AMS-81

AMSAT

Products: AMS-81

Developer(s): Courtney Duncan (N5BF)

Date: 1983

Type: Program

Platform(s): TS 1000

AMS-81 is a satellite pass scheduling and real-time tracking utility designed for amateur radio operators, computing orbital positions from Keplerian elements. The program propagates orbits by iteratively solving Kepler’s equation using an eccentric anomaly refinement loop (lines 5100–5150), then transforms results through a rotation matrix built from inclination, RAAN, and argument of perigee (lines 3740–3790). Ground station coordinates are converted to Earth-centered Cartesian coordinates accounting for the oblate Earth flattening factor (lines 3020–3110). A rich set of symbolic constant aliases—including U, G, TEN, HEX, INF, and others—compresses frequently used numeric literals throughout the code. SLOW/FAST mode switching and a configurable step-size variable PHI allow the tracking loop to balance computational accuracy against display refresh speed.

Program Analysis

Program Structure

The program is organized around a main menu at lines 10–120 that dispatches to four functional areas based on a single keypress. The four activities are scheduling (option 1, lines 130–960), real-time tracking (option 2, lines 970–2290), Keplerian file editing (option 3, lines 2300–2810), and QTH (ground station) configuration (option 4, lines 2820–3120). A save/resave path exists at lines 3130–3230. The remaining lines (roughly 3240–5650) form a library of subroutines shared across all four activities.

Symbolic Constant Aliases

To save memory and reduce token overhead, frequently used numeric values are pre-assigned to short variable names at program start or within initialization routines. Key aliases encountered throughout the listing include:

Variable	Approximate Value / Meaning
`U`	1
`G`	0
`U2`	2
`U3`	3
`U4`	4
`TEN`	10
`HEX`	16
`INF`	A large sentinel value (used for orbit counter initialization)
`P0`	π/180 (degrees-to-radians factor)
`P2`	2π
`HA`	0.5
`HUN`	100
`THO`	1000 (also used as PAUSE duration)
`DYR`	Days per year (365.25 or similar)
`R0`	Earth’s equatorial radius
`G0`	Gravitational parameter (GM)
`G1`	Earth’s rotation rate (radians per day)
`CL`	Speed of light (used for Doppler calculation)
`AF`	Step-size scaling factor
`IN`	Step increment base

Orbital Mechanics Engine

Orbit propagation begins in subroutine KSC (line 3460), which sets up mean motion N, semi-major axis A, and the J2 perturbation corrections for RAAN drift (O) and argument-of-perigee precession (W) using a K2 coefficient at line 3650. The rotation matrix C() (lines 3740–3790) transforms perifocal coordinates to Earth-centered inertial (ECI) coordinates.

Kepler’s equation is solved iteratively in lines 5100–5150:

An initial estimate of eccentric anomaly E is formed from the mean anomaly M plus first- and second-order series terms (line 5100).
The residual M5 = E - e·sin(E) - M is computed (line 5110).
Newton–Raphson correction E = E - M5 / (1 - e·cos(E)) is applied (lines 5130–5140) until convergence to within 1×10⁻⁶.

ECI position is then rotated into Earth-fixed coordinates using the Greenwich sidereal angle G7 (lines 5220–5250), and the ground-station vector (computed at lines 3020–3110 with oblate-Earth correction) is subtracted to yield the topocentric range vector.

Ground Station Geometry

Lines 3020–3110 convert the observer’s geodetic latitude L9, west longitude W9, and altitude H9 into Earth-centered Cartesian coordinates X9, Y9, Z9. The geodetic-to-geocentric latitude conversion at line 3080 uses the standard flattening formula tan(φ_c) = (1-f)² · tan(φ_g), where F is the flattening constant. Elevation E9 and azimuth A9 are derived in the CO4 / AZ subroutine block (lines 5270–5390).

