1000,"R:              PROGRAM KEPL",1010,"R:",1020,"R:   PACIFIC UNION COLLEGE,  L. TURNER,  SEP 73",1030,"R:",1040,"R: THIS PROGRAM IS DESIGNED TO GIVE CAI IN KEPLER'S THIRD LAW TO",1050,"R: BEGINNING ASTRONOMY STUDENTS.",1060,"R:",1070,"R:*****************************************************************",1080,"R:",1090,"T:",1100,"T:KEPLER'S THREE LAWS ARE VERY IMPORTANT IN UNDERSTANDING THE +",1110,"T:ORBITS OF THE PLANETS, COMETS, OR ANY SATELLITE.  THEY MAY BE +"
1120,"T:DERIVED FROM NEWTON'S LAWS AND HIS FORM OF THE GRAVITATIONAL +",1130,"T:FORCE; HOWEVER, THEY ARE A NICE SUMMARY OF THE MOTION OF THE +",1140,"T:PLANETS.",1150,"T:",1160,"T:HAVE YOU STUDIED KEPLER'S LAWS BEFORE +",1170,"A:",1180,".M:[YE,[Y],RIGHT,OF*COURS,[COR,AFF,CERTA",1190,"Y:VERY GOOD!  WE CAN REALLY BLAZE!",1200,"N:WELL, THEN IT IS A GOOD IDEA TO START WITH THE FIRST TWO, SINCE +",1210,"N:WE WILL NEED THE CONCEPTS DEVELOPED WITH THOSE.",1220,"CN:F=1",1230,"T:",1240,"T:BEFORE WE GO TO FAR, I WOULD LIKE YOUR NAME +"
1380,"R:",1390,"T:FIRST $NAME+, +",1400,"T(F):KEPLER'S FIRST LAW DESCRIBES THE SHAPE OF THE ORBIT OF A +",1410,"T(F):PLANET OR SATELLITE.  +",1420,"T:WHAT IS THE SHAPE OF +",1430,"T(F):AN ORBIT +",1440,"T(F=0):A PLANET'S ORBIT +",1450,"A:",1460,"M:ELLIP,ELIP",1470,"Y:THAT IS, OF COURSE, ABSOLUTELY CORRECT $NAME+!  +",1480,"JY:*FIRST",1490,"M:CIRCLE",1500,"Y:WELL, THAT IS A POSSIBLE ORBIT, BUT IT IS A VERY SPECIAL CASE.  +"
1510,"N:I AM AFRAID NOT.  +",1520,"T:IN GENERAL THE ORBIT IS AN ELLIPSE.  (WE WILL RESTRICT +",1530,"T:OURSELVES TO BOUND ORBITS.)",1540,"T:",1550,"C:G=1",1560,"*FIRST T:BEFORE WE STATE KEPLER'S FIRST LAW IN ALL OF ITS GLORY +",1570,"T:LET'S CONSIDER AN ELLIPSE AND DEFINE SOME TERMS.",1580,"T:",1590,"T:                    ***********",1600,"T:                ****     !     ****",1610,"T:             ***         !         ***",1620,"T:           **            !            **",1630,"T:          *              !              *"
1640,"T:         *   F1          !          F2   *",1650,"T:         *---#-----------+-----------#---*",1660,"T:         *-H-'           !-------A-------*",1670,"T:          *              !              *",1680,"T:           **            !            **",1690,"T:             ***         !         ***",1700,"T:                ****     !     ****",1710,"T:                    ***********",1720,"T:",1730,"T:OK, $NAME+, WHAT IS THE DISTANCE 'A' CALLED +",1740,"A:",1750,".M:[SEMI*MAJOR",1760,"Y:BEAUTIFUL $NAME+!"
1770,"JY:*SEMI",1780,".M:[MAJOR",1790,"Y:NOT QUITE, +",1800,"N:WELL, I WILL TELL YOU.  +",1810,"T:THAT IS THE SEMIMAJOR AXIS OF THE ELLIPSE.",1820,"T:AND WHAT IS TWICE THE SEMIMAJOR AXIS CALLED (THE DISTANCE FROM +",1830,"T:ONE END OF THE ELLIPSE TO THE OTHER) +",1840,"A:",1850,".M:[MAJOR",1860,"Y:GOOD!  +",1870,"N:WELL, IT IS THE MAJOR AXIS.",1880,"*SEMI T:",1890,"T:WHAT ARE THE POINTS 'F1' AND 'F2' CALLED +"
