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(41C) Tracking Satellites in Elliptical Orbits
08-20-2019, 09:49 AM
Post: #1
SlideRule Offline
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 		Posts: 1,542
Joined: Dec 2013
(41C) Tracking Satellites in Elliptical Orbits
An extract from Computer program and sample problem for tracking OSCAR , Ham Radio, MAR 1981 (pgs. 46-50)

"The altitude and velocity of a satellite in a circular orbit are nearly constant. However, both altitude and velocity are always changing during an elliptical orbit …
The spot on the earth surface directly beneath the satellite is called the subsatellite point. A plot of the path of this point is the ground track and must include the effects of earth rotation. If the altitude and subsatellite point are known at a given time, the azimuth and elevation can be found using the same equations as for circular orbits …
A program for the HP-41C programmable calculator and printer was written to test the equations and to learn more about elliptic orbits …"

Excellent documentation.

BEST!
SlideRule
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08-20-2019, 10:28 PM
Post: #2
twdeckard Offline
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 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
Excellent post. If you check Celestrak or Heavens Above you can get the "two line element" which is a description of a satellites orbit cataloged by NORAD and other authorities. You can find the orbital elements for the ISS and your hp41 will faithfully point you to an orbiting object you can easily see with the naked eye.

I am still trying to wrangle my own variant but it was largely an exercise to play with an Advantage ROM and I got lost in the matrix math. It does have a simple parser that will pull a TLE out of extended memory and parse it into the individual fields. I have always meant to graft it on this code.

https://github.com/twdeckard/HP41CX-PLAN41

There are other hp41 routines that are rumored to be in AMSAT libraries but I've never surfaced them.

Here is my code, but everything after the parser is worthless. Offered for a better coder than I ...

Code:

; SATTRK 
; DERIVED ENTIRELY FROM PLAN-13 BY J.R. Miller G3RUH
; REQUIRES 41CX WITH ADVANTAGE ROM 
;
; REGISTERS AND MNEMONICS BELOW:
; 
00      4^TMP        ; 00-13 ALSO SCRATCH SPACE FOR ADV SOLVE FUNCTION
01    4^TMP
02    4^TMP
03    4^TMP        
04    4^SX        ; DAMN YOU ADVANTAGE ROM, VECTORS ON Rn+1 BOUNDARIES
05    4^SY
06    4^SZ
07    4^OX
08    4^OY
09    4^OZ
10     4^VOx
11    4^VOy
12    4^VOz
13    4^RX
14    4^RY
15     4^RZ
16    4ELAPST        ; (COMPUTED) ELAPSED TIME (DAYS) SINCE EPOCH [EPTIME] 
17    4CURORB        ; (COMPUTED) CURRENT ORBIT NUMBER
18     4OBJECT        ; (INPUT) SATELLITE OBJECT BEING TRACKED
19    1EPYEAR        ; (TLE) EPOCH YEAR                 1:19-20        
20    2EPTIME        ; (TLE) EPOCH TIME                    1:21-32
21    3INCLIN        ; (TLE) ORBITAL INCLINATION             2:09-16        
22    2R.A.A.N    ; (TLE) ORBITAL RIGHT ASCENSION OF ASCEND. NODE 2:27-33
23    4ECCENT        ; (TLE) ORBITAL ECCENTRICITY
24    2PERIGE        ; (TLE) ORBITAL PERIGEE             2:35-42
25    2MEANAN        ; (TLE) ORBITAL MEAN ANOMOLY             2:44-51
26    3MMDOT1        ; (TLE) ORBITAL ANGULAR MOMENTUM         1:34-43
27    3MMDOT2        ; (TLE) ORBITAL ANGULAR MOMENTUM RATE         1:45-52
28    4DECAYR        ; (TLE) ORBITAL DECAY RATE             1:54-61
29    1ORBITN        ; (TLE) ORBIT NUMBER                
30    6OBSLAT        ; (INPUT) OBSERVERS LATITUDE
31    6OBSLON        ; (INPUT) OBSERVERS LONGITUDE
32    4LAMBDA        ; (COMPUTED) LAMBDA
33    1SATRNG        ; (COMPUTED) SATELLITE RANGE
34    4DOPPLR        ; (COMPUTED) DOPPLER CORRECTION
35    6SATLAT        ; (COMPUTED) SATELLITE LATITUDE        
36    6SATLON        ; (COMPUTED) SATELLITE LONGITUDE
37    1AZIMUT        ; (COMPUTED) SATELLITE AZIMUTH
38    1ELEVAT        ; (COMPUTED) SATELLITE ELEVATION    
39    1OBSHGT        ; (INPUT) OBSERVERS HEIGHT
40     4MEANAT        ; (COMPUTED) MEAN ANOMOLY AT TIME T
41    4KD        ; (COMPUTED) LINEAR DRAG TERM             
42    4KDP        ; (COMPUTED) LINEAR DRAG TERM
;
;
; EXTENDED MEMORY FILES
;
; ISS        ALPHA        TWO-LINE-ELEMENTS
; SATREG    ALPHA        REGISTER MNEMONICS
;
; ENTRY POINTS
;
;SATTRK    SATELLITE TRACKING PROGRAM HP41
;DISTLE    DISPLAY TLE STORED IN EXTENDED MEMORY
;GETTLE    READ ORBITAL PARAMETERS FROM TLE IN EM
;KEPLER    COMPUTE LAMBDA 
;SATPOS    COMPUTE SATELLITE LATITUDE AND LONGITUDE
;AZELEV    COMPUTE AZIMUTH AND ELEVATION
;SATRNG    COMPUTE RANGE TO SATELLITE
;DOPPLR    COMPUTE DOPPLER SHIFT
;OUTPUT AZIMUTH AND ELEVATION
;EVRY20    ACTIVATE TIMER ROUTINE TO COMPUTE AND DISPLAY EVERY TWENTY SECONDS
;UPDATE COMPUTE SATPOS, AZIMUTH AND ELEVATION
;NEXT24    AZIMUTH AND ELEVATION OVER NEXT 24 HOURS
;NEXT12 AZIMUTH AND ELEVATION OVER NEXT 12 HOURS
;DISPLA    PRINT OUT REGISTERS WITH MNEMONICS
;DEORBI END PROGRAM
; 
LBL "PLAN13"
000.04201 
CLRGX            ; CLEAR REGISTERS
"A"            ; CLEAR EXTENDED MEMORY FILES
XEQ 40
"B"
XEQ 40
"C" 
XEQ 40
"D" 
XEQ 40
"RAAN"
XEQ 40
"IN"
XEQ 40
XEQ INPSTA        ; PROMPT FOR OBJECT, OBS LAT/LON/HGT
GTO a            ; ** TEMPORARY SKIP TLE FOR DEBUG
XEQ GETTLE         ; PARSE TLE FILE IN EM
LBL a
XEQ **TEST
GTO b            ; TEMPORARY SKIP TLE DISPLAY FOR DEBUG
XEQ DISTLE        ; DISPLAY TWO LINE ELEMENTS
LBL b
XEQ *ECFENU        ; TRANSFORM MATRIX GEOCENTRIC TO LOCAL CARTESIAN    
XEQ *RADIUS        ; COMPUTE EARTH RADIUS WGS-84 AND SET UP OBS X,Y,Z CALCULATION
XEQ *OBSXYZ        ; COMPUTE OBSERVERS X,Y,Z COORDINATES        
XEQ *OBSVEL        ; COMPUTE OBSERVERS VELOCITY
;
; DEBUG VERSION ONLY PERFORMS CALCULATION         
; ONCE AND USES CURRENT SYSTEM TIME
;
XEQ *MA+ORB        ; COMPUTE CURRENT ORBIT NUMBER             
XEQ *SOLVEA        ; SOLVE KEPLERS EQUATION
XEQ *CELEST        ; [C] = [RAAN]*[IN]*[AP]        
XEQ *SATCEL        ; COMPUTE SATELLITE CELESTIAL COORDINATES
XEQ *SATGEO        ; COMPUTE SATELLITE GEOCENTRIC COORDINATES
XEQ *^RANGE        ; COMPUTE RANGE VECTOR
XEQ *AZIELE        ; COMPUTE AZIMUTH ELEVATION
STOP
;
; READ TWO LINE ELEMENTS FROM EM FILE NAMED IN [OBJECT] 
;
LBL "GETTLE"
0.000
CLA
ARCL 18
SEEKPTA
19
0.0017018
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
2000
ST+ 19
20
0.019031
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
21
1.007015
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
22
1.016024
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
23
1.025032
XEQ 20            ; <*GETEL>
>"."
-1
AROT            ; LEADING DECIMAL PRESUMED
RDN
XEQ 30            ; <*PARSE>
24
1.033041
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
25
1.042050
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
26
0.032042
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
27
0.043051
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
28
0.052060
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
RTN
LBL "*GETEL"
LBL 20
CLA
ARCL 18
SEEKPTA
GETREC
RTN
LBL "*PARSE"
LBL 30
FRC
1000
*
ENTER
INT
X<>Y
FRC
1000
*
X<>Y
-
2
+
42
XEQ "SC"        ; FROM PPC, SUBSTITUTE CHARACTER
ANUM            ; USED TO INSERT NON-NUMERIC TERMINATOR IN ALPHA 
STO IND T        ; TO PARSE NUMBERS FROM TWO LINE ELEMENTS
RTN
LBL "SC"
X<>Y
AROT
-1
AROT
RDN
ATOX
CLX
RDN
X<>Y
XTOA
X<>Y
CHS
AROT
CHS
X<>Y
RTN
;
; PROMPT FOR SATELLITE OBJECT AND OBSERVER COORDINATES
; DEBUG HARD CODED FOR INTERNATIONAL SPACE STATION AND EN34FV 
;
LBL "INPSTA"            
ISS
ASTO 18
44.885077         ; ARLINGTON CT
55.21            ; TEST LATITUDE IN PLAN13    
STO 30
-93.551546        ; ARLINGTON CT
.06            ; TEST LONGITUDE IN PLAN13
STO 31
800            ; ARLINGTON CT
79            ; TEST HEIGHT IN PLAN13
STO 39
RTN
LBL "SATPOS"
RTN
LBL "AZELEV"
RTN
LBL "SATRNG"
RTN
LBL "*SATGEO"
RTN
LBL "*^RANGE"
RTN
LBL "*AZIELE"
RTN
LBL "OUTPUT"
RTN
LBL "NEXT24"
RTN
LBL "NEXT12"
RTN
LBL 40            ; DELETE EM FILE NAMED IN ALPHA
SF 25
PURFL
RTN
LBL "DISTLE"        ; NOTE: CREATE A COMMON SUBROUTINE TO PRINT MNEUMONICS
018.02901
XEQ 36
RTN
LBL "DISALL"
000.03501
XEQ 36
RTN
LBL 36
STO 00
LBL 46
RCL 00
INT
XEQ 47
ISG 00
GTO 46
RTN
LBL 47
"SATREG"
SEEKPTA
GETREC
+":"
RCL IND X
ATOX
ASTO Z
X<>Y
FIX 0
XEQ IND Y
AVIEW
RTN
LBL 48
ARCL X
RTN
LBL 49
FIX 0
ARCL X
RTN
LBL 50
FIX 1
ARCL X
RTN
LBL 51
LBL 52
FIX 2
ARCL X
RTN
LBL 53
CLK24
FIX 4
ATIME24
RTN
LBL 54
FIX 4
HMS
ATIME24
RTN