Scheduling Logic

The scheduler (lines 130–960) uses subroutine SCH (line 5550) to bracket AOS (Acquisition of Signal) and LOS (Loss of Signal) by bisecting the sign of the dot product QS between the satellite position and the ground station vector. The step size PHI is halved whenever a sign change is detected, converging on the horizon crossing. The array A() stores AOS time, AOS range, LOS time, and LOS range for each pass, and the display loop (lines 470–960) formats these into a columnar schedule with day dividers injected by subroutine DD (line 1670).

Real-Time Tracking Display

The tracking activity (lines 970–2290) calls subroutine LP2 in a tight loop, displaying UTC, azimuth, elevation, range, phase angle (for eccentric orbits), and Doppler shift. The Doppler estimate at lines 1580–1600 approximates the radial velocity from consecutive range measurements R5 divided by the elapsed time, scaled by the carrier frequency F(I) and speed of light CL. SLOW/FAST mode is managed by the FS flag: pressing F sets FS=U (fast), pressing D sets FS=G (slow). Page-full pauses at line 2040 prompt the operator to continue or exit.

Date/Time Handling

Two date formats are accepted by the DAY subroutine (lines 4050–4390): a compact decimal epoch like 83 105.46677538 (two-digit year, day-of-year with fractional day) and a calendar format like 15APR83 111209 (DDMMMYY HHMMSS). A 13-element month table M$() stores three-letter abbreviations alongside cumulative day-of-year offsets. Leap-year detection is handled by testing divisibility by 4 and checking whether the day number is at or past day 59 (lines 4350, 4450). The inverse DAO routine (lines 4400–4630) converts an internal day number back to both display formats simultaneously.

Keplerian File Editor

Option 3 (lines 2300–2810) presents each Keplerian element in turn for in-place editing. Elements are stored in parallel arrays: I(I) inclination, O(I) RAAN, E(I) eccentricity, W(I) argument of perigee, M(I) mean anomaly at epoch, N(U,I) mean motion (or semi-major axis if >100), and N(U2,I) mean motion derivative. The satellite name S$(I), catalog ID I$(I), and downlink frequency F(I) are also editable. Any modification sets the dirty flag SV=U, enabling the “NEED TO RESAVE” option 5 on the main menu.

Keypress and Flow-Control Idioms

The program makes heavy use of a polling keypress subroutine KSC (line 3270) that checks INKEY$ without blocking. A PAUSE 0 / INKEY$ construct is used at other points for true blocking waits. The GO variable serves as a global flow-control token: GO=G (0) signals an abort-to-main-menu condition tested after nearly every subroutine call with the pattern IF GO=G THEN GOTO G (branching to line 0, which does not exist—a standard technique to fall through to the top of the program). GO=U9 (9) signals a page-pause condition handled within KSC.

Notable Techniques

The orbital visibility pre-check at line 3920 uses the maximum elevation formula to quickly reject satellite/QTH combinations where passes are geometrically impossible, printing “PASSES CANNOT OCCUR” and aborting.
The adaptive step size in PHI (lines 1360–1390 and 5560–5650) scales the propagation interval by the ratio of the current angular change to a target change angle CA, allowing large steps far from events and fine steps near AOS/LOS and maximum elevation.
Line 3800 indexes a Greenwich sidereal time table G() by year to initialize G2, avoiding recomputation of the epoch sidereal angle from scratch each call.
The VAL E$(J, U5 TO TEN) idiom at line 2620 extracts element values from a string array used as a formatted data file, acting as a simple flat-file database.
SLOW is unconditionally re-entered at line 3940 before error messages to ensure readable display timing regardless of the current FS state.

Potential Anomalies

At line 3480, if N(U,I) is zero it is set to HUN (100) to prevent division by zero, then interpreted as a semi-major axis rather than mean motion—this dual-mode interpretation (lines 3490–3540) may produce unexpected results if an element set is partially initialized.
The Doppler computation (line 1580) divides by (D-T6), which is the elapsed time since the last update in fractional days. When the tracking loop runs very fast, D-T6 can be extremely small, potentially producing noisy Doppler readings; the IF T6<>D guard prevents a divide-by-zero but does not smooth the result.
The azimuth subroutine at line 5320 special-cases X8=0 (satellite exactly north or south) by assigning 90° or 270°, but the IF X8<>G test means any non-zero X8, however small, goes to the ATN branch—correct behavior, but the zero case is intentionally narrowly defined.