1900,"A:",1910,".M:[FOCI,[FOCUS",1920,"Y:VERY GOOD.  +",1930,"N:NO, +",1940,"T:THEY ARE THE FOCI OF THE ELLIPSE (SINGULAR IS 'FOCUS').",1950,"JY:*CONT",1960,"J(G=0):*CONT",1970,"T:IN A CIRCULAR ORBIT, WHAT HAPPENS TO THE TWO FOCI +",1980,"A:",1990,".M:COME*ONE,COME*TOGETH,CENTER,[AP*ROACH,COINCID,SAME",2000,"Y:RIGHT, $NAME+!  +",2010,"N:I AM AFRAID NOT, +",2020,"T:THEY COME TOGETHER AND BECOME THE CENTER OF THE CIRCLE.  IN +"
2030,"T:THIS CASE THE SEMIMAJOR AXIS IS JUST SIMPLY THE RADIUS.",2040,"*CONT T:",2050,"T:KEPLER'S FIRST LAW STATES:",2060,"T:",2070,"T:     ''EACH PLANET MOVES ABOUT THE SUN IN AN ORBIT THAT IS AN",2080,"T:       ELLIPSE, WITH THE SUN AT THE FOCUS OF THE ELLIPSE.''",2090,"T:",2100,"T:NOW IF WE REPLACE THE FOCUS 'F1' WITH THE SUN, WHAT IS THE +",2110,"T:DISTANCE 'H' CALLED +",2120,"A:",2130,".M:[PERI*HEL",2140,"Y:CORRECT $NAME+!  +",2150,"N:NOT EXACTLY, +"
2160,"T:THAT IS THE PERIHELION DISTANCE+",2170,"T(F):, OR THE DISTANCE OF CLOSEST APPROACH OF THE PLANET TO THE +",2180,"T(F):SUN.",2190,"T(F=0):.",2200,"J(F=0):*BEGIN",2210,"T:WE WILL NOT EXPLICITLY NEED KEPLER'S SECOND LAW FOR THIS +",2220,"T:EXERCISE; HOWEVER, FOR THE SAKE OF COMPLETENESS, LET US STATE IT:",2230,"T:",2240,"T:     ''THE STRAIGHT LINE JOINING A PLANET AND THE SUN SWEEPS OUT",2250,"T:       EQUAL AREAS IN SPACE IN EQUAL INTERVALS OF TIME.''",2260,"T:"
2270,"T:THIS BASICALLY TELLS HOW THE PLANET MOVES AROUND ITS ORBIT.  +",2280,"T:WHEN IT IS CLOSE TO THE SUN IT MOVES FASTER THEN WHEN IT IS +",2290,"T:FURTHER AWAY.",2300,"T:",2310,"T:WE ARE NOW READY TO DISCUSS KEPLER'S THIRD LAW.  IT GIVES A +",2320,"T:SIMPLE RELATIONSHIP BETWEEN THE SEMIMAJOR AXIS AND THE PERIOD +",2330,"T:OF THE PLANETARY ORBIT.",2340,"T:WHAT IS THE PERIOD OF AN ORBIT +",2350,"A:",2360,".M:[TIME,HOW*LONG",2370,".M:REVOLU,ORBIT,GO*AROUN,ENCOMPAS,COMPLET",2380,".D:2",2390,"Y:EXCELLENT $NAME+!  +"
2400,"N:NOT EXACTLY, +",2410,"T:IT IS JUST THE TIME IT TAKES FOR THE PLANET TO COMPLETE ONE +",2420,"T:REVOLUTION AROUND THE SUN.",2430,"R:",2440,"R:           THIRD LAW",2450,"R:",2460,"*BEGIN T:",2470,"T:IN WORDS WE CAN STATE KEPLER'S THIRD LAW:",2480,"T:",2490,"T:     ''THE SQUARES OF THE PERIODS OF THE PLANETS ARE IN DIRECT",2500,"T:       PROPORTION TO THE CUBES OF THE SEMIMAJOR AXES OF THEIR",2510,"T:       ORBITS.''",2520,"T:"
2530,"T:IN AN ALGEBRAIC EQUATION THIS BECOMES:",2540,"T:",2550,"T:            P^2 = K*A^3",2560,"T:",2570,"T:WHERE '^' MEANS 'RAISE TO A POWER' AND '*' MEANS MULTIPLY.  +",2580,"T:'P' IS THE PERIOD, 'A' IS THE SEMIMAJOR AXIS, AND 'K' IS A +",2590,"T:CONSTANT AND DEPENDS ON THE UNITS USED.",2600,"T:",2610,"T:WE CAN SOLVE THIS EQUATION FOR EITHER 'P' OR 'A' IN TERMS OF +",2620,"T:THE OTHER.  BUT FIRST WE NEED TO KNOW 'K'.  TO DETERMINE THIS, +",2630,"T:LET US USE QUANTITIES THAT WE KNOW ABOUT THE EARTH'S ORBIT."
2640,"T:WHAT IS THE PERIOD OF THE EARTH'S ORBIT +",2650,"A:#P",2660,"M:YEAR,YR",2670,"JY:*YEAR",2680,"M:DAY",2690,"JY:*DAY",2700,"T:I DON'T RECOGNIZE ANY UNIT, +",2710,".M:THRE*SIX*FIVE",2720,"JY:*SUSPY",2730,"C:X=365-P",2740,"C(X<0):X=-X",2750,"J(X>2):*NEXTD",2760,"*SUSPY T:BUT I SUSPECT YOU MEAN DAYS."
