRINT "PROBABILITY =" 10^(LOGPROB-INT(LOGPROB)), "TEN"INT(LOGPROB) 340 LPRINT 350 END ÿÐa žbž "REM: THIS IS 'LSTBIN', SINGLE TERMS OF THE BINOMIAL DISTRIBUTION")b° L,Y,P,Q,U/b(‘5b2žDb<…; "N:"; NJbF‘WbPž "N=";NebZ…; "R:";Rkbd‘xbnž "R=";Rœbx‘ "RUNTIME =" Zõ9}ôR "SECONDS"¢b‚‘´bŒ…; "THETA"; TÆb–ž "THETA="; TÌb ‘íbª‘ "CALCULATIONS IN PROGRESS"ýb´‚ X ð  Î Rc¾Y ð Y ò ÿŠ(X)õÿŠ( )cȃ.cÒM ð N ó R ò >cÜ‚ Z ð M Î NWcæP ð P ò ÿŠ(Z)õÿŠ( )_cðƒ ZocúNCR ð P ó Y}cS ð  ó T”cQ ð RôÿŠ(T)õÿŠ( )¯cU ð (NóR)ôÿŠ(S)õÿŠ( )Éc"LOGPROB ð NCR ò Q ò UÏc,žÕc6žïc@ž "LOGPROB =" LOGPROB0dJž "PROBABILITY ="  ö(LOGPROBóÿ…(LOGPROB)), "TEN"ÿ…(LOGPROB)6dTžÍY$>ÍY$>ÍY$>ÍY$>ÍY$>ÍY$ÅÍŠ%Í™%ÍF"XÍ™%Íš"Í™%y͹ !,ÍHÍ™%yͺ%>ÍY$>ÍY$>ÍY$>ÍY$ÅÍŠ%ÕX=!’åÍG*,å͙̀%ͺ%>ÍY$>ÍY$>ÍY$>ÍY$ÅÍŠ%Ã×RUNTIME=!ÎåÍGÃåþÌÌÌÍ*á*,åÍ� Ía ÍÍ� ÃSECONDS!ýåÍGÍ™%ͺ%>ÍY$>ÍY$ÅÍŠ%Í™%ͺ%>ÍY$ >ÍY$ ÅÍŠ%Í™%ÍF"LAMBDA =Í™%Íš"Í™%y͹ !,͙͛%yͺ%>ÍY$>ÍY$>ÍY$>ÍY$ÅÍŠ%×LAMBDA=!�åÍGÍ'*,ÍàÍ™%ͺ%>ÍY$>ÍY$>ÍY$>ÍY$ÅÍŠ%ÃêCALCULATIONS IN PROGRESS!ÑåÍGÍ™%ͺ%>ÍY$>ÍY$à *å>!,Íq%ÍB*Í~%å*,åÃ&!$>Íõ)>ÍY$>ÍY$ÃC Í'*,*,åÍ� Ía ÍLÍ3 Í*?ÍLÍ3 ÍbÍÏ>!,ÍB*>ÍY$>ÍY$!.Í®>ÍY$>ÍY$Ú *,åÍ� Í'*,Ía ÍLÍ3 ÍÍ*–ÍLÍ3 Íb>!,ÍB*>ÍY$>ÍY$ÃÝ Í'*,Ío Í*ÙÍLÍ3 Íb>!,ÍB*>ÍY$>ÍY$Í'*,Í'*,ÍÊÍ'*,ÍÊ>!$,ÍB*>ÍY$ >ÍY$ >ÍY$!>ÍY$!ÅÍŠ%ÃTLOGPROB=!KåÍGÍ'*$,ÍàÍ™%ͺ%>ÍY$">ÍY$">ÍY$#>ÍY$#ÅÍŠ%×LOGPROB=!ŽåÍGÍ'*$,ÍàÍ™%ͺ%>ÍY$$>ÍY$$>ÍY$%>ÍY$%ÅÍŠ%Ãß PROBABILITY =!ÑåÍGÃí Í*éÍ'*$,Ía Í'*$,Ía ͺ ÍTÍÍ� ÃTEN!åÍGÍ'*$,Ía ͺ Í� Í™%ͺ%>ÍY$&>ÍY$&>ÍY$'>ÍY$'ÅÍŠ%Ãc PROBABILITY =!UåÍGÃq Í*mÍ'*$,Ía Í'*$,Ía ͺ ÍTÍÍ� ÙTEN!•åÍGÍ'*$,Ía ͺ Í� Í™%ͺ%>ÍY$(>ÍY$(ÅÍŠ%Ã× --ooOOOoo--!ËåÍGÍ™%ͺ%>ÍY$)>ÍY$)>ÍY$0>ÍY$0ÅÍŠ%à --ooOOOoo--! åÍGÍ™%ͺ%>ÍY$1>ÍY$1Ã>ÍY$2ÃÉCopyright (C) 1979, By Topaz programming. All rights reserved. From here on protected by End User License.  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Í.*,ë!#:!Í! >Íõ)!é!ç>Íõ)*¼é!ÑÃ1$ DIVISION BY ZERÏÿÿÿ!)Íø!%·~w# ÂûÉ~w+ÂÉõz«æW~æþ²wñ·ø¯wÉ~2n#~·ú[+~=w~õæþwñ~w+ÂL Â46É:n·ð+~·ø6# ÂfÉɯ>Žw+>ÂyÐ~+2š#"›>+2�~#·Ê þ Ê þ Ê þEÂâ~þ+Êþ-Ê+>+2�#~·Ê {‡‡ƒ‡_~͇ƒ_#à +6E:�þ+{Ê./<2²ͽx//2ž!žÍÛ:šþ+ÊZ:¤ö2¤:²·Ê�!Ãòo/<2²!µ"³>Íõ):²=Ê—2²*³>Íõ)ÍÃw!¼>Íõ)!ž>Íõ)Í*í'>ÍB**í'Í*í'~æýw¯É¯2™G!Ÿ>6#=ÂÉ*›~þEÊg#"›þ.Âê>ÿ2™ÃÐõÅ!Ÿ¥~#ÂôÁ!¤¤Íx!¤¤Íx!¤ªÍx!¤¤Íxñ͇2ª!©>6+=Â-!¤ªÍx:™·ÊE ÂÐ:™·Âg*›ë!²þEÊgþ.Êg4ÃW:Ÿ·ú•!¤¤ÍxɯÅŽw+Â|ÁÉÖ0Ú�þ ØÑÑ>ÿ7Éѯ7ÉýÌÌÌÌÌÌ€ >ÃÑ>€2þá"û! >ÍB*!>ÍB*¯22Í!>Íõ)!éÍš!ÍÕ! ÍÕ*ÿ|­ò>:ÿ·ò8!ÍäÃ>!Íä!¯Ž+ÂG*ÿ}¬}òg·òg!Íä>ÿ2ÿ!¯7ŽwÒ{+Âo:ÿæG!~æþ°w!ÍÛ:·ø¯2É!~_æþw!~Wæþw:þªWë"ÿ! N¹ÈG©òÉ©x¹ÒÏëÍÕ÷~ÍB*!à>ÍB*:è·òÂ:á·òÂ!í~_æþw!æ~Wæþwë"î:à2ð!ίw#ÂD0ÃVÊqÍÿÍÒO·!Úæ Žw+ ÂeÃO:ðG:çO€2Îx©ú¦:Ωò¦x·úÂ*îë!þ>ÿÍQ!ø>Íõ)*¿éÍ*îë!Ô:ÏÍQ!Î>Íõ)!é!ñ>Íõ)*¿éÿÿÿÿÿÿ!æ ·~w+ ÂÉ!è·~w# ÂÉ!Ú ¯7ŽwÒ.+Â"`!Ï~·ø+~=w!Ú ·~w+Â@ Â0¯2ÎÉõz«æW~æþ²wñ·ø¯wÉá"Z!Ò>ÍB*!Ë>ÍB*:Ó·òi:Ì·ò]!Ø~_æþw!Ñ~Wæþwë"Ù:Ë2ÄÍ“0÷!Êͨ Êâ¯!Ñͨ!ØÑ·ž+ÂÀ?Ú¦!ØÑŽ+Âշæ:Òo:Äg•GÆ2Ä|­òx­úx·ò]*Ùë!’>ÿͳ!Œ>Íõ)*Zé!ʯ7ŽwÒ8+Â!ÅÍœ!Ä4#>€¶w!ÄÍÛ!ÄÍ*Ùë!Ê:Åͳ!Ä>Íõ)!é!…>Íõ)*Zé!oÃ1$ DIVISION BY ZERÏÿÿÿÿÿÿ!ÓÍœ!Ì·~w# ŸÉ~w+ªÉõz«æW~æþ²wñ·ø¯wÉ0~2#~·ú+~=w~õæþwñ~w+Âù Âá6É:·ð+~·ø6# Âɯ>Žw+>Â%Ð~Íh"å*~ãÉã"ÚáÍÜBþ0—Ã�!â&6 :Aþ+Ê¥w#·Ê±wÃ¥xþ»60#<62á&:#þÿÊÔ!á&:å'O>Íh"å*ÚãÉã"5á!Bã|·>+2Aòû}/o|/g#>-2A7ÅëN#Fë |·úã,ãÃy/Ox/G ÁãyÆ0w#Ê.ãÅÃáå*5ãÉðØüœÿöÿÿÿåâ&Í: â&ÍÈÚ^ëás#rÉÍdÃI!jÉERROR IN INPUT, RE-ENTER PLEASÅå:é'ͺ%á:é'OÍY%yͺ%!©ÍY%:Þ&͹ É?? !²ÉNUMBER TO LARGE/SMAL̯2ì' þ+ÊÜþ-ÂÝ>ÿ2ì'`i"8 ! ·Ê T])))Ö0þ ?Ú _Ãå:ì'·È|/g}/o#¯É*8 DM! þHÈ·7ÈÖ07øþ Ú* Öþ?Ø_))))à ë"— ë:á&O·Êˆ *ß&~þ ÂZ #ʈ ÃL ~þ,Ê¢ þ Ê¢ þ Ê¢ þE~Ê} þ+Ê¢ þ-Ê¢  #ʯ ÃZ ~þ,Â� # >0ï ~þ,ʈ Ã} ¯°Ê™ ~þ,¯ # "ß&y2á&¯ÉõO>ÍŒ(þʼ!ñO2Þ&!â&"ß&¯2á&ÿÅåÍm*áÁÚ!þ Ê!þÊC!þÊ0!þÊa!þÊ{!þÊ#!wʉ!:ç'þÊ!åÅ~Íð'Áá~#þÂÖ >ÿ�2á&6É:æ'þÿÊ>Ãþ xþÿÊÖ +~ÅåÍð'áÁÃÖ xþÿÊÖ +åÅ>Íð'> Íð'>Íð'ÁáÃÖ åÅÍ!>#Íð'ͺ%!á&>Íh"ÁáÃÖ >#Íð'ͺ%:Þ&ù !œ!ÍÉ$:é'OÍš":Þ&ù TOO MANY CHARECTERS. MAX IS 25µå2Þ&!â&"ß&¯2á&á^#Vë"9">!ä!å*9"å*ß&É*ß&~þ Ê"þÊ""#"ß&:á&Æ2á&ÒÖ!!;"Ã1$>!"å*9"å*ß&É*ß&6!â&"ß&ñÉ#"ß&:á&Æ2á&Ò">ÿ2á&Ã"-ASCII FILÅá~·ÊT"#åÍð'ÃF"#~#åþÈþõy̺%ñÈÍž%É2™"~·Ê‰"2˜"#~·Ê‰"åÍð'Ñ!˜"5ʉ"ëÃs":™"þÊž%þyʺ%É! "ÃY%? 2#á"Ê"þÊÍ"ÍÐ&2#!#Í=&!#"#!#Í$:å'!é*#Æ"Õ~·Èþ#Èþ.Èþ,Èþ-Èþ$Èþ*Èþ^Èþ+Èþ/Èþ&Èþ!Èþ\Â##~·ÈÑå:å'O~Íð'á#ÃÐ"N#å 6á~·Ê)$#Ã$È6#Ã)$^ë"ë#:V$þÿÊN$Íï$:é'ͺ%Ã*ù*W$é2Æ$á~2ê'#~2ë'#å:Æ$!Ç$®þÊ�$:é'O>[Íð'Í %>]Íð'> Íð':È$=2È$Â�$>2È$yͺ%Ím*·ÈæþÊþ¸$:Ç$/2Ç$ÉþÀÍm*þ»$É^ë"ë#Íï$!â$ÍY%:é'ͺ%É WARNING ONLÙ:é'Oåͺ%áÍY%!%ÍY%:ë'þÿÈ!%ÍY%Í %É ERROÒ IN LINE *ê'|æðÆ0åÍð'á|æÆ0åÍð'á}æðÆ0åÍð'á}æÆ0Íð'!è'>†wÉ~·úk%åÍð'!è'4á#ÃY%æÍð'Éë* s#r#" ëÉ* +V+^" ëÉáÁy2å'åþ ØÿÃs*:å'OÉ!J( ~ÖÒ¥%Æõ> Íð'ñ<þ¬%ÉO> Íð'> Íð'¯2è'Éá"&Í&:á&!â&Íõ):ß&þÂê%:á&õ!å:á&!â&Íõ):ß&þÂ&:á&õ!å!éá"&&2ß&þÊ)&!8&O  ~2á&!â&ÍB*!éÍÐ&2á&!á&Í=&Ã%&ã"·&áÑz³Êq&OFx·Êˆ&y·Â[È&#w·Êˆ&ʈ& Â[È&ñO~¹ÚŽ&ʃ&å #6á#yÍB*å*·&ãÉ"µ&á&|ºÂ¢&}»Â¢&qÃs&!â&y2á&ÍB**µ&͹&È&Fá&O #È6 Èw·ÈÃÁ&áÑz³ÊÚ&ÕéñõÕéÿÿÿÿþ Ê (þ Ê (!J( 4þ Â(6Ã(!k( 4þ Ê(6õy2H(>ÍŒ(þÊ*(ñÃs*ñ2I(^#V!@(å!I(>ÕÉ:H(O:I(ɷʪ(!A ˜(Ã(å#~#^#VáÉáN#å!A ¶(Ã(ëá~#ÂÃ(é·Èëá"j*ë^#=Ê*V#=ÕÂý)*j*éÕ*j*éá^#V#ëN#F#ÅN#FÅëéá^#V#ëN#F#ÅN#F#ÅN#F#ÅNÅëé·Èëá"j*ë__{ÑÒ]*s+=Êi*Ñr+=Êi*s+=Â\*!é¢*Ãv*À*Åõå> ¹Ú‰*!D ãÉ!�*Ã1$%BAD CHANNEL NUMBEÒÃê*â+â+Ã+Ã5+Ã&+â+â+â+ç+Ãá*Ã�+Ù+â+â+â+â+â+â+â+â+ñ_ÍÁÉñÍz+|µÂ+*ÿ*ÕéÁæÉ:y+·Â+ÿÍ·Ê +õ¯2y+ñÃÿ*ñÍÁÉñÁ!0+åÅÃ6+ÈÅÃë*ñ:y+·ÂQ+Íz+|µÂX+*Q+ÕéÁ·7È>ÿÉ|þÊk+ÿÍ2y+ÃQ+¯2y+þÍÃQ+*Ž+|¥þÿÀ! Í"Ž+Éÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:ò+·ÂÄ+\Íþÿ!