Content

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AMS-81

A Timex/Sinclair computer port of W3IWI’s BASIC TRACK program for earth satellite tracking.

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Source Code
LET GO=U
LET FS=G
CLS 
SLOW 
PRINT H$
PRINT "    VERSION N5BF 1.4 01APR83"
PRINT AT U8,U7;"%<%<%<% %A%C%T%I%V%I%T%I%E%S% %>%>%>";AT TEN,U7;;"1 = SCHEDULE";TAB U7;"2 = TRACK";TAB U7;"3 = KEPLERIAN FILE";TAB U7;"4 = QTH INFO";AT HEX,TEN;"@@SELECT 1-4@@"
IF SV=1 THEN PRINT AT U14,U7;"5 = NEED TO RESAVE";AT HEX,U20;"5"
LET A$=INKEY$
IF A$="" THEN GOTO 90
PRINT AT HEX,U22;A$
IF A$<>"1" THEN GOTO 970
GOSUB 4890
IF GO=G THEN GOTO G
GOSUB HD1
GOSUB INK
GOSUB CO3
LET LOS=U
GOSUB SCH
IF GO=G THEN GOTO G
LET A(U)=D
LET A(U2)=R5
LET LOS=-U
LET QS=U
GOSUB SCH
IF GO=G THEN GOTO G
LET A(U3)=D
LET A(U4)=R5
LET PHI=G
IF E(I)<U01 AND N>TEN THEN GOTO 430
LET D=D+(INT Q-Q+HA)/N
LET T=G
GOSUB CO1
IF A(U)>D OR A(U3)<D OR E(I)<U01 THEN GOTO 370
LET E9=R0*(COS (E9*P0)*ASN (R5/R)+ACS (R0/R))
GOTO LP1
LET D=A(U)
IF A(U4)>A(U2) THEN LET D=A(U3)
LET T=U
GOSUB CO1
LET E9=U2*R0*ACS (R0/R)
GOTO LP1
LET D=(A(U)+A(U3))/U2
GOSUB CO1
LET T=U2
GOTO LP1
CLS 
GOSUB DAO
PRINT AT G,G;H$;"ACCESS SKED FROM: ";D$;"  >>";C$;" VIA ";S$(I);"<<","% %D%A%Y% % % %A%O%S% % %L%O%S% % % %M%A%X% %D%X%/%E%L% % % %A%Z"
LET LP=U4
RETURN 
IF GO=G THEN GOTO G
LET A(U5)=D
LET D=A(U)
GOSUB DAO
LET D$=D$( TO U5)+D$(U8 TO U12)+N$
LET J=U12
LET D=A(U3)
GOSUB TIM
LET D$(HEX TO 17)=" "
LET D=A(U5)
LET J=U18
GOSUB TIM
LET D$=D$( TO U21)+" "
IF T=U2 THEN GOTO 720
LET D$=D$+STR$ INT E9+"  "
IF LEN D$>=29 THEN GOTO 700
LET D$=D$( TO U22)+D$(U22 TO )
GOTO 670
IF T=U THEN LET D$(U28)="*"
GOTO 740
GOSUB LZ2
LET D$=D$( TO 24)+" %E%L  "
GOSUB LZ3
PRINT AT LP,G;D$( TO U32)
LET LP=LP+U
IF A(U3)-A(U)<U THEN GOTO 840
LET D=A(U3)
LET D$=N$+"  "
LET J=U9
GOSUB DAO
PRINT AT LP,U4;"(LOS DATE = ";D$( TO U7);")"
LET LP=LP+U1
IF LP<U20 THEN GOTO 930
LET GO=U9
PRINT "## RETURN = 0, CONT = 1 ##"
GOSUB KSC