2770,"J:*CONTP",2780,"*NEXTD .M:[ONE",2790,"JY:*SUSPD",2800,"C:X=1-P",2810,"C(X<0):X=-X",2820,"J(X>.1):*NEXTTA",2830,"*SUSPD T:BUT I SUSPECT YOU MEAN YEAR.",2840,"J:*CONTP",2850,"*NEXTTA T:AND I +",2860,"*NEXTT T:DON'T QUITE RECOGNIZE THE NUMBER.",2870,"J:*CONTP",2880,"*YEAR .M:[ONE",2890,"JY:*GOOD"
2900,"C:X=1-P",2910,"C(X<0):X=-X",2920,"J(X<.1):*GOOD",2930,"*BAD T:YOU HAVE A CORRECT UNIT, BUT I +",2940,"J:*NEXTT",2950,"*DAY .M:THRE*SIX*FIVE",2960,"JY:*GOOD",2970,"C:X=365-P",2980,"C(X<0):X=-X",2990,"J(X>6):*BAD",3000,"*GOOD T:VERY FINE $NAME+!  +",3010,"*CONTP T:THE PERIOD OF THE EARTH'S ORBIT IS 365 DAYS (ACTUALLY +",3020,"T:365.2564 DAYS) OR ONE YEAR!"
3030,"T:",3040,"J(F=0):*EARTHC",3050,"J(G=0):*EARTHM",3060,"T:WHAT IS THE SHAPE OF THE EARTH'S ORBIT +",3070,"A:",3080,"M:ELLIP,ELIP",3090,"Y:THAT IS PRECISELY CORRECT; HOWEVER, +",3100,"JY:*EARTHN",3110,"M:CIRCLE,CIRCUL",3120,"Y:WELL, +",3130,"N:I AM AFRAID NOT, +",3140,"T:IT IS ACTUALLY AN ELLIPSE, BUT +",3150,"*EARTHN T:IT IS VERY CLOSE TO A TRUE CIRCLE."
3160,"T:THEREFORE, +",3170,"*EARTHM T:THE SEMIMAJOR AXIS OF THE EARTH'S ORBIT IS THE SAME AS +",3180,"T:THE MEAN DISTANCE FROM THE EARTH TO THE SUN WHICH IN TURN IS +",3190,"T:APPROXIMATELY THE RADIUS OF THE ORBIT.",3200,"R:",3210,"*EARTHC T:OK, WHAT IS THE MEAN DISTANCE FROM THE EARTH TO THE SUN??",3220,"A:#R",3230,"C:Y=1",3240,".M:[AU,[ASTR*UNIT,[A.U,[A U",3250,"JY:*ASTRUNIT",3260,".M:[MILE",3270,"JY:*MILE",3280,".M:METER,METRE,[M],[CM,[KM"
3290,"JY:*METER",3300,"T:I DON'T RECOGNIZE THAT.  +",3310,"TB:",3320,"TG:YOU SHOULD SPECIFY BOTH A VALUE AND A UNIT.",3330,"J:*MEAND",3340,"*ASTRUNIT .M:[ONE",3350,"JY:*ASTRGUD",3360,"C:X=1-R",3370,"C(X<0):X=-X",3380,"J(X<.1):*ASTRGUD",3390,"*ASTRBAD T:YOU HAVE A CORRECT UNIT, BUT YOUR VALUE IS NOT QUITE +",3400,"T:RIGHT.",3410,"J:*MEAND"
3420,"*MILE M:MILLION,MILION",3430,"CY:Y=1E6",3440,".M:NIN*TY*[THRE",3450,".D:2",3460,"JY:*ASTRGUD",3470,"C:X=9.3E7-R*Y",3480,"C(X<0):X=-X",3490,"J(X<3E6):*ASTRGUD",3500,"J:*ASTRBAD",3510,"*METER M:MILLION,MILION",3520,"CY:Y=1E6",3530,".M:CENTI,[CM",3540,"CY:Y=Y/100"
3550,".M:KILO,[KM",3560,"CY:Y=Y*1000",3570,".M:ONE*FIFTY",3580,"CY:R=150",3590,"C:X=1.5E11-R*Y",3600,"C(X<0):X=-X",3610,"J(X>1E10):*ASTRBAD",3620,"*ASTRGUD T:YOU ARE WITH IT TODAY $NAME+!  +",3630,"*MEAND T:THE MEAN DISTANCE (OR THE SEMIMAJOR AXIS) OF THE EARTH +",3640,"T:TO THE SUN IS 93 MILLION MILES, 150 MILLION KILOMETERS, 1.5E11 +",3650,"T:METERS, 1.5E13 CENTIMETERS, OR SIMPLY 1 AU (ASTRONOMICAL UNIT)!",3660,"T:    (THE 'E' IN NUMBERS INDICATE A POWER OF TEN.)",3670,"R:"
3680,"R:           DETERMINE 'K'",3690,"R:",3700,"T:",3710,"T:IN TERMS OF THE UNITS 'YEARS' AND 'ASTRONOMICAL UNITS', THE +",3720,"T:VALUE OF 'K' IS ESPECIALLY SIMPLE.  WHAT DO YOU SUPPOSE IT IS +",3730,"A:#K",3740,".M:[ONE,[UNIT",3750,"CY:K=1",3760,"T(K#1):NOT QUITE, K SIMPLY BECOMES 1.  +",3770,"T(K=1):THAT IS ABSOLUTELY RIGHT $NAME+!  +",3780,"T:WITH THIS CHOICE OF 'K' WE CAN JUST IGNORE IT IN THE +",3790,"T:CALCULATIONS, AND KEPLER'S THIRD LAW BECOMES:",3800,"T:"