ó+Ê1$>ÿ2ò+:ñ+þ€Âã+€Í\Í!ó+·Â1$_<2ñ+!€~ÁÉ€&INPUT FILE REAÄÚ<ýtPoisson.* is an S-Basic program designed to work in the extended range. Like Binomial.* it is written making use of logarithms. The same procedure is used to find out the number of good digits in the answer. # good = 5 - #of digits in characteristic - # of iterations of X. The Poisson distribution is used where the mean number of events is know (on the average 158.394 telephone calls come in an hour at a certain buisness, what is the probability only 23 coming in an hour on a certain day?) Mean = lambda = 158.394; number of occurances (must be integer) = 23. Logprob = -40.6081... ; probability = 2.46E-41. Note that this program will work for Probabliity < 1E-128. For instance if we have a poisson process with X = 452, Lambda = 35.612; we wind up with a proability = 2.03 E -320. This is reported as 2.03 Ten -320 by the progrem. A Nevada Basic version of the program is available on this disk. This program was written by \ Michael P Finerty 2358 E Parkside Drive Tucson, Arizona 85713 omial.* it is written making use of logarithms.10 REM THIS IS PROGRAM "POSITION" BY M. FINERTY 20 REM THIS PROGRAM CALCULATES DECLINATION AND RIGHT ASCENTION 30 REM FROM ALTITUDE, AZMUTH, LATITUDE AND SIDERIAL TIME 40 REM************************************************** 50 C1 = 180/3.1415926# 60 C2 = 1/C1 70 REM 80 PRINT "PLEASE INPUT DATA" 90 INPUT "LATITUDE =", LAT 100 LAT = LAT*C2 110 INPUT "ALTITUDE = ", ALT 120 ALT = ALT*C2 130 INPUT "AZMUTH =", AZ 140 AZ = AZ*C2 150 DECSIN = SIN(LAT)*SIN(ALT) + COS(LAT)*COS(ALT)*COS(AZ) 160 DECLINAT = ATN(DECSIN/((1-DECSIN^2)^.5)) 170 DEC = DECLINAT*C1 180 PRINT "DECLINATION = "; DEC; 190 IF DEC < 0 THEN PRINT " S" 200 IF DEC >=0 THEN PRINT " N" 210 TSIN = SIN(AZ)*COS(ALT)/COS(DECLINAT) 220 TCOS = (SIN(ALT) - SIN(LAT)*SIN(DECLINAT))/(COS(LAT)*COS(DECLINAT)) 230 HA = ATN(TSIN /((1-TSIN^2)^.5)) 240 HA = HA*C1 260 HA = ABS(HA) 270 IF TSIN < 0 AND TCOS >=0 THEN PRINT "HOUR ANGLE ="; HA;" DEGREES" 280 IF TSIN < 0 AND TCOS >= 0 THEN TIMEANG = HA 290 IF TSIN < 0 AND TCOS < 0 THEN PRINT "HOUR ANGLE ="; 180 - HA;" DEGREES" 300 IF TSIN < 0 AND TCOS < 0 THEN TIMEANG = 180 - HA 310 IF TSIN >= 0 AND TCOS < 0 THEN PRINT "HOUR ANGLE ="; 180 + HA;" DEGREES" 320 IF TSIN >= 0 AND TCOS >=0 THEN PRINT "HOUR ANGLE ="; 360 - HA;" DEGREES" 330 IF TSIN >= 0 AND TCOS < 0 THEN TIMEANG = 180 + HA 340 IF TSIN >= 0 AND TCOS >= 0 THEN TIMEANG = 360 - HA 350 INPUT "LOCAL SIDERIAL TIME HRS,MINS = "; HRS,MINS 360 SIDTIME = 15*HRS + MINS/4 370 RA = SIDTIME + 360 - TIMEANG 380 IF RA > 360 THEN RA = RA -360 390 PRINT "RIGHT ASCENTION ="; RA;"DEGREES" 400 RTASC = INT(RA/15) 410 PLUSMINS = 60*(RA/15 - RTASC) 420 PRINT "RIGHT ASCENTION = ";RTASC;"HRS "; PLUSMINS;"MINS" 430 PRINT "DO YOU WANT ANOTHER OBJECT Y/N?" 440 INPUT ANS$ 450 IF ANS$ = "Y" THEN 110 460 END SC;"HRS "; PLUSMINS;"MINS" 430 PRINT "DO YOU WANT ANOTHER OBJECT Y/N?" 440 INPUT ANS$ 450 IF ANS$ = "Y" THEN 110 460 EN POSITION.BAS is an MBASIC program used to identify objects seen in a dobsonian alt-azmuth telescope using setting circles and a clock. Siderial time may be computed if the longitude of the observer is known using program TIME.BAS. If siderial time is known for the begining of an observing session, in 6 hours siderial time will be out of synchronization by 1 minute of time or a quarter of degree of arc (approximately). This amount is insignificant when one considers the accuracy of dobsonian seeting circles +/- 0.5 degrees. Longitude may be determined by looking on a map for the nearest degree of longitude (horizontal measure). Locations of famous observatories are found in the Astronomical Almanac. Program TIME.BAS will calculate local siderial time given the date (Year, eg 1984; Month, eg 7 (July), day eg 14) the hour, minute and second of Universal Time (A derivitive of Greenwich Mean Time). UT is broadcast by WWV, Colorado in the shortwave band. Using POSITION: enter the latitude of the observer, the altitude and azmuth (to the nearest 1/2 degree or so, if possible) of the observed body. The program will immediately comput the declination and after a slight pause the local hour angle of the body. The program will then ask the siderial time, which you will enter to the nearest minute or two from the clock that you wisely have set to Siderial time, using program TIME at the beginning of your observing session. Add 1/2 minute for each 3 hours of time elapsed since you set the clock (easily done using a digital watch in stopwatch mode, set going at the same time the clock was set to siderial time initially.) Having entered siderial time, the computer will spit out the Right Ascention of the body in question. This may be compared with any good chart of the sky to pinpoint the