IF F$="Z" AND PRIN=U THEN COPY 
IF GO=U9 THEN GOTO 870
GOSUB CLB
IF GO=G THEN GOTO G
GOSUB HD1
LET D=A(U3)
GOSUB INK
LET QS=-U
GOTO 180
IF A$<>"2" THEN GOTO 2300
LET CT=1.2*CA
LET CB=.8*CA
GOSUB 4890
LET LOS=U
IF GO=G THEN GOTO G
GOSUB HD2
GOSUB INK
GOSUB CO1
IF GO=G THEN GOTO G
IF E9>G THEN GOTO 1140
LET QS=-U
LET LOS=U
GOSUB SCH
LET PHI=G
GOSUB CO1
IF GO=G THEN GOTO G
LET FS=G
LET F8=G
LET T6=D
LET R6=R5
LET PHI=CA*R*AF
GOSUB LP2
IF GO=G THEN GOTO G
IF LP=U4 THEN GOSUB LP2
IF LOS=-U THEN GOTO 1080
GOSUB INK
LET D2=D
LET E8=E9
LET A8=A9
LET PH2=PHI
FOR L=U TO U5
GOSUB CO1
IF GO=G THEN GOTO G
GOSUB DD
IF DAZ>CT OR DEL>CT THEN GOTO 1340
IF (DAZ>CB OR DEL>CB) AND INT Q=INT Q1 THEN GOTO 1540
LET D1=DAZ
IF DEL>DAZ THEN LET D1=DEL
LET PHI=CA*PHI/D1
LET D=D2
IF INT Q=INT Q1 AND PHI>1E-5 THEN NEXT L
LET PHI=PH2
LET ER=G
GOSUB CO1
IF GO=G THEN GOTO G
GOSUB DD
IF DAZ>CT OR DEL>CT THEN GOTO 1470
IF DAZ>CB OR DEL>CB THEN GOTO 1530
IF ER=G THEN GOTO LSC
LET ER=U
LET D1=DAZ
IF DEL>DAZ THEN LET D1=DEL
LET D1=SGN (D1-CA)
LET PHI=-HA*ABS PHI*D1
GOTO LSC
LET PHI=PH2
IF E9>HA THEN GOTO 1580
LET LOS=-U
GOSUB SCH
IF GO=G THEN GOTO G
IF T6<>D THEN LET F8=F(I)*(R6-R5)/(D-T6)/CL
LET R6=R5
LET T6=D
GOTO 1190
LET DAZ=ABS (A9-A8)
IF DAZ>180 THEN LET DAZ=360-DAZ
LET DAZ=ABS (DAZ*(COS (E9*P0)))
LET DEL=ABS (E9-E8)
RETURN 
IF INT D=D0 THEN GOTO 1760
LET D$=N$
LET J=U9
GOSUB DAO
IF GO=U2 OR GO=U7 THEN GOSUB SS
PRINT AT LP,G;"       ----";D$( TO U7);"----          "
LET D0=INT D
LET LP=LP+U
IF LP>U20 AND GO<>U2 AND GO<>U7 THEN GOTO HD2
LET D$="       "
LET J=U
GOSUB TIM
IF GO=G THEN RETURN 
GOSUB LZ3
GOSUB LZ2
LET D$=D$( TO U4)+":"+D$(U5 TO )+STR$ INT R5+" "
IF LEN D$>=U21 THEN GOTO 1860
LET D$=D$( TO U15)+D$(U15 TO )
GOTO 1830
IF E(I)>=U01 THEN LET D$=D$+STR$ INT (M/P2*256)+" "
IF E(I)<U01 THEN LET D$=D$+"--- "
IF LEN D$>=U25 THEN GOTO 1910
LET D$=D$( TO U21)+D$(U21 TO )
GOTO 1880
LET A$=STR$ (INT (F8/HUN+HA)/TEN)
IF INT VAL A$=VAL A$ THEN LET A$=A$+".0"
IF F8=G THEN LET A$=STR$ F(I)