3810,"T:     P^2 = A^3     (P IN YEARS AND A IN AU)",3820,"T:",3830,"J(F=0):*OVER",3840,"T:LET US TRY THIS FOR THE EARTH.  NOW P=1 SO THAT P^2=1 AND +",3850,"T:A=1 SO A^3=1, THUS THE EQUATION IS SATISFIED.",3860,"T:IF WE CHOSE OTHER UNITS FOR P AND A, THEN K IS NOT SO NICE, +",3870,"T:INDEED:",3880,"T:",3890,"T:             P      !      A      !      K",3900,"T:       -------------+-------------+-------------",3910,"T:           MILES    !    YEARS    !  8.04 E23",3920,"T:        CENTIMETERS !    YEARS    !  3.38 E39"
3930,"T:            AU      !    YEARS    !     1",3940,"T:           MILES    !    DAYS     !  6.04 E18",3950,"T:            AU      !    DAYS     !  7.51 E-6",3960,"T:",3970,"R:",3980,"R:           PLANETS",3990,"R:           SOLVE FOR 'P'",4000,"R:",4010,"*OVER T:WE ARE NOW READY TO GET DOWN TO BUSINESS.  THE PLANETS +",4020,"T:ARE THE EASIEST SINCE THEY ALL HAVE NEARLY CIRCULAR ORBITS.",4030,"J(F=0):*MECURY",4040,"T:WHAT IS THE CLOSEST PLANET TO THE SUN +",4050,"A:"
4060,"M:MERCURY",4070,"N:IT IS MERCURY!  AND +",4080,"JN:*MECURY",4090,"T:OF COURSE, AND WHAT IS ITS SEMIMAJOR AXIS (IN AU PLEASE) +",4100,"A:#M",4110,"C:X=0.387-M",4120,"C(X<0):X=-X",4130,"T(X<.02):THAT IS VERY GOOD $NAME+!  +",4140,"T(X>=.02):NOT QUITE, +",4150,"*MECURY T:MERCURY HAS A SEMIMAJOR AXIS OF 0.387 AU.",4160,"J(F=0):*MERRY",4170,"T:IS ITS ORBITAL PERIOD LESS THAN OR GREATER THAN ONE YEAR +",4180,"A:"
4190,".M:LES*THAN,<,SHORT,[LESS",4200,"Y:RIGHT ON!",4210,"N:WELL, SINCE ITS SEMIMAJOR AXIS IS LESS THAN THAT OF EARTH +",4220,"N:(LESS THAN 1 AU), ITS PERIOD IS ALSO MUCH LESS.",4230,"*MERRY T:LET'S APPLY KEPLER'S THIRD LAW TO FIND ITS PERIOD, +",4240,"T:NAMELY:",4250,"T:",4260,"T:         P = SQR(A^3)",4270,"T:",4280,"T(F):WHERE 'SQR' MEANS TO TAKE THE SQUARE ROOT OF THE QUANTITY +",4290,"T(F):IN PARENTHESES, 'A' CUBED.",4300,"T:FIRST LET US CUBE A.  YOU TRY IT!  WHAT DO YOU GET +",4310,"*PIG A:#A"
4320,"TB:COME ON, TRY A NUMBER +",4330,"JB:*PIG",4340,"C:X=0.387-A",4350,"C(X<0):X=-X",4360,"T(X<.03):YOU MUST CUBE THE NUMBER (A*A*A)!",4370,"C:X=.15-A",4380,"C(X<0):X=-X",4390,"T(X<.03):WELL, YOU SQUARED IT, MULTIPLY IT BY 0.387 AGAIN!",4400,"J(X<.03):*PIG",4410,"C:X=0.058-A",4420,"C(X<0):X=-X",4430,"T(X<.005):THAT IS VERY GOOD, I AM PROUD OF YOU!  +",4440,"T(X>=.005):I AM AFRAID THAT IS NOT QUITE CORRECT.  +"
4450,"T:I GET:  A^3 = 0.058, NOW LET'S TAKE THE SQUARE ROOT AND WE WILL +",4460,"T:HAVE 'P'!!  +",4470,"T(F):THIS IS A BIT MORE DIFFICULT, BUT NOT IMPOSSIBLE.  +",4480,"T:ALRIGHT NOW, WHAT DO YOU GET +",4490,"*NON A:#A",4500,"TB:BE BRAVE, TRY A NUMBER (NOTE:  .2*.2=.04 AND .3*.3=.09) +",4510,"JB:*NON",4520,"C:X=0.241-A",4530,"C(X<0):X=-X",4540,"T(X<.015):VERY, VERY, GOOD $NAME+!  +",4550,"C(X>=.015):G=1",4560,"T(X>=.015):NO, THAT IS NOT VERY CLOSE.  +",4570,"T:THE CORRECT ANSWER IS 0.241 YEARS, AND THAT COMES OUT TO BE +"
4580,"T:88.0 DAYS!",4590,"T:",4600,"T:THE NEXT PLANET, VENUS, FOLLOWS IN LIKE MANNER.  IT HAS A +",4610,"T:SEMIMAJOR AXIS OF 0.723 AU AND A PERIOD OF 0.615 YEARS. +",4620,"T(F):YOU MIGHT TRY VERIFYING THAT!",4630,"T(F):THE THIRD PLANET FROM THE SUN IS THE EASIEST OF ALL.  WE +",4640,"T(F):HAVE ALREADY DONE THE EARTH!",4650,"T:",4660,"T:WHAT IS THE FOURTH PLANET +",4670,"A:",4680,"M:MARS",4690,"N:COME NOW!  IT IS MARS, THE RED PLANET!",4700,"JN:*PERM"
