REM PROGRAM D9_ACOR
REM THIS PROGRAM IS DESIGNED TO ILLUSTRATE THE CORIOLIS FORCE
REM BY SHOWING BOTH INERTIAL AND ROTATING FRAMES OF REFERENCE
DIM XTR(500), YTR(500), RTR(500), THTR(500)
NS = 30
DIM RS(NS), XS(NS), YS(NS), THS(NS)
DIM XSOLD(NS), YSOLD(NS)
SCREEN 12
LINE (0, 0)-(640, 10), 10, BF
LINE (0, 0)-(10, 480), 10, BF
LINE (630, 0)-(640, 480), 10, BF
LINE (0, 470)-(640, 480), 10, BF
COLOR 13: LOCATE 3, 27: PRINT "VIEWING THE CORIOLIS FORCE": SLEEP 2
COLOR 11: LOCATE 6, 17: PRINT "OBJECTS THAT MOVE STRAIGHT IN AN ABSOLUTE SENSE": SLEEP 2
LOCATE 7, 20: PRINT "CURVE WITH RESPECT TO THE ROTATING EARTH": SLEEP 2
COLOR 10: LOCATE 10, 31: PRINT "FRAMES OF REFERENCE": SLEEP 2
COLOR 9: LOCATE 12, 5: PRINT "VIEWPOINT FROM SPACE (NONROTATING OR INERTIAL)": SLEEP 2
LOCATE 13, 8: PRINT "1. THE EARTH IS SEEN TO ROTATE": SLEEP 2
LOCATE 14, 8: PRINT "2. BALLS ARE SEEN TO MOVE STRAIGHT": SLEEP 2
LOCATE 15, 8: PRINT "3. BALLS LEAVE CURVED TRAILS ON THE EARTH": SLEEP 2
COLOR 6: LOCATE 17, 5: PRINT "VIEWPOINT FROM EARTH (ROTATING)": SLEEP 2
LOCATE 18, 8: PRINT "1. THE UNIVERSE APPEARS TO SPIN": SLEEP 2
LOCATE 19, 8: PRINT "2. MOVING BALLS APPEAR TO CURVE": SLEEP 2
LOCATE 20, 8: PRINT "3. BALLS LEAVE CURVED TRAILS ON THE EARTH": SLEEP 2
COLOR 14: LOCATE 23, 5: PRINT "BOTH VIEWPOINTS WILL BE SHOWN": SLEEP 2
LOCATE 24, 8: PRINT "FIRST,  THE VIEWPOINT FROM SPACE": SLEEP 2
LOCATE 25, 8: PRINT "SECOND, THE VIEWPOINT FROM EARTH": SLEEP 2
COLOR 15
DO WHILE INKEY$ = ""
LOCATE 27, 26: PRINT "HIT ANY KEY TO START PROGRAM": SLEEP 1
TT = TIMER + .25
DO UNTIL TIMER > TT
LOCATE 27, 26: PRINT "                                    "
LOOP
LOOP
CLS : COLOR 15

WINDOW (-320, -240)-(320, 240)
NC = 12
PI = 3.141592: DRC = PI / 180
RC = 4: RE = 200: RU = 500
C1 = .25: REM FLATTENING OF CORIOSEL
DELTH = PI / 6
DT = 1 / 3600
DTH = PI * DT
VB = 5 * RE * DT: REM IN ROTATING FRAME START SLOWLY
DYB = 10 * RE * DT * C1
RCIN = VB / DTH: THB = PI
RPOS = RE
DIM A(210)
CIRCLE (0, 0), RC, NC
PAINT (0, 0), NC
GET (-1.5 * RC, -1.5 * RC)-(1.5 * RC, 1.5 * RC), A
CLS
XB = 0: YBI = -RE * C1
YB = YBI
XBOLD = XB: YBOLD = YB
PUT (XB, YB), A, XOR
CLS
FOR ROT = 1 TO 2
CIRCLE (0, -RE * C1 / 2), RU, 1, , , C1
PAINT (0, 0), 1
CIRCLE (0, 0), RE + 1, 6, PI, 2 * PI, C1
CIRCLE (0, -RE * C1 / 2), RE + 1, 6, PI, 2 * PI, C1
LINE (-RE - 2, -RE * C1 / 2)-(-RE - 2, 0), 6
LINE (RE + 1, -RE * C1 / 2)-(RE + 1, 0), 6
PAINT (0, -RE * 5 * C1 / 4), 6
CIRCLE (0, 0), RE + 1, 2, , , C1
PAINT (0, 0), 2
RANDOMIZE TIMER
FOR I = 1 TO NS: REM POSITION STARS
RS(I) = RE * 1.5 + RND * (RU - RE * 1.5)
THS(I) = RND * 2 * PI
NEXT I