LET D$=D$+A$+" "
IF LEN D$>=U32 THEN GOTO 1980
LET D$=D$( TO U25)+D$(U25 TO )
GOTO 1950
IF GO=U2 OR GO=U7 THEN GOSUB SS
IF GO=G THEN RETURN 
PRINT AT LP,G;D$( TO U32)
LET LP=LP+U
IF LP<U21 OR GO=U2 OR GO=U7 THEN RETURN 
IF GO=U3 THEN GOTO HD2
LET GO=U9
PRINT J$
GOSUB KSC
IF GO=U9 THEN GOTO 2060
GOSUB CLB
IF GO=G OR GO=U2 OR GO=U7 THEN RETURN 
CLS 
LET D0=INT D
GOSUB DAO
PRINT AT G,G;H$;"  TRACKING FROM ";D$,"  >>";C$;" VIA ";S$(I);"<<","% % %U%T%C% % % % %A%Z% %E%L% %R%A%N%G%E% %P%H%S% %D%O%P%P%L%E%R"
LET LP=U4
LET GO=U
RETURN 
IF GO=U2 AND ST=U9 THEN GOTO 2240
PRINT AT U21,G;J$
LET GO=U9
GOSUB KSC
IF GO=U9 THEN GOTO 2200
GOSUB CLB
IF GO<>U2 AND GO<>U7 AND GO<>G THEN LET GO=U3
SCROLL 
LET LP=U20
PRINT AT U21,U31;
RETURN 
PRINT AT U21,G;N$;N$;" "
RETURN 
IF A$<>"3" THEN GOTO 2820
GOSUB SAT
IF GO=G THEN GOTO G
CLS 
PRINT H$;AT U2,G;"%N%A%M%E% ";AT U2,U7;S$(I)
PRINT AT U18,G;L$;K$
INPUT A$
IF A$="" THEN GOTO 2410
LET SV=U
LET S$(I)=A$
PRINT AT U2,U7;S$(I);N$
PRINT AT U3,G;"%I%D% % % ";AT U3,U7;I$(I)
INPUT A$
IF A$="" THEN GOTO 2470
LET SV=U
LET I$(I)=A$
PRINT AT U3,U7;I$(I);N$
LET D=T(I)
GOSUB DAO
IF GO=G THEN GOTO G
PRINT AT U4,G;"%E%P%O%C%H";AT U4,U7;D$
INPUT D$
IF D$="" THEN GOTO 2610
PRINT AT U4,U7;D$;X$
GOSUB DAY
IF ER=G THEN GOTO 2570
GOSUB 3250
GOTO 2500
LET T(I)=D
LET SV=U
GOSUB DAO
PRINT AT U4,U7;D$;N$
FOR J=U TO U8
LET A(J)=VAL E$(J,U5 TO TEN)
PRINT AT J+U4,G;E$(J, TO U4);"%   ";A(J);X$
INPUT A$
IF A$="" THEN GOTO 2690
LET A(J)=VAL A$
PRINT AT J+U4,U7;A(J);X$
LET SV=U
NEXT J
LET N(U2,I)=A(U7)
LET I(I)=A(U)
LET O(I)=A(U2)
LET E(I)=A(U3)
LET W(I)=A(U4)
LET M(I)=A(U5)
LET N(U,I)=A(U6)
LET F(I)=A(U8)
IF A$="" THEN GOTO G
PRINT AT U18,G;"##";K$;N$
INPUT A$
GOTO G
IF A$<>"4" THEN GOTO 3130
CLS 
PRINT H$,,"%C%A%L%L%   ";C$;AT U18,G;L$;K$
INPUT A$
IF A$="" THEN GOTO 2900
LET C$=A$
PRINT AT U2,U7;C$;N$
LET SV=U
FOR J=U9 TO 11
LET A(J-U8)=VAL E$(J,U6 TO U9)
PRINT AT J-U6,G;E$(J, TO U5);TAB U7;A(J-U8)
INPUT A$
IF A$="" THEN GOTO 2980
LET A(J-U8)=VAL A$