4710,"T:EXACTLY!  DO YOU KNOW ITS SEMIMAJOR AXIS +",4720,"A:#A",4730,".M:[Y],[YE,RIGHT,OF COURS,CERT",4740,"Y:VERY GOOD, WHAT IS IT +",4750,"JY:*MARSP",4760,".M:[N],[NO,N'T,NOT",4770,"Y:WELL MAKE A GUESS ANYWAY +",4780,"*MARSP AY:#A",4790,"JB:*PERM",4800,"C:X=1.52-A",4810,"C(X<0):X=-X",4820,"T(X<.1):RIGHT ON THE BUTTON!  +",4830,"T(X>=.1):SORRY, +"
4840,"*PERM T:THE SEMIMAJOR AXIS OF MARS IS 1.524 AU.  THEREFORE $NAME +",4850,"J(G=0):*MARE",4860,"*MARP T:WE CUBE A, AND GET +",4870,"A:#A",4880,"TB:YOU'RE NOT COOPERATING!  +",4890,"JB:*MARP",4900,"C:X=3.51-A",4910,"C(X<0):X=-X",4920,"T(X<.2):BEAUTIFUL $NAME+!  +",4930,"T(X>=.2):NOT QUITE, +",4940,"T:I GET:  A^3 = 3.54, NOW WHAT IS P +",4950,"*MARD A:#A",4960,"TB:DON'T BE AFRAID, MAKE A GUESS +"
4970,"JB:*MARD",4980,"C:X=1.88-A",4990,"C(X<0):X=-X",5000,"T(X<.05):YOU'VE GOT IT!  +",5010,"T(X>=.05):SIGH, IT REALLY IS NOT THAT HARD.  +",5020,"*MARE T:THE PERIOD OF MARS IS 1.88 YEARS.",5030,"R:",5040,"R:           SOLVE FOR 'A'",5050,"R:",5060,"T:",5070,"T:FOR THE NEXT PLANET, JUPITER, LET'S TRY SOMETHING DIFFERENT!  +",5080,"T:IT HAS A PERIOD OF 11.86 YEARS SO LET'S FIND ITS SEMIMAJOR +",5090,"T:AXIS!  +"
5100,"T(F):TO DO THIS SIMPLY INVERT OUR PREVIOUS EQUATION SO +",5110,"T:KEPLER'S THIRD LAW MAY BE WRITTEN AS:",5120,"T:",5130,"T:         A = CUB(P^2)",5140,"T:",5150,"T(F):WHERE 'CUB' MEANS TO TAKE THE CUBE ROOT OF THE QUANTITY IN +",5160,"T(F):PARENTHESES.  THIS IS ADMITTEDLY SOMEWHAT MORE DIFFICULT +",5170,"T(F):THAN TAKING A SQUARE ROOT, BUT IT IS POSSIBLE.",5180,"T:OK, NOW FOR JUPITER, WE FIRST SQUARE P.  WHAT DO YOU GET +",5190,"*JUP A:#P",5200,"TB:I WON'T BITE!  TRY A NUMBER +",5210,"JB:*JUP",5220,"C:X=140.7-P"
5230,"C(X<0):X=-X",5240,"T(X<4):YOU'RE ON THE RIGHT TRACK!  +",5250,"T(X>=4):STRIKE THREE!  +",5260,"T:P^2 IS PRECISELY 140.7, NOW WHAT IS THE CUBE ROOT OF THAT +",5270,"*JUPIT A:#P",5280,"TB:DON'T BE SO CAUTIOUS, GUESS +",5290,"JB:*JUPIT",5300,"C:X=5.20-P",5310,"C(X<0):X=-X",5320,"T(X<.4):I'LL BUY THAT!  +",5330,"J(X<.4):*BUYT",5340,"T:WELL, THIS IS A BIT MORE DIFFICULT, AS A FIRST GUESS NOTE THAT +",5350,"T:5^3 = 125 AND 6^3 = 216, SINCE 140.7 IS CLOSER TO 125, I WOULD +"
5360,"T:GUESS THAT THE PERIOD IS SLIGHTLY GREATER THAN 5, IN FACT +",5370,"*BUYT T:IT IS EXACTLY 5.20 AU!",5380,"T:",5390,"T:IN LIKE MANNER WE CAN SOLVE FOR ALL THE PLANETS.  +",5400,"T(F):SATURN HAS A PERIOD OF 29.46 YEARS SO ITS SEMIMAJOR AXIS IS +",5410,"T(F):9.54 AU.  URANUS HAS A SEMIMAJOR AXIS OF 19.18 AU SO ITS +",5420,"T(F):PERIOD IS 84.01 YEARS.  AND SO FORTH.  +",5430,"T:THUS WE CAN MAKE A TABLE:",5440,"T:",5450,"T:          PLANET   !  SEMIMAJOR AXIS  !  PERIOD"
5460,"T:                   !      (AU)        !  (YEARS)",5470,"T:       ------------+------------------+-----------",5480,"T:          MERCURY  !      0.387       !    0.241",5490,"T:          VENUS    !      0.723       !    0.615",5500,"T:          EARTH    !      1           !    1",5510,"T:          MARS     !      1.524       !    1.88",5520,"T:          JUPITER  !      5.20        !   11.86",5530,"T:          SATURN   !      9.54        !   29.46",5540,"T:          URANUS   !     19.18        !   84.0"