probable identity of the object. If no object is marked in the circle surrounding the object with a diameter of 1 degree (four minutes of the hour circle at the equator), consider the posibility that you have made a mistake; at the same time consider the possibility that you have just discovered an Comet. Fame and Fortune? It is always a possibility! CONVENTIONS: West and North are positive East and South are negative Universal time for TIME.BAS All computations are in decimal degreesiderial time, u10 REM THIS IS PROGRAM "QUADROOT" 20 REM THIS PROGRAM CALCULATES THE ROOTS OF A QUADRATIC EQUATION 30 REM Y = A*X^2 + B*X + C HAS TWO ROOTS AT Y = O 40 LPRINT "PROGRAM QUADROOT" 50 PRINT "PROGRAM QUADROOT" 60 INPUT "A=";A 70 LPRINT "A=";A 80 INPUT "B=";B 90 LPRINT "B=";B 100 INPUT "C=";C 110 LPRINT "C=";C 120 DIS = B^2 - 4*A*C 130 IF DIS > 0 THEN 170 140 IF DIS < 0 THEN 190 150 LPRINT "EQUAL ROOTS ="; -B/(2*A); ","; -B/(2*A) 160 GOTO 210 170 LPRINT "REAL ROOTS=" (-B+(DIS)^.5)/(2*A) "&" (-B-(DIS)^.5)/(2*A) 180 GOTO 210 190 IMAG = ABS(DIS) 200 LPRINT "COMPLEX ROOTS="; -B/(2*A);"+i*";((IMAG)^.5)/(2*A); "&"; -B/(2*A);"-i*";((IMAG)^.5)/(2*A) 210 PRINT "ROOTS ARE ON PRINTOUT" 220 PRINT "--ooOOOoo--" 230 LPRINT "--ooOOOoo--" 240 LPRINT 250 PRINT 260 PRINT "DO YOU WANT ANOTHER QUADRATIC? Y/N?" 270 INPUT ANS$ 280 IF ANS$ = "Y" THEN 10 290 PRINT "RETURN TO MBASIC COMMAND LEVEL" 300 END WANT ANOTHER QUADRATIC? Y/N?" 270 INPUT ANS$ 280 IF ANS$ = "Y" THEN 10 290 PRINT "RETURN TO MBASIREM PROGRAM QUADROOT;PROGRAMMER MICHAEL P FINERTY, 9/5/84 REM THIS IS THE LISTING FOR PROGRAM QUADROOT.COM, AN S-BAISC PROGRAM REM THAT EVALUATES THE ROOTS OF QUADRATIC EQUATIONS USING THE REM COEFFICIENTS OF THE INDIVIDUAL TERMS: A,B,&C OF THE EQUATION: REM A*X^2 + B*X + C = 0 TO FIND THE POINTS OF INTERSECTION (TWO) REM OF THE CURVE WITH THE LINE Y = 0. THE ROOTS MAY BE EITHER REAL REM OR COMPLEX AND EITHER EQUAL OR UNEQUAL. IN THIS IMPLEMENTATION REM "A" CANNOT BE EQUAL TO ZERO. REM REM *** DECLARATION OF VARIABLES *** REM 10 VAR AXIS, A, B, C, DIF, DISCRIM = REAL VAR ANS = STRING REM REM *** INPUT OF VARAIABLES AND MESSAGES *** REM CONSOLE PRINT "PLEASE INPUT THE COEFFICIENTS OF YOUR QUADRATIC" INPUT "A = ";A IF A = 0 THEN PRINT "YOUR EQUATION IS NOT QUADRATIC" IF A = 0 THEN 10 LPRINTER PRINT "A = ";A CONSOLE REM INPUT "B = ";B LPRINTER PRINT "B = ";B CONSOLE REM INPUT "C = ";C LPRINTER PRINT "C = ";C CONSOLE REM REM *** AXIS IS AXIS OF SYMMETRY OF PARABOLA *** REM AXIS = -B/(2*A) REM REM *** ROOTS ARE AT DISTANCE DIF FROM AXIS *** REM IF B*B = 4*A*C THEN DIF = 0 IF B*B = 4*A*C THEN 20 REM DIF = ((ABS(B*B - 4*A*C))^0.5)/(2*A) REM REM *** ROOTS ARE REAL OR COMPLEX DEPENDING ON SIGN OF DISCRIM *** REM *** THEY ARE EQUAL IF DISCRIM IS ZERO *** REM 20 DISCRIM = B*B - 4*A*C REM REM REM ***************************************************************** REM REM LOGICAL PORTION OF PROGRAM : SGN(A) = 1 IF A GREATER THAN ZERO REM = 0 IF A EQUALS ZERO REM =-1 IF A LESS THAN ZERO REM CASE SGN(DISCRIM) OF -1: BEGIN PRINT "ROOTS ARE: "; AXIS;" +i*";DIF PRINT "AND: "; AXIS;" -i*";DIF PRINT "--ooO0Ooo--" LPRINTER PRINT "ROOTS ARE: "; AXIS;" +i*";DIF PRINT "AND: "; AXIS;" -i*";DIF PRINT "--ooO0Ooo--" CONSOLE END 0: BEGIN PRINT "ROOTS ARE: ";AXIS PRINT "AND: "; AXIS PRINT "--ooO0Ooo--" LPRINTER PRINT "ROOTS ARE: ";AXIS PRINT "AND: "; AXIS PRINT "--ooO0Ooo--" CONSOLE END 1: BEGIN PRINT "ROOTS ARE: "; AXIS + DIF PRINT "AND: "; AXIS - DIF PRINT "--ooO0Ooo--" LPRINTER PRINT "ROOTS ARE: "; AXIS + DIF PRINT "AND: "; AXIS - DIF PRINT "--ooO0Ooo--" CONSOLE END END PRINT LPRINTER PRINT CONSOLE REM REM *** CONDITIONAL LOOP FOR MORE QUADRATICS *** REM PRINT " DO YOU WANT TO USE ANOTHER QUADRATIC? Y/N?" INPUT ANS IF ANS = "Y" THEN 10 ELSE END  =-1 IF A LESS THAN ZERO REM CASE SGN(DISCRIM) OF -1: BEGIN PRINT "ROOTS ARE: "; AXIS;ÃÃ%‹",",*ùÍá >Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=# >Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#>Í=#ÅÍU$ÃØ/PLEASE INPUT THE COEFFICIENTS OF YOUR QUADRATIC!¨åÍ�Íd$Í…$>Í=#ÅÍU$Íd$Í*!A = Íd$Í~!Íd$yÍ�!½+ÍÍd$yÍ…$>Í=# Ã&Íæ)½+Íæ)"ÍËÍŸÊu>Í=# ÅÍU$ÃhYOUR EQUATION IS NOT QUADRATIC!IåÍ�Íd$Í…$>Í=#!ÃÍæ)½+Íæ)ÍËÍŸÊ™Ãn>Í=#">Í=##ÅÍU$õA = !°åÍ�Íæ)½+Í3Íd$Í…$>Í=#$>Í=#%>Í=#&ÅÍU$Íd$Í*!B = Íd$Í~!Íd$yÍ�!Á+ÍÍd$yÍ…$>Í=#'>Í=#(ÅÍU$Ã'B = !"åÍ�Íæ)Á+Í3Íd$Í…$>Í=#)>Í=#0>Í=#1ÅÍU$Íd$Í*!C = Íd$Í~!Íd$yÍ�!Å+ÍÍd$yÍ…$>Í=#2>Í=#3ÅÍU$ÙC = !”åÍ�Íæ)Å+Í3Íd$Í…$>Í=#4>Í=#5>Í=#6>Í=#7>Í=#8ÃØ€Íæ)Á+ÍïÍæ)ÔÍæ)½+Íj͵>!¹+Í÷)>Í=#9>Í=#@>Í=#A>Í=#BÃ€Íæ)Á+Íæ)Á+ÍjÍæ)Íæ)½+ÍjÍæ)Å+ÍjÍËÍŸÊa>Í=#BÃTÍæ)P>!É+Í÷)>Í=#CÃo€Íæ)Á+Íæ)Á+ÍjÍæ)kÍæ)½+ÍjÍæ)Å+ÍjÍËÍŸÊ�Ã+>Í=#D>Í=#Eò€Ã¹€ÃÀ€Íæ)Á+Íæ)Á+ÍjÍæ)®Íæ)½+ÍjÍæ)Å+ÍjÍ?ÍœÍæ)µÍR Íæ)¼Íæ)½+Íj͵>!É+Í÷)>Í=#F>Í=#G>Í=#H>Í=#I>Í=#P>Í=#PÃ9€Íæ)Á+Íæ)Á+ÍjÍæ)5Íæ)½+ÍjÍæ)Å+ÍjÍ?>!Í+Í÷)>Í=#Q>Í=#R>Í=#S>Í=#T>Í=#U>Í=#V>Í=#W>Í=#X>Í=#YÍæ)Í+ÍY>Í•$ù€Íæ)µÍïÍâÂL>Í=#`>Í=#aÅÍU$Ãê ROOTS ARE: !ÞåÍ�Íæ)¹+Í3à +i*!üåÍ�Íæ)É+Í3Íd$Í…$>Í=#bÅÍU$Ã,AND: !