PRINT AT J-U6,U7;A(J-U8);N$
LET SV=U
NEXT J
LET L9=A(U)
LET W9=A(U2)
LET H9=A(U3)
LET L8=L9*P0
LET S9=SIN L8
LET C9=COS L8
LET S8=SIN (-W9*P0)
LET C8=COS (W9*P0)
LET R9=R0*(U-F/U2+F/U2*COS (U2*L8))+H9/THO
LET L8=ATN ((U-F)**U2*S9/C9)
LET Z9=R9*SIN L8
LET X9=R9*COS L8*C8
LET Y9=R9*COS L8*S8
GOTO 2780
IF A$<>"5" OR SV=G THEN GOTO G
CLS 
PRINT H$,TAB U2;"@@START RECORDER.....";K$
LET A$=INKEY$
IF A$="" THEN GOTO 3160
IF A$="0" THEN GOTO G
PRINT ,,TAB U3;" SAVE BEGINS IN 20 SECONDS"
PAUSE THO
LET SV=G
SAVE "AMS8%1"
GOTO G
CLS 
PRINT AT U6,G;D$;AT U7,G;"EPOCH INPUT ERROR. USE FORMAT:","83 105.46677538",,"   > OR <",,"15APR83 111209"
RETURN 
IF GO=U9 AND ST=U9 OR FS=G THEN SLOW 
LET F$=INKEY$
IF F$="" THEN GOTO 3410
PRINT AT U21,U31;F$
IF F$<>"0" THEN GOTO 3350
LET GO=G
LET ST=U9
RETURN 
IF CODE F$<38 AND CODE F$>27 THEN GOTO 3400
IF F$="F" THEN LET FS=U
IF F$="D" THEN LET FS=G
IF F$="T" THEN LET D0=INF
GOTO KSE
LET ST=VAL F$
IF GO<>U9 THEN GOTO KSE
LET GO=ST
LET ST=U9
IF FS=U AND GO<>U9 THEN FAST 
RETURN 
GOSUB KSC
IF GO=G OR K=K9 THEN RETURN 
IF N(U,I)=G THEN LET N(U,I)=HUN
IF N(U,I)>HUN THEN GOTO 3530
LET N0=N(U,I)
LET A0=(G0/N0/N0)**(U/U3)
GOTO 3550
LET A0=N(U,I)
LET N0=SQR (G0/N(U,I)**U3)
LET N=N0+U2*(D-T(I))*N(U2,I)
LET A=(G0/N/N)**(U/U3)
IF N<G OR A<R0 THEN GOTO 3930
IF E(I)>=0 AND E(I)<1 THEN GOTO 3610
PRINT "BAD ECCENTRICITY"
GOTO 3940
LET E2=U-E(I)**U2
LET E1=SQR E2
LET Q0=M(I)/360
LET AF=U/ABS (U-SQR ABS (COS (I(I)*P0)*COS (L9*P0))/N)/A/N/360
LET K2=9.95*(R0/A)**3.5/E2**U2
LET S1=SIN (I(I)*P0)
LET C1=COS (I(I)*P0)
LET O=O(I)-(D-T(I))*K2*C1
LET S0=SIN (O*P0)
LET C0=COS (O*P0)
LET W=W(I)+(D-T(I))*K2*(2.5*C1*C1-HA)
LET S2=SIN (W*P0)
LET C2=COS (W*P0)
LET C(U,U)=C2*C0-S2*S0*C1
LET C(U2,U)=C2*S0+S2*C0*C1
LET C(U3,U)=S2*S1
LET C(U,U2)=-S2*C0-C2*S0*C1
LET C(U2,U2)=-S2*S0+C2*C0*C1
LET C(U3,U2)=C2*S1
LET G2=G(INT (T(I)/DYR)+U3)
LET D1=D
LET D=INT (T(I)/DYR)+U81
LET D$=STR$ D+" 000."
GOSUB DAY
LET Y0=D
LET K9=K
LET D=D1
LET D1=P2/U4
IF L9<G THEN LET D1=D1*U3