5550,"T:          NEPTUNE  !     30.06        !  164.8",5560,"T:          PLUTO    !     39.4         !  247.7",5570,"T:",5580,"T:EXAMINE THE TABLE.  NOTICE THAT THE SEMIMAJOR AXES INCREASE, +",5590,"T:BUT THE PERIOD INCREASES MUCH FASTER, PLUTO IS ONLY 40 TIMES +",5600,"T:AS FAR FROM THE SUN AS THE EARTH, BUT IT TAKES ALMOST 250 YEARS!!",5610,"T:WHAT DO YOU THINK ACCOUNTS FOR THIS +",5620,"A:",5630,"T:THE PERIOD IS RAISED TO THE THIRD POWER WHEREAS THE SEMIMAJOR +"
5640,"T:AXIS IS ONLY SQUARED, THUS THE PERIOD INCREASES AT A FASTER +",5650,"T:RATE.",5660,"T:",5670,"T:WELL, THAT PRETTY MUCH TAKES CARE OF THE PLANETS.  +",5680,"J(F=0):*COMT",5690,"T:DO YOU REMEMBER WHAT APPROXIMATE SHAPE CHARACTERIZES ALL OF THE +",5700,"T:PLANETS' ORBITS +",5710,"A:",5720,".M:[Y],[YE,RIGHT,OF COURS,CERT",5730,"JN:*AGIN",5740,"T:OK, WHAT IS IT +",5750,"A:",5760,"*AGIN M:ELLIP,ELIP"
5770,"Y:YES, IT IS TRUE THAT ALL BOUND ORBITS ARE STRICTLY ELLIPSES; +",5780,"Y:HOWEVER, IN THE CASE OF THE PLANETS +",5790,"JY:*CICLER",5800,"M:CIRCLE,CIRCUL",5810,"Y:THAT IS RIGHT, STRICTLY SPEAKING THE ORBITS ARE ELLIPSES, BUT +",5820,"N:WELL, +",5830,"*CICLER T:THE ORBITS ARE VERY CLOSE TO CIRCULAR.  THIS MEANS THAT +",5840,"T:EACH PLANET IS CLOSE TO THE SAME DISTANCE FROM THE SUN AT ALL +",5850,"T:TIMES.  +",5860,"R:",5870,"R:           COMETS",5880,"R:"
5890,"*COMT T:HOWEVER, THE OTHER MEMBERS OF OUR SOLAR FAMILY DO NOT +",5900,"T:HAVE SUCH NICE ROUND ORBITS.  THE COMETS ESPECIALLY HAVE HIGHLY +",5910,"T:ELONGATED ELLIPTICAL ORBITS.",5920,"J(F=0):*CWORK",5930,"T:DO YOU THINK KEPLER'S THIRD LAW WORKS FOR COMETS +",5940,"A:",5950,".M:[Y],[YE,CERT,RIGHT,OF COURS,[COR*ECT,PRECIS,EXACT",5960,"Y:YOU ARE ABSOLUTELY RIGHT $NAME+!  HOWEVER, +",5970,"N:OH MY!  IT MOST CERTAINLY DOES!  BUT +",5980,"*CWORK T:THESE ORBITS DO HAVE AN ADDITIONAL CONSIDERATION.  +"
5990,"T:KEPLER'S THIRD LAW GIVES THE SEMIMAJOR AXIS, BUT WITH A HIGHLY +",6000,"T:ELLIPTICAL ORBIT THE PERIHELION DISTANCE IS SMALL SO THE COMET +",6010,"T:MAY REACH A DISTANCE FROM THE SUN OF ALMOST TWICE THE +",6020,"T:SEMIMAJOR AXIS!  CONSIDER:",6030,"T:",6040,"T:      !----------------- 2*A -----------------!",6050,"T:        +                                   + ",6060,"T:       +                                     + ",6070,"T:       +                                     + "
6080,"T:      +                     ******************+**************",6090,"T:      +                  **                   +               **",6100,"T:      +                 * O                 # +                 *",6110,"T:      +                  **                   +               **",6120,"T:      +                     ******************+**************",6130,"T:       +                                     + ",6140,"T:       +                !----------------- 2*A -----------------!",6150,"T:"