&åÍ�Íæ)¹+Í3ÃC -i*!>åÍ�Íæ)É+Í3Íd$Í…$>Í=#cÅÍU$Ãt --ooO0Ooo--!håÍ�Íd$Í…$>Í=#d>Í=#eÅÍU$ä ROOTS ARE: !˜åÍ�Íæ)¹+Í3û +i*!¶åÍ�Íæ)É+Í3Íd$Í…$>Í=#fÅÍU$ÃæAND: !àåÍ�Íæ)¹+Í3Ãý -i*!øåÍ�Íæ)É+Í3Íd$Í…$>Í=#gÅÍU$Ã. --ooO0Ooo--!"åÍ�Íd$Í…$>Í=#h>Í=#iÃì >Í•$ÃXÍæ)TÍâÂŒ>Í=#p>Í=#qÅÍU$Æ ROOTS ARE: !zåÍ�Íæ)¹+Í3Íd$Í…$>Í=#rÅÍU$ñAND: !«åÍ�Íæ)¹+Í3Íd$Í…$>Í=#sÅÍU$Ãâ --ooO0Ooo--!ÖåÍ�Íd$Í…$>Í=#t>Í=#uÅÍU$à ROOTS ARE: !åÍ�Íæ)¹+Í3Íd$Í…$>Í=#vÅÍU$Ã=AND: !7åÍ�Íæ)¹+Í3Íd$Í…$>Í=#wÅÍU$Ãn --ooO0Ooo--!båÍ�Íd$Í…$>Í=#x>Í=#yÃì >Í•$Ø€Íæ)”ÍâÂì >Í=#€>Í=#�ÅÍU$ÃÆ ROOTS ARE: !ºåÍ�Íæ)¹+Íæ)É+Í:Í3Íd$Í…$>Í=#‚ÅÍU$ÃùAND: !óåÍ�Íæ)¹+Íæ)É+Í?Í3Íd$Í…$>Í=#ƒÅÍU$Ã2 --ooO0Ooo--!& åÍ�Íd$Í…$>Í=#„>Í=#…ÅÍU$Ãb ROOTS ARE: !V åÍ�Íæ)¹+Íæ)É+Í:Í3Íd$Í…$>Í=#†ÅÍU$Õ AND: !� åÍ�Íæ)¹+Íæ)É+Í?Í3Íd$Í…$>Í=#‡ÅÍU$ÃÎ --ooO0Ooo--! åÍ�Íd$Í…$>Í=#ˆ>Í=#‰Ãì >ÍÒ$>Í=#‘ÅÍU$Íd$Í…$>Í=#’>Í=#“ÅÍU$Íd$Í…$>Í=#”>Í=#•>Í=#–>Í=#—>Í=#˜ÅÍU$Ãv + DO YOU WANT TO USE ANOTHER QUADRATIC? Y/N?!J åÍ�Íd$Í…$>Í=#™ÅÍU$Íd$Í~!Íd$yÍ�!Ñ+Í„%Íd$yÍ…$>Í=#ö Y!Ñ+å!´ åÍÍ¿ÊÍ ÃnÃ× >Í=#Ã>Í=#ÃÉCopyright (C) 1979, By Topaz programming. All rights reserved. From here on protected by End User License.  á"j !n >Í÷)!r >Í÷):u æþ2u :q õ2~ ñæþ2q !n >ÍÅ)ÍjÍá"l !n >ÍÅ)!n >ÍÅ)ÍñÍ?!r >ÍÅ)̓ Íj!v >Í÷)!v >ÍÅ)!z >Í÷)!v >ÍÅ)! >ÍÅ)Í:!v >ÍÅ)!z >ÍÅ)Í—*l |µÊD ! >ÍÅ)¯*l |g}o"l Ò# !r >ÍÅ)Íj*l |µÊA !r >ÍÅ)!r >ÍÅ)Íj!r >Í÷)à Íj:~ ·òf !n >Í÷)! >ÍÅ)!n >ÍÅ)͵*j é€á"!>Í÷)!":·ò÷ :Ú÷ !>ÍÅ)!f>ÍÅ)ÍâÚÞ *#"!>ÍÅ)!f>ÍÅ)͵!>Í÷)ã *|µÂ! !>ÍÅ)!b>ÍÅ)ÍâÒ! *+"!>ÍÅ)!f>ÍÅ)Íj!>Í÷)Ãæ !>ÍÅ)ÍjÍÁ!üÿy=Â7 :>ÍÅ)!>ÍÅ)!>ÍÅ)Íñ͵!b>ÍÅ)Í?!>Í÷)!>ÍÅ)!>ÍÅ)!">ÍÅ)!&>ÍÅ)!*>ÍÅ)!.>ÍÅ)!2>ÍÅ)!6>ÍÅ)>2!>ÍÅ)ÍjÍ::=° !>ÍÅ)ÍjÍ:*|µÊó åÍÆ͘!^>ÍÅ)ÍjÍ:*é!ý Ã#LOG <=0 OR A^X A<=°ÿÿÄÿÿï�ÿ©áŽþö‚íþ«­‚ýÃ<ü“цùÓxA±rŒŸR±rÎåX^ù”…’ŒŸR“]Ž€ á"Ž!‘>Í÷):”Wæþ2”zæ2—!‘>ÍÅ)!éá"¼!¿>Í÷):ÅæW:Âæþ²2Â!¿>ÍÅ)!éá" á|2·òØåÍÀá)}lg"!>6#=Âä>/!wÍ:·ò:ö2!>ÍÅ)!éá"U!^>Í÷)*_}lg:^·ò7!åÃTÖÒX·ÊLG|g}ox<Ã<:dåÜÀ!é!ÿÃLá"É!Ô>Í÷)!Ô>ÍÅ)!Ø>Í÷)!Ô>ÍÅ)!é>ÍÅ)Í:ð>2èá"É!Ø>Í÷)!Ô>Í÷)!Ì>Í÷)!é>ÍÅ)!Ü>Í÷)!í>ÍÅ)!ä>Í÷)!Ì>ÍÅ)!Ð>Í÷)!Üà~#Âð!Ü>ÍÅ)!ä>ÍÅ)Íj!Ü>Í÷)!Ô>ÍÅ)!Ø>ÍÅ)Íj!Ô>Í÷)!Ì>ÍÅ)!Ô>ÍÅ)!é>ÍÅ)!Ü>ÍÅ)͵ÍjÍ:!Ì>Í÷)!Ì>ÍÅ)!Ð>ÍÅ)ÍâÊÀ!Üà¾Â’#Â}:è=ÊÀ2è!Ì>ÍÅ)!Ð>Í÷)!ä>ÍÅ)!é>ÍÅ)Í:!ä>Í÷)Ãè!Ì>ÍÅ)!退á"A!P>Í÷):S2X:P·úDþÒ$!P4·#~wÂ:Pà !S:XæG~æþ°w!PÍ!P>ÍÅ)!é!T>ÍÅ)*Aéá"¹!¼>Í÷):½·òˆ:¿·òw>!>2›!˜>ÍÅ)*¹é!”>ÍÅ)*¹é€á"¹!¼>Í÷):¿æþ2¿!¼>ÍÅ)!éáã|/g}/o#ãéá"ìÍâ>ÿÊèÃæá"ìÍâ>ÿÂè>Í€!éá" !­%>Í÷):°%î2°%!­%>ÍÅ)!éá"0Í„>ÿÊ,Ã*á"0Í„>ÿÂ,>Ía!é>2ƒá"c¯2­%2a2f!i>Í÷):j·ÊË:l2bæþ2l!i>ÍÅ)>Í•$!w>ÍÅ)ÍâÚ�!s>ÍÅ)͵!a4Ãj>Í•$!{>ÍÅ)ÍâÒ´!s>ÍÅ)Íj!a5Ã�:f·ÂÍ/2f!>ÍÅ)Í:Ãj!i>Í÷)!a~·òß/<þÒç^~“w>“2h{2g!mÍ w#Âùÿ+~þ0Ê:b·> ò>-2­%:g·ò6€òd:g=2a>2g>2h!m®%:g·ÊN=2g~#Ã<>.:h·Ê‹=2h~#ÃR!®%m:g/<6.#60=Âq:gG:h€G#wÂ�ëë+~þ0Ê‹þ.Ê™#6:a·ÊË6E#+ò®/<-p#Ö Ú»òÆ:Ox·ÊÇÆ0w#q#6!­%~·Ââ60#6>2¬%Ãí#~·Ââx2¬%:ƒþÿÊ :ô!þÿÊ :°&O>!¬%ÍL!*céåÅ!i>ÍÅ)!s>ÍÅ)Íj!i>Í÷)¯2e!i~·ÊSúS=w!l·~w+ ÂA:e2eÃ.!iÍ:eÆ0ÁáÉ €ýÌÌÌì†7¼á"·!´&6ÿÍ%!¬%6ÿÍ%!µ&­%ÿ~·ÊÏO·Êº¹Â¶# ¯!é ~·ÊµOz¹Â¶#¼õ ·Êµ¹Â¶ÂÑõá"B!­%>Í÷)!±%>Í÷)!´%:°%®Ò~öþÃA:°%±%!­%ÍEÊ*Bé!°%´%~æýwæý!®%²%Ò4ë¾ÂA#Â6!éÒJë®ò^O·òVë·yÀ?ɾÉá"q!u·Âo!zå!éTrueFalseá"”!—·ÂŽ!›>ÍÅ)!é€>æ>á"¼!­%Í÷):®%·>ÿúº/·!éá"âÑ{²ÊÏåÃçÕ!¬%6ÿÍ%*âå:­%Ãçáã}þTÊþtÊþYÊþyÊþÿÊ>·É>ÿ·É"1!3͆:9æW:6æþ²26*13w#Â(É>ÃA>€2ná"k!v>Í÷)!q>Í÷)¯2u2zÍ{!q>ÍÅ)!éÍ!qÍ?!vÍ?*o|­ò¨:o·ò¢!uÍLè!zÍL!zu¯Ž+±*o}¬}òÑ·òÑ!uÍL>ÿ2o!t¯7ŽwÒå+ÂÙ:oæG!t~æþ°w!qÍ:r·ø¯2tÉ!t~_æþw!y~Wæþw:nªWë"o!qvN¹ÈG©ò3©x¹Ò9ëÍ?Ã!4·#~wÂCÉå~/w+ÂOá·~Æw+~ˆwÐ Â`Éá"'!C>Í÷)!?>Í÷):D·ò*:@·ò*!F~_æþw!B~Wæþwë"G:?2I!6 ¯w#¬þÊÙÍRÍaÒ··!<BŽw+ ÂÍ÷:IG:CO€26x©ú:6©òx·ú**Gë!Q>ÿͤ!N>ÍÅ)*'éÍp*Gë!9:7ͤ!6>ÍÅ)!é!J>ÍÅ)*'éÿÿÿ!B·~w+ ÂXÉ!D·~w# ÂgÉ!<¯7ŽwÒ�+Âu0!7~·ø+~=w!<·~w+“ ƒ¯26Éõz«æW~æþ²wñ·ø¯wÉá"§!>Í÷)!>Í÷):·ò¶:·òª!~_æþw!~Wæþwë":2 ÍÚà !Íï Ê5¯!Íï!·ž+Â?Úù!Ž+Â(·Ãù:o: g•GÆ2 |­òkx­úkx·òª*ë!Ù>ÿÍú!Ö>ÍÅ)*§é!¯7ŽwÒ‹+Âp! 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Í"C+Éÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:§+·Ây+\Íþÿ!¨+Ê#>ÿ2§+:¦+þ€Â˜+€Í\Í!¨+·Â#_<2¦+!€~ÁÉ€&INPUT FILE REAÄPÚ<ýt0001:00 REM PROGRAM QUADROOT;PROGRAMMER MICHAEL P FINERTY, 9/5/84 0002:00 REM THIS IS THE LISTING FOR PROGRAM QUADROOT.COM, AN S-BAISC PROGRAM 0003:00 REM THAT EVALUATES THE ROOTS OF QUADRATIC EQUATIONS USING THE 0004:00 REM COEFFICIENTS OF THE INDIVIDUAL TERMS: A,B,&C OF THE EQUATION: 0005:00 REM A*X^2 + B*X + C = 0 TO FIND THE POINTS OF INTERSECTION (TWO) 0006:00 REM OF THE CURVE WITH THE LINE Y = 0. THE ROOTS MAY BE EITHER REAL 0007:00 REM OR COMPLEX AND EITHER EQUAL OR UNEQUAL. IN THIS IMPLEMENTATION 0008:00 REM "A" CANNOT BE EQUAL TO ZERO. 0009:00 REM 0010:00 REM *** DECLARATION OF VARIABLES *** 0011:00 REM 0012:00 10 VAR AXIS, A, B, C, DIF, DISCRIM = REAL 0013:00 VAR ANS = STRING 0014:00 REM 0015:00 REM *** INPUT OF VARAIABLES AND MESSAGES *** 0016:00 REM 0017:00 CONSOLE 0018:00 PRINT "PLEASE INPUT THE COEFFICIENTS OF YOUR QUADRATIC" 0019:00 INPUT "A = ";A 0020:00 IF A = 0 THEN PRINT "YOUR EQUATION IS NOT QUADRATIC" 0021:00 IF A = 0 THEN 10 0022:00 LPRINTER 0023:00 PRINT "A = ";A 0024:00 CONSOLE 0025:00 REM 0026:00 INPUT "B = ";B 0027:00 LPRINTER 0028:00 PRINT "B = ";B 0029:00 CONSOLE 0030:00 REM 0031:00 INPUT "C = ";C 0032:00 LPRINTER 0033:00 PRINT "C = ";C 0034:00 CONSOLE 0035:00 REM 0036:00 REM *** AXIS IS AXIS OF SYMMETRY OF PARABOLA *** 0037:00 REM 0038:00 AXIS = -B/(2*A) 0039:00 REM 0040:00 REM *** ROOTS ARE AT DISTANCE DIF FROM AXIS *** 0041:00 REM 0042:00 IF B*B = 4*A*C THEN DIF = 0 0043:00 IF B*B = 4*A*C THEN 20 0044:00 REM 0045:00 DIF = ((ABS(B*B - 4*A*C))^0.5)/(2*A) 0046:00 REM 0047:00 REM *** ROOTS ARE REAL OR COMPLEX DEPENDING ON SIGN OF DISCRIM *** 0048:00 REM *** THEY ARE EQUAL IF DISCRIM IS ZERO *** 0049:00 REM 0050:00 20 DISCRIM = B*B - 4*A*C 0051:00 REM 0052:00 REM 0053:00 REM ***************************************************************** 0054:00 REM 0055:00 REM LOGICAL PORTION OF PROGRAM : SGN(A) = 1 IF A GREATER THAN ZERO 0056:00 REM = 0 IF A EQUALS ZERO 0057:00 REM =-1 IF A LESS THAN ZERO 0058:00 REM 0059:00 CASE SGN(DISCRIM) OF 0060:00 -1: BEGIN 0061:01 PRINT "ROOTS ARE: "; AXIS;" +i*";DIF 0062:01 PRINT "AND: "; AXIS;" -i*";DIF 0063:01 PRINT "--ooO0Ooo--" 0064:01 LPRINTER 0065:01 PRINT "ROOTS ARE: "; AXIS;" +i*";DIF 0066:01 PRINT "AND: "; AXIS;" -i*";DIF 0067:01 PRINT "--ooO0Ooo--" 0068:01 CONSOLE 0069:01 END 0070:00 0: BEGIN 0071:01 PRINT "ROOTS ARE: ";AXIS 0072:01 PRINT "AND: "; AXIS 0073:01 PRINT "--ooO0Ooo--" 0074:01 LPRINTER 0075:01 PRINT "ROOTS ARE: ";AXIS 0076:01 PRINT "AND: "; AXIS 0077:01 PRINT "--ooO0Ooo--" 0078:01 CONSOLE 0079:01 END 0080:00 1: BEGIN 0081:01 PRINT "ROOTS ARE: "; AXIS + DIF 0082:01 PRINT "AND: "; AXIS - DIF 0083:01 PRINT "--ooO0Ooo--" 0084:01 LPRINTER 0085:01 PRINT "ROOTS ARE: "; AXIS + DIF 0086:01 PRINT "AND: "; AXIS - DIF 0087:01 PRINT "--ooO0Ooo--" 0088:01 CONSOLE 0089:01 END 0090:00 END 0091:00 PRINT 0092:00 LPRINTER 0093:00 PRINT 0094:00 CONSOLE 0095:00 REM 0096:00 REM *** CONDITIONAL LOOP FOR MORE QUADRATICS *** 0097:00 REM 0098:00 PRINT " DO YOU WANT TO USE ANOTHER QUADRATIC? Y/N?" 0099:00 INPUT ANS 0100:00 IF ANS = "Y" THEN 10 ELSE END 0101:00 ****** End of program ****** 10 REM PROGRAM "RISE-SET.BAS," A MBASIC PROGRAM CALCULATING THE LOCAL HOUR ANGLE 20 REM AND THE LOCAL AZMUTH OF THE RISING OF AN ASTRONOMICAL BODY 30 REM GIVEN ITS DECLINATION AND THE OBSERVERS LATITUDE 40 REM REVISED 4-19-1985, MIKE FINERTY, TUCSON 50 REM *********************************************************************** 60 PI = 3.1415926# 70 INPUT "DECLINATION OF BODY IN DEC. DEGREES";D 80 INPUT "LATITUDE OF OBSERVER IN DEGREES.MINS "; LAT 90 DEC = D*PI/180 100 LATITUDE = 100/60*(LAT - INT(LAT))+INT(LAT) 110 L = LATITUDE*PI/180 120 TEST = ABS(DEC) 130 IF TEST > PI/2-ABS(L) THEN 330 140 LHACOS = - TAN(L)*TAN(DEC) 150 AZCOS = SIN(DEC)/COS(L) 160 LHA =PI/2-ATN(LHACOS/(1-LHACOS^2)^.5) 170 AZ = PI/2-ATN(AZCOS/(1-AZC0S^2)^.5) 180 AZ = AZ/PI*180 190 LHA=LHA/PI*12 200 LHA = 24-LHA 210 PRINT "RISING AZMUTH =";AZ;"DEGREES, SETTING AZMUTH =";360-AZ;"DEGREES" 220 PRINT "LHA RISING =";LHA;"HOURS, LHA SETTING =";24-LHA;"HOURS" 230 PRINT "OBJECT VISIBLE FOR";2*(24-LHA);"HOURS." 240 PRINT "ALTITUDE AT UPPER CULMINATION (TRANSIT) =";90-ABS(L-DEC)*180/PI;"DEGREES" 250 IF DEC = L THEN PRINT "CULMINATION AT ZENITH" 260 IF DEC = L THEN GOTO 330 270 IF DEC>L THEN PRINT "TRANSIT NORTH OF ZENITH" ELSE PRINT"TRANSIT SOUTH OF ZENITH" 280 PRINT 290 PRINT "DO YOU WANT ANOTHER OBJECT ? Y/N?" 300 INPUT ANS$ 310 IF ANS$ = "Y" GOTO 10 320 END 330 IF SGN(DEC) = SGN(L) THEN PRINT "OBJECT DOES NOT SET" 340 IF SGN(DEC) = -1*SGN(L) THEN PRINT "OBJECT DOES NOT RISE ABOVE HORIZON" 350 GOTO 240 ) THEN PRINT "OBJECT DOES NOT SET" 340 IF SGN(DEC) = -1*SGN(L) THEN PRINT "OBJECT DOES NOT RISE ABOVE HORIZON" 350 GOTO RISE-SET.DOC ****************************************************************************** RISE-SET.BAS IS A MBASIC PROGRAM TO CALCULATE THE AZMUTH AND LOCAL HOUR ANGLE OF THE RISE AND SET OF ASTRONOMICAL BODIES THE ALTITUDE OF UPPER CULMINATION (TRANSIT) OF THOSE BODIES WHICH DO ACTUALLY RISE AND THE DIRECTION FROM ZENITH OF TRANSIT. IT WAS WRITTEN BY MIKE FINERTY APRIL 18, 1985, USING FORMULAE FROM SMART'S TEXTBOOK ON SPHERICAL ASTRONOMY, AND A LITTLE OF HIS OWN RECCONING. ****************************************************************************** THE PROGRAM WILL RETURN A "Illegal function call" ERROR IF THE ASTRONOMICAL BODY IN QUESTION DOES NOT RISE OR DOES NOT SET, THAT IS IF THE BODY IS IN THE CIRCUMPOLAR REGION AND IS ALWAYS ABOVE THE HORIZON OR ALWAYS BELOW THE HORIZON, THE INTERSECTION OF ITS PATH WITH THE HORIZON IS "IMMAGINARY" AND THE SOLUTION REQUIRES THE USE OF COMPLEX NUMBERS (WHICH MBASIC DOESN'T LIKE), SO IT RETURNS AN ERROR MESSAGE. I LABORED IN VAIN TO HAVE IT RETURN A MORE MEANINGFUL ERROR MESSAGE, BUT IT APPEARS THAT WE ARE STUCK WITH "Illegal function call." AFTER ALL. MIKE FINERTY, TUCSON. APRIL 18, 1985.TH AND LOCAL HOUR ANGLE OF THE RISE AND SET OF ASTRONOMICAL BODIES THE ALTITUDE OF UPPER CULMINATION (TRÿb � PROGRAM "RISE-SET.BAS," A MBASIC PROGRAM CALCULATING THE LOCAL HOUR ANGLE^b� AND THE LOCAL AZMUTH OF THE RISING OF AN ASTRONOMICAL BODY›b� GIVEN ITS DECLINATION AND THE OBSERVERS LATITUDEÓb(� REVISED 4-19-1985, MIKE FINERTY, TUCSON!c2� ***********************************************************************4c<PI ð U–hÚI‚JcFCONST ð 5•]?