LET J=I(I)*P0
IF J>PI/U2 THEN LET J=PI-J
IF ACS (R0*(U+E(I)*COS (D1-W*P0))/A/(U-E(I)**U2))+J>ABS L9*P0 THEN RETURN 
PRINT "##PASSES CANNOT OCCUR ";K$
SLOW 
LET GO=G
IF INKEY$="" THEN GOTO 3960
RETURN 
LET D2=D
LET D=D+PHI
LET Q1=Q
LET Q=Q0+(D-T(I))*(N0+N(U2,I)*(D-T(I)))
LET K=INT Q
LET M=(Q-K)*P2
RETURN 
GOSUB KSC
IF GO=G THEN RETURN 
LET ER=U
IF LEN D$<U7 THEN RETURN 
IF CODE D$(U3)>37 THEN GOTO 4220
FOR L=U TO LEN D$
IF L=U3 OR L=U7 THEN GOTO 4130
IF CODE D$(L)>U37 OR CODE D$(L)<U28 THEN RETURN 
NEXT L
IF D$(U7)<>"." AND D$(U7)<>" " THEN RETURN 
LET D=INT (VAL D$(U4 TO U6)+DYR*(VAL D$(U TO U2)-U81))
IF D$(U7)="." THEN LET D=D+VAL D$(U7 TO LEN D$)
IF LEN D$>=U13 THEN GOTO 4190
LET D$=D$+"000000"
IF D$(U7)<>"." THEN LET D=D+((VAL D$(U12 TO U13)/U60+VAL D$(TEN TO 11))/U60+VAL D$(U8 TO U9))/U24
LET ER=G
RETURN 
IF LEN D$<U8 THEN RETURN 
FOR L=U TO U12
IF D$(U3 TO U5)=M$(L,U TO U3) THEN GOTO 4270
NEXT L
RETURN 
LET D$(U3 TO U5)=M$(L,U4 TO U6)
FOR L=U TO LEN D$
IF L=U8 THEN GOTO 4310
IF CODE D$(L)>U37 OR CODE D$(L)<U28 THEN RETURN 
NEXT L
LET Y3=VAL D$(U6 TO U7)
IF Y3<TEN THEN RETURN 
LET F9=G
IF Y3/U4=INT (Y3/U4) AND VAL D$(U3 TO U5)>58 THEN LET F9=U
LET D=INT ((Y3-U81)*DYR)
LET D=D+VAL D$(U3 TO U5)+VAL D$(U TO U2)+F9
LET D$=D$(U2 TO LEN D$)
GOTO 4160
LET ER=G
LET Y3=U81+(INT D-U01)/DYR
LET D1=INT (DYR*(Y3-INT Y3))
LET Y3=INT Y3
LET F9=G
IF Y3/U4=INT (Y3/U4) AND D1>=59 THEN LET F9=U
LET D1=D1-F9
FOR L=U TO U12
IF D1>=VAL M$(L,U4 TO U6) THEN NEXT L
LET D$=M$(L-U,U TO U3)
IF F9=U AND D1=58 THEN LET D1=59
LET D1=D1+U-VAL M$(L-U,U4 TO U6)
LET D$=STR$ INT D1+D$+STR$ Y3
IF D1<TEN THEN LET D$="0"+D$
LET J=U9
LET D$=D$+"       "
LET D1=(D-INT D+5E-6)*24
GOSUB KSC
FOR L=J TO J+U4 STEP U2
LET D$(L TO L+U)=STR$ INT D1
IF D1<TEN THEN LET D$(L TO L+U)="0"+STR$ INT D1
LET D1=(D1-INT D1)*U60
NEXT L
RETURN 
CLS 
PRINT H$,
IF A$="1" THEN PRINT TAB U2;"%<%<%<% %S%C%H%E%D%U%L%I%N%G% % %A%C%T%I%V%I%T%Y% %>%>%>"
IF A$="2" THEN PRINT TAB U3;"%<%<%<% %T%R%A%C%K%I%N%G% % %A%C%T%I%V%I%T%Y% %>%>%>"