6160,"T:HERE THE 'PLUSES' INDICATE A CIRCULAR (PLANETARY??) ORBIT WITH +",6170,"T:THE SAME MAJOR AXIS (AND SEMIMAJOR AXIS) AS THE 'ASTERISK' +",6180,"T:OUTLINED HIGHLY ELLIPTICAL (COMETARY??) ORBIT.  +",6190,"T(F):THE 'O' REPRESENTS THE SUN WHICH IS AT A FOCUS OF BOTH +",6200,"T(F):ORBITS, IN THE CASE OF THE CIRCULAR ORBIT IT IS AT THE +",6210,"T(F):CENTER.  AND THE '#' IS AT THE CENTER OF THE ELLIPSE.  +",6220,"T:",6230,"T:HOW DO THEIR PERIODS COMPARE +",6240,"A:",6250,"M:SAME,EQUAL,=,IDENTIC",6260,"Y:EXACTLY $NAME+!  +"
6400,"T:BE ONLY A LITTLE LESS THAN THE 19.18 AU OF URANUS!",6410,"T:TRY A GUESS +",6420,"J:*HAL",6430,"*GUDGES C:X=664-A",6440,"C(X<0):X=-X",6450,"T(X<50):I THINK YOU GOT KEPLER'S LAW BACKWARDS!   P = CUB(A^2)   +",6460,"J(X<50):*HINT",6470,"C:X=44E4-A",6480,"C(X<0):X=-X",6490,"T(X<3E4):YOU CUBED P!  THAT'S BACKWARDS!   P = CUB(A^2)   +",6500,"J(X<3E4):*HINT",6510,"C:X=5776-A",6520,"C(X<0):X=-X"
6530,"T(X<200):SO FAR SO GOOD, I GET P^2=5776.  NOW TAKE THE SQUARE +",6540,"T(X<200):ROOT!",6550,"J(X<200):*HAL",6560,"C:X=17.95-A",6570,"C(X<0):X=-X",6580,"T(X<.3):THAT IS VERY GOOD $NAME+!  +",6590,"J(X<.3):*ABSCOR",6600,"T(X<1.1):THAT IS CLOSE, BUT +",6610,"J(X<1.1):*ABSCOR",6620,"T:I AM AFRAID THAT IS NOT CORRECT.  ACTUALLY ONE CAN GET A GOOD +",6630,"T:ESTIMATE WITHOUT DOING ANY ARITHMETIC!  YOU CAN COMPARE WITH +",6640,"T:THE KNOWN VALUES OF THE PLANETS AND MAKE AN EDUCATED GUESS.  +",6650,"J:*HINT"
6660,"*ABSCOR T:THE ACTUAL VALUE IS 17.95 AU, WHICH IS SLIGHTLY LESS +",6670,"T:THAN THAT OF URANUS.  HOWEVER, HALLEY'S COMET TRAVELS AROUND A +",6680,"T:HIGHLY ELLIPTICAL ORBIT WITH A PERIHELION DISTANCE OF A +",6690,"T:FRACTION OF AN AU.",6700,"T:HOW FAR AWAY FROM THE SUN CAN IT REACH +",6710,"*NOEX A:#D",6720,"TB:THERE IS NO EXCUSE, LAY ON ME A NUMBER +",6730,"JB:*NOEX",6740,"J(D<35):*BADDI",6750,"T(D<=35.9):VERY GOOD $NAME+!",6760,"J(D<=35.9):*GOODI",6770,"*BADDI T:NO WAY, THE MAXIMUM DISTANCE IS 35.9 AU.  ACTUALLY, IT +"
6780,"T:WILL BE SLIGHTLY LESS THAN THIS.",6790,"*GOODI T:DOES IT REACH TO PLUTO'S ORBIT +",6800,"A:",6810,"T:WELL, IT DEPENDS ON THE RELATIVE ORIENTATIONS OF THE ORBITS.  +",6820,"T:PLUTO'S ORBIT IS SUFFICIENTLY ELLIPTICAL SO THAT AT TIMES IT IS +",6830,"T:WITHIN NEPTUNE'S ORBIT.  HALLEY'S COMET DEFINATELY GOES OUT +",6840,"T:FURTHER THAN NEPTUNE, BUT IT DOESN'T QUITE REACH AS FAR AS +",6850,"T:PLUTO DOES AT PLUTO'S MAXIMUM DISTANCE.",6860,"T:",6870,"J(F=0):*ENDT"
6880,"T:AS A LAST PROBLEM, ESTIMATE THE SHORTEST PERIOD FOR A COMET +",6890,"T:WHICH REACHES OUT TO PLUTO'S ORBIT.  ASSUME THE PERIHELION +",6900,"T:DISTANCE IS VERY SMALL COMPARED TO 1 AU.",6910,"T:WELL, WHAT DO YOU GET +",6920,"*TRYPL A:#S",6930,"TB:YOU CAN AT LEAST TRY!  SINCE PLUTO ORBITS ABOUT 40 AU FROM THE +",6940,"TB:SUN, USE 20 AU AS A SEMIMAJOR AXIS.  OK +",6950,"JB:*TRYPL",6960,"C:X=90-S",6970,"C(X<0):X=-X",6980,"T(X<5):QUITE GOOD $NAME+!  +",6990,"T(X>=5):WELL, +"
7000,"T:ANY COMET WITH A PERIOD OF OVER ABOUT 90 YEARS COMES FROM THE +",7010,"T:TRANS-PLUTO REGION (ASSUMING A SMALL PERIHELION DISTANCE)!",7020,"T:",7030,"*ENDT T:YOU HAVE DONE WELL $NAME+.  I HOPE YOU HAVE LEARNED +",7040,"T:SOMETHING ABOUT KEPLER'S THIRD LAW.  SINCE YOU NOW KNOW ABOUT +",7050,"T:IT AND HOW TO USE IT, YOU MAY NOW TRY SOME VALUES OF YOUR OWN.  +",7060,"T:THE COMPUTER WILL DO ALL THE GRUNGY ARITHMETIC!",7070,"T:",7080,"R:",7090,"R:----------- A MINIPROGRAM TO SOLVE KEPLER'S THIRD LAW -----------"