·Y�xcP… "DECLINATION OF BODY IN DEC. DEGREES";D«cZ… "LATITUDE OF OBSERVER IN DEGREES.MINS "; LAT½cdDEC ð DôPIõ´êcnLATITUDE ð dõ<ô(LAT ó ÿ…(LAT))òÿ…(LAT)dxL ð LATITUDEôPIõ´d‚TEST ð ÿ†(DEC)2dŒ‹ TEST ï PIõóÿ†(L) Ï ÌOd–LHACOS ð ó ÿ�(L)ôÿ�(DEC)id AZCOS ð ÿ‰(DEC)õÿŒ(L)•dªLHA ðPIõóÿŽ(LHACOSõ(óLHACOSö)ö€)¿d´AZ ð PIõóÿŽ(AZCOSõ(óAZC0Sö)ö€)Ñd¾AZ ð AZõPIô´ãdÈLHAðLHAõPIô ôdÒLHA ð óLHA-C. 140 REM THIS VERSION BY M. P. FINERTY, MAY 31, 1984 150 REM ALTITUDE AND AZMUTH FROM RA AND DEC + LST 160 LET P=3.141592654 170 LET R1=P/180 175 CONSOLE 180 PRINT "INPUT OBJECT NAME" 185 LPRINTER 190 INPUT N$ 200 PRINT N$ 205 CONSOLE 210 PRINT "INPUT RIGHT ASCENTION" 220 INPUT "H= ",A1 230 INPUT "M= ",A2 240 INPUT "S= ",A3 250 PRINT "RA = ";A1;" HRS ";A2;" MINS ";A3;" SECS" 260 PRINT "IS THIS CORRECT? Y?/N?" 270 INPUT A$ 280 IF A$="N" THEN 210 290 IF A$<>"Y" THEN 210 300 GOSUB 1340 310 LET R=A*15*R1 315 LPRINTER 320 PRINT "RIGHT ASCENTION IN DECIMAL DEGREES IS: ";R/R1 325 CONSOLE 330 PRINT "INPUT DECLINATION" 340 INPUT "DEGREES ",A1 350 INPUT "MINUTES ",A2 360 INPUT "SECONDS ",A3 370 PRINT "IS THIS NORTH OR SOUTH, N?/S?" 380 INPUT S$ 390 PRINT "DECLINATION = ";A1;" DEG ";A2;" MIN ";A3;" SEC ";S$ 400 PRINT "IS THIS CORRECT? Y?/N?" 410 INPUT A$ 420 IF A$="N" THEN 330 430 IF A$<>"Y" THEN 330 440 GOSUB 1340 450 LET D1=A*R1 460 IF F9=2 THEN RETURN 465 LPRINTER 470 PRINT "DECLINATION IN DECIMAL DEGREES IS: ";D1/R1 474 CONSOLE 480 PRINT "INPUT LATITUDE" 490 INPUT "DEGREES ",A1 500 INPUT "MINUTES ",A2 510 INPUT "SECONDS ",A3 520 PRINT "IS LATITUDE NORTH OR SOUTH? N?/S?" 530 INPUT S$ 540 PRINT "LATITUDE IS: ";A1;" DEGREES ";A2;" MINUTES ";A3;" SECONDS ";S$ 550 PRINT "IS THIS CORRECT? Y?/N?" 560 INPUT A$ 570 IF A$="N" THEN 480 580 IF A$<>"Y" THEN 480 590 GOSUB 1340 600 LET L1=A*R1 605 LPRINTER 610 PRINT "OBSERVERS POSITION" 620 PRINT "LATITUDE IN DECIMAL DEGREES IS: ";L1/R1 625 CONSOLE 630 PRINT "INPUT LONGITUDE" 640 INPUT "DEGREES ",A1 650 INPUT "MINUTES ",A2 660 INPUT "SECONDS ",A3 670 PRINT "IS LONGITUDE EAST OR WEST? E?/W?" 680 INPUT E$ 690 IF E$="E" THEN LET S$="N" ELSE LET S$="S" 700 PRINT "LONGITUDE IS: ";A1;" DEGREES ";A2;" MINUTES ";A3;" SECONDS ";E$ 710 PRINT "IS THIS CORRECT? Y?/N?" 720 INPUT A$ 730 IF A$="N" THEN 630 740 IF A$<>"Y" THEN 630 750 GOSUB 1340 760 LET L2=A*R1 765 LPRINTER 770 PRINT "LONGITUDE IN DECIMAL DEGREES IS: ";L2/R1 780 GOSUB 1370 790 GOSUB 1470 800 GOSUB 1740 810 LET A1=H 820 LET A2=M 830 LET A3=S 840 LET S$="N" 850 GOSUB 1340 860 LET T=A*15*R1 870 REM T5 IS LHA 880 LET T5=T-R+L2 890 IF T5<0 THEN LET T5=T5+2*P 900 IF T5>2*P THEN LET T5=T5-2*P 910 PRINT "LOCAL HOUR ANGLE: ";T5/R1;" DEGREES" 920 LPRINTER 930 PRINT "LOCAL HOUR ANGLE: ";T5/R1;" DEGREES" 940 REM CALCULATE AZMUTH (A) AND ALTITUDE(H) 950 LET S1=SIN(L1)*SIN(D1) 960 LET S1=S1+COS(L1)*COS(D1)*COS(T5) 970 LET C1=1-S1*S1 980 IF C1>0 THEN LET C1=SQR(C1) 990 IF C1<=0 THEN 1020 1000 LET H=ATN(S1/C1) 1010 GOTO 1030 1020 LET H=SGN(S1)*P/2 1030 LET C2=COS(L1)*SIN(D1) 1040 LET C2=C2-SIN(L1)*COS(D1)*COS(T5) 1050 LET S2=-(COS(D1)*SIN(T5)) 1060 IF C2=0 THEN LET A=SGN(S2)*P/2 1070 IF C2=0 THEN 1120 1080 LET A=ATN(S2/C2) 1090 IF S2<0 AND C2>0 THEN LET A=2*P-ABS(A) 1100 IF S2<0 AND C2<0 THEN LET A=P+ABS(A) 1110 IF S2>0 AND C2<0 THEN LET A=P-ABS(A) 1120 IF A<0 THEN LET A=A+2*P 1130 IF A>2*P THEN LET A=A-2*P 1135 CONSOLE 1140 PRINT "ALTITUDE: ";H/R1 1150 IF H<=0 THEN PRINT "DOWN" ELSE PRINT "UP" 1160 PRINT "AZMUTH: ";A/R1 1170 PRINT "--ooOOOoo--" 1180 PRINT 1190 PRINT 1195 LPRINTER 1200 PRINT 1210 PRINT "ALTITUDE IN DEGREES: ";H/R1;" AZMUTH IN DEGREES: ";A/R1 1220 PRINT "--ooOOOoo--" 1230 PRINT 1240 PRINT 1245 CONSOLE 1250 PRINT "DO YOU WANT ANOTHER TIME AND DAY? Y?/N?" 1260 INPUT A$ 1270 IF A$="Y" THEN 780 1280 PRINT "DO YOU WANT ANOTHER OBJECT?" 1290 INPUT A$ 1300 LET F9=2 1310 IF A$="Y" THEN GOSUB 30 ELSE END 1320 GOTO 870 1330 REM HERE BEGIN THE SUBROUTINES 1340 IF S$<>"S" THEN LET S=1 ELSE LET S=-1 1350 LET A=S*(A1+A2/60+A3/3600) 1360 RETURN 1370 REM CALCULATE GST 1375 CONSOLE 1380 PRINT "INPUT YEAR, MONTH, DAY, GREGORIAN CALENDAR" 1390 INPUT "YEAR ",Y 1400 INPUT "MONTH ",M 1410 INPUT "DAY ",D2 1420 PRINT Y;" YEAR ";M;" MONTH ";D2;" DAY " 1430 PRINT "IS THIS CORRECT? Y?/N?" 1440 INPUT A$ 1450 IF A$="N" THEN 1380 1460 RETURN 1470 IF A$<>"Y" THEN 1380 1475 LPRINTER 1480 PRINT "DATE OF OBSERVATION OR PROJECTION" 1490 PRINT D2;" DAY ";M;" MONTH,";Y 1500 REM CALCULATE FRACTION OF A DAY 1505 CONSOLE 1510 PRINT "INPUT HOURS MINUTES AND SECONDS, GREGORIAN CALANDAR" 1520 INPUT "HOURS ",A1 1530 INPUT "MINUTES ",A2 1540 INPUT "SECONDS ",A3 1550 PRINT A1;" HOURS ";A2;" MINUTES AND ";A3;" SECONDS" 1560 PRINT "IS THIS CORRECT? Y?