IF A$="3" THEN PRINT TAB U2;"%<%<% %K%E%P%L%E%R%I%A%N% %F%I%L%E% %U%P%D%A%T%E% %>%>%>"
PRINT 
FOR I=U TO U14
PRINT CHR$ (I+U37);" = ";S$(I)
LET A$=INKEY$
IF A$<>"" THEN GOTO 4780
NEXT I
PRINT ,,"##SELECT A-N (RETURN=0)##";
LET A$=INKEY$
IF A$="" THEN GOTO 4760
PRINT AT U19,U24;A$
LET I=CODE A$-U37
IF I>U14 OR I<U THEN LET GO=G
RETURN 
IF E9<U9H THEN LET D$=D$+"0"
LET D$=D$+STR$ INT (E9+HA)+" "
RETURN 
IF A9<99.5 THEN LET D$=D$+"0"
IF A9<U9H THEN LET D$=D$+"0"
LET D$=D$+STR$ INT (A9+HA)+" "
RETURN 
LET K9=INF
LET PHI=G
GOSUB SAT
IF GO=G THEN RETURN 
PRINT ,,S$(I, TO U9);" EPOCH: ";AT U19,G;"@@ENTER EPOCH DATE+TIME ";K$
INPUT D$
LET FS=U
PRINT AT U21,17;D$
IF D$<>"S" THEN GOTO 5000
LET D=D3
RETURN 
IF D$<>"0" THEN GOTO 5030
LET GO=G
RETURN 
GOSUB DAY
IF ER<>G THEN GOTO 5070
LET D3=D
RETURN 
GOSUB 3240
SLOW 
GOTO 4940
LET E=M+E(I)*SIN M+HA*E(I)**U2*SIN (U2*M)
LET M5=E-E(I)*SIN E-M
LET R3=U-E(I)*COS E
IF ABS M5<1E-6 THEN GOTO 5160
LET E=E-M5/R3
GOTO 5110
LET X=A*(COS E-E(I))
LET Y=A*E1*SIN E
LET R=A*R3
LET Z=X*C(U3,U)+Y*C(U3,U2)
LET X0=X*C(U,U)+Y*C(U,U2)
LET Y=X*C(U2,U)+Y*C(U2,U2)
LET G7=(D-Y0)*G1+G2
LET G7=(G7-INT G7)*P2
LET X=X0*COS G7+Y*SIN G7
LET Y=-X0*SIN G7+Y*COS G7
RETURN 
GOSUB CO4
IF GO=G THEN RETURN 
LET X8=-X5*C8*S9-Y5*S8*S9+Z5*C9
LET Y8=Y5*C8-X5*S8
GOSUB KSC
IF X8<>G THEN GOTO 5360
LET A9=90
IF Y8<G THEN LET A9=270
RETURN 
LET A9=ATN (Y8/X8)/P0
IF X8<G THEN LET A9=A9+180
IF A9<G THEN LET A9=A9+360
RETURN 
GOSUB 3980
GOSUB KSC
IF GO=G THEN RETURN 
GOSUB 5100
LET X5=X-X9
LET Y5=Y-Y9
LET Z5=Z-Z9
LET QS=X5*X9+Y5*Y9+Z5*Z9
GOSUB KSC
RETURN 
GOSUB CO3
IF GO=G THEN RETURN 
LET R5=SQR (X5*X5+Y5*Y5+Z5*Z5)
LET E9=ASN ((X5*C8*C9+Y5*S8*C9+Z5*S9)/R5)/P0
RETURN 
LET E8=SGN QS
LET PHI=-SGN QS*IN*R*AF*LOS
GOSUB INK
GOSUB CO3
IF GO=G THEN RETURN 
IF SGN QS=E8 THEN GOTO 5560
LET PHI=-HA*ABS PHI*SGN QS*LOS
GOSUB CO4
IF GO=G THEN RETURN 
IF ABS E9<HA THEN RETURN 
GOTO 5610

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