7100,"R:",7110,"*PROGK T:",7120,"T:      ********** PROGRAM KEPLER **********",7130,"T:",7140,"T:WELCOME $NAME+!  WOULD YOU LIKE INSTRUCTIONS +",7150,"A:",7160,".M:[Y],[YE,PLS,PLEAS,CERT,RIGHT,OF COURS",7170,"Y:",7180,"Y:WHEN THE COMPUTER PRINTS 'NEW ORBIT ?' PLEASE ENTER A PERIOD OR +",7190,"Y:A SEMIMAJOR AXIS AS:",7200,"Y:",7210,"Y:      PERIOD = 37.9       OR        P = 42",7220,"Y:      SEMIMAJOR = 19      OR        S = 2.7"
7230,"Y:",7240,"Y:AFTER THE ENTRY OF A PERIOD THE COMPUTER WILL ADDITIONALLY +",7250,"Y:REQUEST A PERIHELION DISTANCE AND THEN PRINT THE INFORMATION +",7260,"Y:ABOUT THE ORBIT.  (ALL IN AU OR YEARS PLEASE!)",7270,"Y:AN ENTRY OF 'END' WILL EXIT THE PROGRAM.",7280,"R:",7290,"*NEXOR T:",7300,"*NEWOR T:NEW ORBIT +",7310,"A:#S",7320,".M:[END],[E]",7330,"JY:*ENDP",7340,"TB:I REALLY DO NEED A NUMBER!",7350,"JB:*NEWOR"
7360,"T(S<0):NO NEGATIVE VALUES PLEASE.",7370,"J(S<0):*NEWOR",7380,".M:[P],[PERIOD",7390,"JY:*PERIODCAL",7400,".M:[S],[SEMI",7410,"N:I DON'T RECOGNIZE THAT!",7420,"JN:*NEWOR",7430,"C:P=S^1.5",7440,"C:X=100*P",7450,"C(P<5):X=10*X",7460,".I:X",7470,"C(P<5):P=X/1000",7480,"C(P>=5):P=X/100"
7490,"T:AN ORBIT WITH A SEMIMAJOR AXIS OF #S+AU HAS A PERIOD OF #P+YEARS.",7500,"J:*NEXOR",7510,"*PERIODCAL T:WHAT PERIHELION DISTANCE +",7520,"A:#H",7530,"T(H<0):COME NOW, NO NEGATIVE DISTANCES!",7540,"J(H<0):*PERIODCAL",7550,"TB:I WILL ASSUME A CIRCULAR ORBIT!",7560,"CB:H=0",7570,"C:A=S^(2/3)",7580,"C:X=100*A",7590,"C(A<5):X=10*X",7600,".I:X",7610,"C(A<5):A=X/1000"
7620,"C(A>=5):A=X/100",7630,"T(H>A):YOUR PERIHELION DISTANCE IS BIGGER THAN THE SEMIMAJOR +",7640,"T(H>A):AXIS.  I WILL ASSUME A CIRCULAR ORBIT.",7650,"C(H>A):H=A",7660,"CB:H=A",7670,"C:D=2*A-H",7680,"T:AN ORBIT WITH A PERIOD OF #S+YEARS HAS A SEMIMAJOR AXIS OF +",7690,"T:#A+AU.  WITH A PERIHELION DISTANCE OF #H+AU IT REACHES A +",7700,"T:DISTANCE OF #D+AU FROM THE SUN.  THIS IS +",7710,"T(D<.387):INSIDE MERCURY'S ORBIT!",7720,"J(D<.387):*NEXOR",7730,"T(D<.723):BETWEEN MERCURY AND VENUS!",7740,"J(D<.723):*NEXOR"
7750,"T(D<1):STILL INSIDE THE EARTH'S ORBIT BUT OUTSIDE VENUS'.",7760,"J(D<1):*NEXOR",7770,"T(D<1.524):BETWEEN EARTH AND MARS!",7780,"J(D<1.524):*NEXOR",7790,"T(D<5.2):OUT IN THE ASTEROID BELT, BETWEEN MARS AND JUPITER!",7800,"J(D<5.2):*NEXOR",7810,"T(D<9.54):BEYOND GIANT JUPITER BUT NOT QUITE TO SATURN.",7820,"J(D<9.54):*NEXOR",7830,"T(D<19.18):BETWEEN SATURN AND URANUS!",7840,"J(D<19.18):*NEXOR",7850,"T(D<30.06):WAY OUT BETWEEN URANUS AND NEPTUNE!",7860,"J(D<30.06):*NEXOR"
7870,"T(D<39.4):ALMOST OUT TO PLUTO, BEYOND NEPTUNE!",7880,"J(D<39.4):*NEXOR",7890,"T(D<100):WAY OUT BEYOND EVEN PLUTO!",7900,"J(D<100):*NEXOR",7910,"T:REALLY GETTING WAY OUT THERE BEYOND THE FARTHEST REACHES OF +",7920,"T:EVEN COLD PLUTO!",7930,"J:*NEXOR",7940,"R:",7950,"R:------------------ END OF THE MINIPROGRAM -----------------------",7960,"R:",7970,"*ENDP T:",7980,"T:SO LONG $NAME+, ITS GOOD TO HAVE BEEN ABLE TO ASSIST YOU!",7990,"E:"