IF ROT = 1 THEN
   LINE (0, 1.1 * RE * C1)-(0, 2.1 * RE * C1), 12
   LINE (0, -1.6 * RE * C1)-(0, -2.6 * RE * C1), 12
   LOCATE 3, 30: PRINT "VIEWPOINT FROM SPACE"
   LOCATE 8, 11: PRINT "BALLS MOVE IN STRAIGHT LINE  --  PARALLEL TO THE RED LINES"
ELSE
   LOCATE 3, 30: PRINT "VIEWPOINT FROM EARTH"
   LOCATE 6, 29: PRINT "IN NORTHERN HEMISPHERE"
   LOCATE 7, 9: PRINT "BALLS CURVE RIGHT (CLOCKWISE)  --  UNIVERSE ROTATES CLOCKWISE"
   FOR I = 1 TO 6
   THTI = I * DELTH
   X(I) = RE * COS(I * DELTH)
   Y(I) = RE * SIN(I * DELTH) * C1
   LINE (-X(I), -Y(I))-(X(I), Y(I))
   SS = -SGN(Y(I))
   LINE (X(I) * SS, -ABS(Y(I)) - 1)-(X(I) * SS, -ABS(Y(I)) - RE * C1 / 2)
   NEXT I
END IF
LOCATE 26, 5: PRINT "BALLS CURVE WITH RESPECT TO EARTH  --"

SELECT CASE ROT
REM ****** ROUTINE FOR INERTIAL FRAME OF REFERENCE
CASE 1
FOR I = 1 TO NS: REM DRAW STARS
XS(I) = RS(I) * COS(THS(I))
YS(I) = (RS(I) * SIN(THS(I)) - RE / 2) * C1
CIRCLE (XS(I), YS(I)), 1
PAINT (XS(I), YS(I))
NEXT I

FOR TH = 0 TO 2 * PI STEP DTH
IF CTR = 4 AND CTR2 = 0 THEN
   LOCATE 26, 44: PRINT "AND LEAVE CURVED TRAILS ON EARTH"
   CTR2 = 1
END IF
IF CTR = 5 THEN 500
K = K + 1
IF CTR = 4 AND (INT(K / 10) = K / 10) THEN
   NTR = NTR + 1
   RTR(NTR) = ABS((YBOLD) / C1 - 2 * RB)
   IF YBOLD > 0 THEN THTR(NTR) = PI / 2 ELSE THTR(NTR) = 3 * PI / 2
   END IF
FOR I = 1 TO 6
LINE (-XOLD(I), -YOLD(I))-(XOLD(I), YOLD(I)), 2
SS = -SGN(YOLD(I))
LINE (XOLD(I) * SS, -ABS(YOLD(I)) - 1)-(XOLD(I) * SS, -ABS(YOLD(I)) - RE * C1 / 2), 6
NEXT I
IF YBOLD < RE * C1 THEN PUT (XBOLD, YBOLD), A, XOR