LBL *RAAN        ; CREATE ROTATION ABOUT Z OF RAAN
"RAAN"
RCL 22            ; [RAAN]
XEQ *ROTZ        
RTN
LBL *IN0        ; CREATE ROTATION ABOUT X OF INCLINATION              
"IN"
RCL 21            ; [INCL]
XEQ *ROTX        
RTN
LBL *AP            ; CREATE ROTATION ABOUT Z OF ARGUMENT OF PERIGEE 
"AP"
RCL 24            ; [PERIGEE]
XEQ ROTZ
RTN
LBL *CELEST        ; ORBITAL PLANE TO CELESTIAL COORDINATE TRANSFORMATION
3.003
"C"
MATDIM
"B"
MATDIM
XEQ "*RAAN"
XEQ "*IN0"
"RAAN,IN,B"
M*M
"RAAN"
XEQ 40
"IN"
XEQ 40
XEQ "*AP"
"B,AP,C"
M*M            ; [C] = [RAAN]*[IN]*[AP]
"AP"
XEQ 40
"B"
XEQ 40
RTN    
;
; TRANSFORMATION FROM EAST NORTH UP TO EARTH CENTERED EARTH FIXED COORDINATES
;
; clockwise rotation over east-axis by angle (90-phi) to align up-axis with z-axis
; 
; clockwise rotation over z-axis by angle (90+lambda) to align east axis with x-axis
; 
; >>>>>USING THIS INSTEAD R3(PI)*R2(PHI-PI/2)*R3(LAMBDA-PI)
; 
; http://gis.stackexchange.com/questions/82998/trasformation-from-ecef-to-enu
;
LBL "*ECFENU"        ;
3.003
ENU
MATDIM
"C"
MATDIM
-90
"A"
XEQ "*ROT3"
RCL 30
90
-
"B"
XEQ "*ROT2"
"A,B,C"
M*M
"A"
PURFL
"B" 
PURFL
RCL 31
180
-
"D"
XEQ "*ROT3"
"C,D,ENU"
M*M
"C"
PURFL
"D"
PURFL 
RTN
; ENU MATRIX DOES NOT LOOK CORRECT
;
; TEST RESULTS
; Ux=0.6127688125485028
; Uy=0.0006416902235684213
; Uz=0.7902619632764536
; 
; Ex=-0.001047197341936584
; Ey=0.9999994516887132
; Ez=0
; 
; Nx=-0.7902615299668996
; Ny=-0.0008275602273766885
; Nz=0.6127691485367431
;
;
; A*B=ENU (-LAT,-LON)
;
; 1:1= 0.79026=Uz   1:2= 0.00064=Uy  1:3= 0.61277=Ux
; 2:1= 0.61277=Nz   2:2=-0.00083=Ny  2:3=-0.79026=Nx
; 3:1= 0.00000=Ez   3:2= 1.00000=Ey  3:3=-0.00105=Ex
;
; 1:1= 0.79026=Uz   2:1= 0.61277=Nz  3:1= 0.00000=Ez
; 1:2= 0.00064=Uy   2:2=-0.00083=Ny  3:2= 1.00000=Ey
; 1:3= 0.61277=Ux   2:3=-0.79026=Nx  3:3=-0.00105=Ex
;