/N?" 1570 INPUT A$ 1580 IF A$="N" THEN 1510 1590 IF A$<>"Y" THEN 1510 1595 LPRINTER 1600 PRINT "TIME OF OBSERVATION OR PROJECTION" 1610 PRINT A1;":";A2;":";A3 1620 LET F1=(A3+60*A2+3600*A1)/86400-0.5 1630 LET J=-INT(7*(INT((M+9)/12)+Y)/4) 1640 LET S=SGN(M-9) 1650 LET A4=ABS(M-9) 1660 LET J1=INT(Y+S*INT(A4/7)) 1670 LET J1=-INT((INT(J1/100)+1)*3/4) 1680 LET J=J+INT(275*M/9)+D2+J1 1690 LET J=J+1721028+367*Y 1695 CONSOLE 1700 PRINT "JULIAN DAY ";J;" FRACTION OF A DAY ";F1 1705 LPRINTER 1710 PRINT 1720 PRINT "JULIAN DAY NUMBER: ";J;" FRACTION OF DAY: ";F1 1730 RETURN 1740 REM CDOMPUTE GREENWICH MEAN SIDERIAL TIME 1750 LET D=J-2451545 1760 LET T=D/36525 1770 LET T1=INT(T) 1780 LET J0=T1*36525+2451545 1790 LET T2=(J-J0+0.5)/36525 1800 LET S0=24110.54841+184.812866*T1 1810 LET S0=S0+8640184.81286*T2 1820 LET S0=S0+(0.093104*T*T) 1830 LET S0=S0-(0.0000062*T*T*T) 1840 LET S0=S0/86400 1850 LET S1=INT(S0) 1860 LET S0=S0-S1 1870 LET S0=24*(S0+(F1+0.5)*1.002737909) 1880 IF S0<0 THEN LET S0=S0+24 1890 IF S0>24 THEN LET S0=S0-24 1900 LET H=INT(S0) 1910 LET M1=60*(S0-H) 1920 LET M=INT(M1) 1930 LET S=60*(M1-M) 1935 CONSOLE 1940 PRINT "GMST: ";H;" HOURS ";M;" MINUTES AND ";S;" SECONDS" 1950 RETURN SGN(M-9) 1650 LET A4=ABS(M-9)ÃÃ%‹vSvS*ùÍç+>ÍÓH>ÍÓHÅÍëIÃG***PROGRAM STARFIX***!1åÍDÍúIÍJ>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓHï€Í|O«>!RͨO>ÍÓH>ÍÓHÅÍëIÃá OBJECT NAME: !ÓåÍD>ÍÓH >ÍÓH >ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH>ÍÓH >ÍÓH >ÍÓH!>ÍÓH!èÉÚ¢’0Í�O¡>!jQͨO>ÍÓH">ÍÓH"ÃÍ´Í�OjQÍ�OÆÍ2B>!qQͨO>ÍÓH#>ÍÓH#>ÍÓH$>ÍÓH$ÅÍëIÃINPUT OBJECT NAME!åÍDÍúIÍJ>ÍÓH%>ÍÓH%>ÍÓH&>ÍÓH&ÅÍëIÍúIÍGÍúIyÍ3E!%SÍKÍúIyÍJ>ÍÓH'>ÍÓH'ÅÍëI!%SåÍDÍúIÍJ>ÍÓH(>ÍÓH(>ÍÓH)>ÍÓH)ÅÍëIþINPUT RIGHT ASCENTION!¨åÍDÍúIÍJ>ÍÓH0>ÍÓH0ÅÍëIÍúIÍÀFH= ÍúIÍGÍúIyÍ3E!&RÍí8ÍúIyÍJ>ÍÓH1>ÍÓH1ÅÍëIÍúIÍÀFM= ÍúIÍGÍúIyÍ3E!*RÍí8ÍúIyÍJ>ÍÓH2>ÍÓH2ÅÍëIÍúIÍÀFS= ÍúIÍGÍúIyÍ3E!.RÍí8ÍúIyÍJ>ÍÓH3>ÍÓH3ÅÍëIÓRA = !�åÍDÍ|O&RÍ2ë HRS !¥åÍDÍ|O*RÍ2ÃÄ MINS !½åÍDÍ|O.RÍ2ÃÜ SECS!ÖåÍDÍúIÍJ>ÍÓH4>ÍÓH4ÅÍëIÃIS THIS CORRECT? Y?/N?!åÍDÍúIÍJ>ÍÓH5>ÍÓH5ÅÍëIÍúIÍGÍúIyÍ3E!ƒRÍKÍúIyÍJ>ÍÓH6>ÍÓH6ÃeN!ƒRå!cåÍÝ1ͤ8ÊyØ>ÍÓH7>ÍÓH7ÃŒY!ƒRå!ŠåÍì1ͤ8Ê Ø>ÍÓH8>ÍÓH8ÍÓ>ÍÓH9>ÍÓH9ÃÉðÍ�O�QÍ�OÂÍÒ@Í�OqQÍÒ@>!”QͨO>ÍÓH@>ÍÓH@>ÍÓHA>ÍÓHAÅÍëIÃ3'RIGHT ASCENTION IN DECIMAL DEGREES IS: ! åÍDÍ�O”QÍ�OqQÍ2BÍR4ÍúIÍJ>ÍÓHB>ÍÓHB>ÍÓHC>ÍÓHCÅÍëIÇINPUT DECLINATION!uåÍDÍúIÍJ>ÍÓHD>ÍÓHDÅÍëIÍúIÍÀFDEGREES ÍúIÍGÍúIyÍ3E!&RÍí8ÍúIyÍJ>ÍÓHE>ÍÓHEÅÍëIÍúIÍÀFMINUTES ÍúIÍGÍúIyÍ3E!*RÍí8ÍúIyÍJ>ÍÓHF>ÍÓHFÅÍëIÍúIÍÀFSECONDS ÍúIÍGÍúIyÍ3E!.RÍí8ÍúIyÍJ>ÍÓHG>ÍÓHGÅÍëIÃIS THIS NORTH OR SOUTH, N?/S?!eåÍDÍúIÍJ>ÍÓHH>ÍÓHHÅÍëIÍúIÍGÍúIyÍ3E!ÔRÍKÍúIyÍJ>ÍÓHI>ÍÓHIÅÍëIÃäDECLINATION = !ÕåÍDÍ|O&RÍ2Ãü DEG !öåÍDÍ|O*RÍ2à MIN !åÍDÍ|O.RÍ2Ã, SEC !&åÍD!ÔRåÍDÍúIÍJ>ÍÓHP>ÍÓHPÅÍëIÃnIS THIS CORRECT? Y?/N?!WåÍDÍúIÍJ>ÍÓHQ>ÍÓHQÅÍëIÍúIÍGÍúIyÍ3E!ƒRÍKÍúIyÍJ>ÍÓHR>ÍÓHRüN!ƒRå!ºåÍÝ1ͤ8ÊÐÃe>ÍÓHS>ÍÓHSÃãY!ƒRå!áåÍì1ͤ8Ê÷Ãe>ÍÓHT>ÍÓHTÍÓ>ÍÓHU>ÍÓHUÍ�O�QÍ�OqQÍÒ@>!›QͨO>ÍÓHV>ÍÓHVÃ@ €Í|ORÍ|O< Í™1Í{8Ê[ >ÍÓHVÉ>ÍÓHW>ÍÓHW>ÍÓHX>ÍÓHXÅÍëIä #DECLINATION IN DECIMAL DEGREES IS: !€ åÍDÍ�O›QÍ�OqQÍ2BÍR4ÍúIÍJ>ÍÓHY>ÍÓHY>ÍÓH`>ÍÓH`ÅÍëIÃõ INPUT LATITUDE!æ åÍDÍúIÍJ>ÍÓHa>ÍÓHaÅÍëIÍúIÍÀFDEGREES ÍúIÍGÍúIyÍ3E!&RÍí8ÍúIyÍJ>ÍÓHb>ÍÓHbÅÍëIÍúIÍÀFMINUTES ÍúIÍGÍúIyÍ3E!*RÍí8ÍúIyÍJ>ÍÓHc>ÍÓHcÅÍëIÍúIÍÀFSECONDS ÍúIÍGÍúIyÍ3E!.RÍí8ÍúIyÍJ>ÍÓHd>ÍÓHdÅÍëIÃõ !IS LATITUDE NORTH OR SOUTH? N?/S?!Ó åÍDÍúIÍJ>ÍÓHe>ÍÓHeÅÍëIÍúIÍGÍúIyÍ3E!ÔRÍKÍúIyÍJ>ÍÓHf>ÍÓHfÅÍëIÃU LATITUDE IS: !G åÍDÍ|O&RÍ2Ãq DEGREES !g åÍDÍ|O*RÍ2Ã� MINUTES !ƒ åÍDÍ|O.RÍ2é SECONDS !Ÿ åÍD!ÔRåÍDÍúIÍJ>ÍÓHg>ÍÓHgÅÍëIÃë IS THIS CORRECT? Y?/N?!Ô åÍDÍúIÍJ>ÍÓHh>ÍÓHhÅÍëIÍúIÍGÍúIyÍ3E!ƒRÍKÍúIyÍJ>ÍÓHi>ÍÓHiÃ9 N!ƒRå!7 åÍÝ1ͤ8ÊM ÃÖ >ÍÓHp>ÍÓHpÃ` Y!ƒRå!^ åÍì1ͤ8Êt ÃÖ >ÍÓHq>ÍÓHqÍÓ>ÍÓHr>ÍÓHrÍ�O�QÍ�OqQÍÒ@>!¢QͨO>ÍÓHs>ÍÓHs>ÍÓHt>ÍÓHtÅÍëIÃà OBSERVERS POSITION!Í åÍDÍúIÍJ>ÍÓHu>ÍÓHuÅÍëIÃ% LATITUDE IN DECIMAL DEGREES IS: ! åÍDÍ�O¢QÍ�OqQÍ2BÍR4ÍúIÍJ>ÍÓHv>ÍÓHv>ÍÓHw>ÍÓHwÅÍëIÃw INPUT LONGITUDE!g åÍDÍúIÍJ>ÍÓHx>ÍÓHxÅÍëIÍúIÍÀFDEGREES ÍúIÍGÍúIyÍ3E!&RÍí8ÍúIyÍJ>ÍÓHy>ÍÓHyÅÍëIÍúIÍÀFMINUTES ÍúIÍGÍúIyÍ3E!*RÍí8ÍúIyÍJ>ÍÓH€>ÍÓH€ÅÍëIÍúIÍÀFSECONDS ÍúIÍGÍúIyÍ3E!.RÍí8ÍúIyÍJ>ÍÓH�>ÍÓH�ÅÍëIÃv IS LONGITUDE EAST OR WEST? E?/W?!UåÍDÍúIÍJ>ÍÓH‚>ÍÓH‚ÅÍëIÍúIÍGÍúIyÍ3E!2RÍKÍúIyÍJ>ÍÓHƒ>ÍÓHƒÃÄE!2Rå!ÂåÍÝ1ͤ8Êî>ÍÓHƒÃáN!ßå!ÔRÍžJÃ>ÍÓHƒÃúS!øå!ÔRÍžJ>ÍÓH„>ÍÓH„ÅÍëIÃ*LONGITUDE IS: !åÍDÍ|O&RÍ2ÃF DEGREES !<åÍDÍ|O*RÍ2Ãb MINUTES !XåÍDÍ|O.RÍ2Ã~ SECONDS !tåÍD!2RåÍDÍúIÍJ>ÍÓH…>ÍÓH…ÅÍëIÃÀIS THIS CORRECT? 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Í"ôPÉÿÿñ_ÍÁÉñ_ÍÁÉñÁ¯7Éñ:XQ·Â*Q\Íþÿ!YQÊ«H>ÿ2XQ:WQþ€ÂIQ€Í\Í!YQ·Â«H_<2WQ!€~ÁÉ€&INPUT FILE REAÄPPPPÚ<ýt10 REM THIS IS PROGRAM "TIME" LOCAL SIDERIAL TIME IS CALCULATED 20 REM GIVEN THE DATE, HOUR, MINIT AND SECOND AND THE OBSERVER'S LONGITUDE 30 REM PROGRAM IS BY MIKE FINERTY MAKING USE OF PROGRAMS IN SKY AND TELESCOPE'S 40 REM COMPUTER SECTION. 