FOR I = 1 TO 6
XOLD(I) = X(I)
YOLD(I) = Y(I)
LINE (-X(I), -Y(I))-(X(I), Y(I))
THTI = I * DELTH
X(I) = RE * COS(TH + I * DELTH)
Y(I) = RE * SIN(TH + I * DELTH) * C1
SS = -SGN(Y(I))
LINE (X(I) * SS, -ABS(Y(I)) - 1)-(X(I) * SS, -ABS(Y(I)) - RE * C1 / 2)
NEXT I
IF CTR > 3 THEN
   FOR JJ = 1 TO NTR
   FOR LL = 27.5 * NTR TO 2000 STEP NTR: NEXT LL: REM THIS KEEPS SPINNING CONSTANT
   CIRCLE (XTR(JJ), YTR(JJ)), 1, 2: REM ERASE OLD POSITIONS
   THTR(JJ) = THTR(JJ) + DTH
   XTR(JJ) = RTR(JJ) * COS(THTR(JJ))
   YTR(JJ) = RTR(JJ) * SIN(THTR(JJ)) * C1
   CIRCLE (XTR(JJ), YTR(JJ)), 1, 12
   NEXT JJ
ELSE
   FOR QQ = 1 TO 2000: NEXT QQ
END IF
REM BALL MOVING ROUTINE
IF YB > RE * C1 THEN
YB = YBI
CTR = CTR + 1
PUT (XB, YB), A, XOR
END IF
PUT (XB, YB), A, XOR
XB = 0: YB = YB + DYB
XBOLD = XB: YBOLD = YB
NEXT TH
500 REM LEAVING THE INERTIAL REFERENCE FRAME
DO WHILE INKEY$ = ""
COLOR 12: LOCATE 28, 25: PRINT "HIT ANY KEY FOR VIEW FROM EARTH": SLEEP 1
TT = TIMER + .25
DO UNTIL TIMER > TT
LOCATE 28, 25: PRINT "                               "
LOOP
LOOP
CLS : COLOR 15: GOTO 1000
CASE 2
REM ****** ROUTINE FOR ROTATING FRAME OF REFERENCE
REM PARTICLE PATH IS AN INERTIA CIRCLE WITH R = V/F:F = 2*DTH
CTR = 0: CTR2 = 0
RPOS = RE
RANDOMIZE TIMER
FOR I = 1 TO NS
RS(I) = RE * 1.5 + RND * (RU - RE * 1.5)
THS(I) = RND * 2 * PI
NEXT I

FOR TH = O TO 2 * PI STEP DTH
IF CTR = 1 AND CTR2 = 0 THEN
   LOCATE 26, 44: PRINT "AND LEAVE CURVED TRAILS ON EARTH"
   LOCATE 8, 2: COLOR 10: PRINT "EACH BALL MOVES FASTER THAN THE PRIOR -- AND HAS LESS TIME TO CURVE": COLOR 15
   CTR2 = 1
END IF
IF CTR = 5 THEN 1000
REM STAR ERASE
FOR I = 1 TO NS
CIRCLE (XSOLD(I), YSOLD(I)), 1, 1
PAINT (XSOLD(I), YSOLD(I)), 1
NEXT I
REM BALL ERASE IF STILL ON EARTH NEED EQUATION FOR RPOS
IF RPOS < RE THEN
   PUT (XBOLD, YBOLD), A, XOR
   CIRCLE (XBOLD, YBOLD - 2 * RB), 1, 12: REM LEAVE TRACE
   END IF
REM BALL DRAW
IF RPOS > RE THEN
   YB = YBI: XB = 0: THB = PI: REM INITIAL POSITION
   RPOS = RE
   CTR = CTR + 1
   VB = VB * 2: REM SPEED UP EACH SUCCESSIVE BALL
   RCIN = VB / DTH
   PUT (XB, YB), A, XOR
END IF
XBOLD = XB: YBOLD = YB
PUT (XB, YB), A, XOR
THB = THB - DTH
XB = RCIN * (1 + COS(THB))
YB = (RCIN * SIN(THB) - RE) * C1
RPOS = SQR(XB ^ 2 + (YB / C1) ^ 2)

REM STAR DRAW
FOR I = 1 TO NS
THS(I) = THS(I) - DTH
XSOLD(I) = XS(I): YSOLD(I) = YS(I)
XS(I) = RS(I) * COS(THS(I))
YS(I) = (RS(I) * SIN(THS(I)) - RE / 2) * C1
CIRCLE (XS(I), YS(I)), 1
PAINT (XS(I), YS(I))
NEXT I
NEXT TH
END SELECT
1000 NEXT ROT