LBL *ROTX        ;         |  1     0     0     | 
STO 00            ;        |                    |        
3.003            ; Rx(T) =     |  0  COS(T) -SIN(T) |    
MATDIM            ;         |                    |
0            ;         |  0  SIN(T)  COS(T) |
MSIJ
1
MSC+    ; MSR+    ; OOOPS
0
MSC+    ; MSR+
MSC+    ; MSR+
MSC+     ; MSR+
RCL 00
ENTER
SIN
X<>Y
COS
MSC+    ; MSR+
X<>Y
MSC+     ; MSR+
0
MSC+     ; MSR+
RDN
CHS
MSC+    ; MSR+
X<>Y
MS
RTN            ; VERIFIED 9/17/16


LBL *ROTZ        ;        | COS(T) -SIN(T)  0  |
STO 00            ;        |                    |    
3.003            ; Rz(T) =       | SIN(T)  COS(T)  0  |
MATDIM            ;        |                    |    
0            ;        |   0       0     1  |
MSIJ
RCL 00
ENTER
SIN
X<>Y
COS
MSC+    ;    MSR+
X<>Y
MSC+    ;    MSR+
0
MSC+    ;    MSR+
RDN
CHS
MSC+    ;    MSR+
X<>Y
MSC+    ;    MSR+
0
MSC+    ;    MSR+
MSC+    ;    MSR+
MSC+    ;    MSR+
1
MS
RTN            ; VERIFIED 9/17/2016