50 DEFDBL A-Z 60 PRINT "PLEASE INPUT DATA: " 70 INPUT "LONGITUDE = ";L2 80 LPRINT "LONGITUDE = ";L2;" DEGREES" 90 L2 = L2/15 100 REM L2 IS NOW LONGITUDE IN DECIMAL HOURS 110 INPUT "YEAR =";Y 120 LPRINT "YEAR = ";Y 130 INPUT "MONTH = ";M 140 LPRINT "MONTH = ";M 150 INPUT "DAY = ";D2 160 LPRINT "DAY =";D2 170 REM THIS IS UNIVERSAL TIME 180 INPUT "HOURS =";A1 190 LPRINT "HOURS =";A1 200 INPUT "MINUTES =";A2 210 LPRINT "MINUTES =";A2 220 INPUT "SECONDS =";A3 230 LPRINT "SECONDS =";A3 240 F1 = (A3+60*A2+3600*A1)/86400!-.5 250 J = - INT(7*(INT((M+9)/12)+Y)/4) 260 S = SGN(M-9) 270 A4 = ABS(M-9) 280 J1 = INT(Y+S*INT(A4/7)) 290 J1 = - INT((INT(J1/100)+1)*3/4) 300 J = J + INT(275*M/9)+D2+J1 310 J = J+1.72103E+06+367*Y 320 J = J - 2 330 PRINT "JULIAN DAY: ";J;" FRACTION OF A DAY:";F1 340 LPRINT "JULIAN DAY: ";J;" FRACTION OF A DAY:";F1 350 REM CALCULATE GREENWICH SIDERIAL TIME FIRST 360 D = J -2.45155E+06 370 D = D - 5 380 T = D/36525! 390 T1 = INT(T) 400 J0 = T1*36525!+2.45155E+06 410 J0 = J0 -5 420 T2 =(J - J0 +.5)/36525! 430 S0 = 24110.54841#+184.812866#*T1 440 S0 = S0 + 8640184.812860002#*T2 450 S0 = S0 + (.093104*T*T) 460 S0 = S0 -(.0000062*T*T*T) 470 S0 = S0/86400! 480 S1 = INT(S0) 490 S0 = S0 - S1 500 S0 = 24*(S0+(F1+.5)*1.002737909#) 510 IF S0<0 THEN S0 = S0+24 520 IF S0>24 THEN S0 = S0 - 24 530 LST = S0 - L2 540 LSTDEG = LST*15 550 IF LST < 0 THEN LST = LST + 24 560 PRINT "LOCAL SIDERIAL ANGLE (ARIES) IN DECIMAL DEGREES: ";LSTDEG 570 H = INT(LST) 580 M1 = 60 * (LST - H) 590 M = INT(M1) 600 S = 60 * (M1 - M) 610 PRINT "LOCAL SIDERIAL TIME:";H;"HRS";M;"MINS";S;"SECS" 620 LPRINT "LOCAL SIDERIAL TIME:";H;"HRS";M;"MINS";S;"SECS" 630 PRINT "DO YOU WANT A DIFFERENT TIME? Y/N?" 640 INPUT ANS$ 650 IF ANS$ = "Y" THEN 100 660 END ;"HRS";M;"MINS";S;"SECS" 630 PRINT "DO YOU WANT A DIFFERENT TIME? Y/N?" 640 INPUT ANS$ 650 IF ANS$ = "Y" THEN 100 Perfect Format output for device: DiabloPS – ð–P–ˆâ10 REM THIS IS PROGRAM "TIME" LOCAL SIDERIAL TIME IS CALCULATED –ˆâˆö20 REM GIVEN THE DATE, HOUR, MINIT AND SECOND AND THE OBSERVER'S LONGITUDE –ˆâˆö30 REM PROGRAM IS BY MIKE FINERTY MAKING USE OF PROGRAMS IN SKY AND TELESCOPE'S –ˆâˆö40 REM COMPUTER SECTION. –ˆâˆö50 DEFDBL A-Z –ˆâˆö60 PRINT "PLEASE INPUT DATA: " –ˆâˆö70 INPUT "LONGITUDE = ";L2 –ˆâˆö80 LPRINT "LONGITUDE = ";L2;" DEGREES" –ˆâˆö90 L2 = L2/15 –ˆâˆö100 REM L2 IS NOW LONGITUDE IN DECIMAL HOURS –ˆâˆö110 INPUT "YEAR =";Y –ˆâˆö120 LPRINT "YEAR = ";Y –ˆâˆö130 INPUT "MONTH = ";M –ˆâˆö140 LPRINT "MONTH = ";M –ˆâˆö150 INPUT "DAY = ";D2 –ˆâˆö160 LPRINT "DAY =";D2 –ˆâˆö170 REM THIS IS UNIVERSAL TIME –ˆâˆö180 INPUT "HOURS =";A1 –ˆâˆö190 LPRINT "HOURS =";A1 –ˆâˆö200 INPUT "MINUTES =";A2 –ˆâˆö210 LPRINT "MINUTES =";A2 –ˆâˆö220 INPUT "SECONDS =";A3 –ˆâˆö230 LPRINT "SECONDS =";A3 –ˆâˆö240 F1 = (A3+60*A2+3600*A1)/86400!-.5 –ˆâˆö250 J = - INT(7*(INT((M+9)/12)+Y)/4) –ˆâˆö260 S = SGN(M-9) –ˆâˆö270 A4 = ABS(M-9) –ˆâˆö280 J1 = INT(Y+S*INT(A4/7)) –ˆâˆö290 J1 = - INT((INT(J1/100)+1)*3/4) –ˆâˆö300 J = J + INT(275*M/9)+D2+J1 –ˆâˆö310 J = J+1.72103E+06+367*Y –ˆâˆö320 J = J - 2 –ˆâˆö330 PRINT "JULIAN DAY: ";J;" FRACTION OF A DAY:";F1 –ˆâˆö340 LPRINT "JULIAN DAY: ";J;" FRACTION OF A DAY:";F1 –ˆâˆö350 REM CALCULATE GREENWICH SIDERIAL TIME FIRST –ˆâˆö360 D = J -2.45155E+06 –ˆâˆö370 D = D - 5 –ˆâˆö380 T = D/36525! –ˆâˆö390 T1 = INT(T) –ˆâˆö400 J0 = T1*36525!+2.45155E+06 –ˆâˆö410 J0 = J0 -5 –ˆâˆö420 T2 =(J - J0 +.5)/36525! –ˆâˆö430 S0 = 24110.54841#+184.812866#*T1 –ˆâˆö440 S0 = S0 + 8640184.812860001#*T2 –ˆâˆö450 S0 = S0 + (.093104*T*T) –ˆâˆö460 S0 = S0 -(.0000062*T*T*T) –ˆâˆö470 S0 = S0/86400! –ˆâˆö480 S1 = INT(S0) –ˆâˆö490 S0 = S0 - S1 –€–ˆâ؈ä- 1 - –ˆâø – ð–P–ˆâˆö500 S0 = 24*(S0+(F1+.5)*1.002737909#) –ˆâˆö510 IF S0<0 THEN S0 = S0+24 –ˆâˆö520 IF S0>24 THEN S0 = S0 - 24 –ˆâˆö530 LST = S0 - L2 –ˆâˆö540 LSTDEG = LST*15 –ˆâˆö550 PRINT "LOCAL SIDERIAL ANGLE (ARIES) IN DECIMAL DEGREES: ";LSTDEG –ˆâˆö560 H = INT(LST) –ˆâˆö570 M1 = 60 * (LST - H) –ˆâˆö580 M = INT(M1) –ˆâˆö590 S = 60 * (M1 - M) –ˆâˆö600 PRINT "LOCAL SIDERIAL TIME:";H;"HRS";M;"MINS";S;"SECS" –ˆâˆö610 LPRINT "LOCAL SIDERIAL TIME:";H;"HRS";M;"MINS";S;"SECS" –ˆâˆö620 PRINT "DO YOU WANT A DIFFERENT TIME? Y/N?" –ˆâˆö630 INPUT ANS$ –ˆâˆö640 IF ANS$ = "Y" THEN 100 –ˆâˆö650 END –ˆâ –6€–ˆâ؈ä- 2 - –ˆâø ˆâˆö420 T2 =(J - J0 +.5)/36525! –ˆâˆö430 S0 = 24110.54841#+184.812866#*T1 –ˆÿb � PROGRAM "RISE-SET.BAS," A MBASIC PROGRAM CALCULATING THE LOCAL HOUR ANGLE^b� AND THE LOCAL AZMUTH OF THE RISING OF AN ASTRONOMICAL BODY›b� GIVEN ITS DECLINATION AND THE OBSERVERS LATITUDEÓb(� REVISED 4-19-1985, MIKE FINERTY, TUCSON!c2� ***********************************************************************4c<PI ð U–hÚI‚JcFCONST ð 5•]?·Y�xcP… "DECLINATION OF BODY IN DEC. DEGREES";D«cZ… "LATITUDE OF OBSERVER IN DEGREES.MINS "; LAT½cdDEC ð DôPIõ´êcnLATITUDE ð dõ<ô(LAT ó ÿ…(LAT))òÿ…(LAT)dxL ð LATITUDEôPIõ´d‚TEST ð ÿ†(DEC)2dŒ‹ TEST ï PIõóÿ†(L) Ï ÖOd–LHACOS ð ó ÿ�(L)ôÿ�(DEC)id AZCOS ð ÿ‰(DEC)õÿŒ(L)•dªLHA ðPIõóÿŽ(LHACOSõ(óLHACOSö)ö€)¿d´AZ ð PIõóÿŽ(AZCOSõ(óAZC0Sö)ö€)Ñd¾AZ ð AZõPIô´ãdÈLHAðLHAõPIô ôdÒLHA ð óLHA