LBL *ROTY        ;        | COS(T)   0   SIN(T) |
STO 00            ;        |                     |
3.003            ; Ry(T) =       |    0     1     0    |
MATDIM            ;         |                     |
0            ;               |-SIN(T)   0   COS(T) |
MSIJ
RCL 00
ENTER
SIN
X<>Y
COS
MSC+
0
MSC+
X<>Y
MSC+
X<>Z
MSC+
1
MSC+
RDN
MSC+
X<>Z
MSC+
RDN
MS
RTN

LBL *ROT1        ;         |  1     0     0     | 
STO 00            ;        |                    |        
3.003            ; R1(T) =     |  0  COS(T)  SIN(T) |    
MATDIM            ;         |                    |
0            ;         |  0 -SIN(T)  COS(T) |
MSIJ
1
MSC+    ;
0
MSC+    ; 
MSC+    ; 
MSC+     ; 
RCL 00
ENTER
SIN
CHS
X<>Y
COS
MSC+    ; 
X<>Y    
MSC+     ; 
0
MSC+     ; 
RDN
CHS
MSC+    ; 
X<>Y
MS
RTN    

LBL *ROT3        ;        | COS(T)  SIN(T)  0  |
STO 00            ;        |                    |    
3.003            ; R3(T) =       | -SIN(T) COS(T)  0  |
MATDIM            ;        |                    |    
0            ;        |   0       0     1  |
MSIJ
RCL 00
ENTER
SIN
CHS
X<>Y
COS
MSC+    ;    
X<>Y
MSC+    ;
0
MSC+    ;    
RDN
CHS
MSC+    ;    
X<>Y
MSC+    ;    
0
MSC+    ;    
MSC+    ;    
MSC+    ;    
1
MS
RTN
;
;
;            
LBL *ROT2        ;        | COS(T)   0   -SIN(T) |
STO 00            ;        |                      |
3.003            ; R2(T) =       |    0     1     0     |
MATDIM            ;         |                      |
0            ;               |SIN(T)   0   COS(T)   |
MSIJ
RCL 00
ENTER
SIN
;;  CHS
X<>Y
COS
MSC+
0
MSC+
X<>Z
MSC+
X<>Z
MSC+
1
MSC+
RDN
MSC+
X<>Z
CHS
MSC+
X<>Z
MSC+
RDN
MS
RTN

;
; RE = 6378.137
; RP = 6256.752
;
; D  = SQRT(RE*RE*CL*CL + RP*RP*SL*SL)
; Rx = RE*RE/D + HT: Rz = RP*RP/D + HT
;
LBL *RADIUS
6378.137        ; RADIUS OF EARTH AT EQUATOR 
X^2            ; X=XX
STO 07            ; [OX]
STO 08            ; [OY]
6256.752        ; RADIUS OF EARTH THRU POLES 
X^2            ; 
STO 09            ; [OZ]          
RCL 30            ; [OBSLAT]
COS
X^2
RCL 07
*
RCL 30
SIN
X^2
RCL 09
+
SQRT
ST/ 07
ST/ 08
ST/ 09
RCL 40            ; [OBSHGT]
1000
/
ST+ 07            ; [OX]
ST+ 08            ; [OY]
ST+ 09            ; [OZ]
RTN
LBL *OBSXYZ
"ENU"
3.001
MSIJ
MRR+            ; UX
ST* 07            ; OPOS,X
MRR+            ; UY
ST* 08            ; OPOS,Y
MRR+            ; UZ
ST* 09            ; OPOS,Z
RTN
LBL *OBSVEL
RCL 08
STO 10
RCL 07
STO 11
CLX
STO 12
PI                 ; ERROR!!! CALC IN DEGREES
2 
* 
365.2421874 
/ 
/ 
ST* 11 
* 
+ 
86400 
ST* 11 
CHS 
ST* 10 
RTN 
; Calculate Satellite Position at DN,TN
; T  = (DN - DE) + (TN-TE) Elapsed T since epoch, days

LBL *MA+ORB
RCL 19                ; EPYEAR
1E6
/
1.01
+
DATE
DDAYS
RCL 20                ; EPTIME
INT
- 
TIME
24
/
RCL 20
FRC
-
+
STO 16                ; ELAPST SINCE EPOCH, DAYS
; DRAG COEFF = -2*M2/MM/3: (Angular momentum rate)/(Ang mom)  s^-1
RCL 27                ; MMDOT2 
-2
*
RCL 26                ; MMDOT1
/
3
/
*
; LINEAR DRAG TERMS KD = 1+4*DT:KDP= 1-7*DT
; Mean anomaly at YR,TN M = MA + MM*T*(1-3*DT)
STO 40                ; MEANAT
STO 41                ; KD
STO 42                ; KDP
4 
ST* 41                ; KD
-7
ST* 42                ; KDP
-3
ST* 40                ; MEANAT
1 
ST+ 41                ; KD
ST+ 42                ; KDP
ST+ 40                ; MEANAT
RCL 16                ; ELAPST
ST* 40                ; MEANAT
RCL 25                ; MMDOT1
ST* 40                ; MEANAT
RCL 24                ; MEANAN
ST+ 40                ; MEANAT
RCL 40                ; MEANAT
RTN
STOP
360
/
INT
ENTER
360
*
ST- 40                ; MEANAT
X<>Y
RCL 28                ; ORBITN
+
STO 17                ; CURORB
RTN

 2100 EA = M:                 REM Initial solution
 2110 REPEAT
 2120   C = COS(EA): S = SIN(EA): DNOM=1-EC*C
 2130   D = (EA-EC*S-M)/DNOM:   REM Change to EA for better solution
 2140   EA = EA - D:            REM by this amount
 2150 UNTIL ABS(D) < 1E-5:      REM Until converged

LBL *SOLVEA
RCL 40
STO 01
STO 02
"*KEPLE"
STO 06
XEQ SOL                ; IMPORTANT - MY HP41CX HAS BOTH MATH/STAT AND 
                ; ADVANTAGE.  REMOVE MATH MODULE WHEN ENTERING
                ; INSTRUCTION.  SHOULD BE XROM XX

                ; DISREGARD USING MATH SOL
RTN
LBL "*KEPLE"
;
;
LBL *KEPLER
;
;
; M = EA - EC*SIN(EA)
ENTER
SIN
X<>Y
RCL 23 ; ECCENTRICITY
*
-
RCL 40 ; MEANAT 
-
RTN
;
; ADVANTAGE <SOLVE> FUNCTION CONSUMES 13 REGISTERS
; MATH      <SOLVE> FUNCTION CONSUMES 7  REGISTERS
; NOTE: CHECK WHEN VECTORS COMPUTED
; 
;    RCL 41                ; [M]
;    STO 32                ; [LAMBDA]
;    
;    LBL 60
;    RCL 32                ; [LAMBDA]
;    RCL 32                ; [LAMBDA]
;    SIN
;    RCL 23                ; [ECCENT]
;    -
;    RCL 41
;    -
;    1
;    RCL 23                ; [ECCENT]
;    RCL 32                ; [LAMBDA]
;    COS
;    *
;    -
;    /
;    ST- 32                ; [LAMBDA]
;    ABS
;    1E-5
;    X>Y?
;    GTO 60
;    RTN
;
; Cambridge UK 52.2053? N, 0.1218? E
;
;
LBL **TEST
1990 
STO 19                ; EPYEAR
191.145409
STO 20                ; EPOTIM
59.9975
STO 21                ; INCLIN
146.4527
STO 22                ; RAAN
0.6986        
STO 23                ; ECCENT
231.0027
STO 24                ; PERIGE
43.2637 
STO 25                ; MEANAN
2.09695848
STO 26                ; MMDOT1
1E-8 
STO 27                ; MMDOT2
1585
STO 29                ; ORBITN
52.21
STO 30
0.06
STO 31
79
STO 39
RTN
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08-21-2019, 12:55 AM
Post: #3
SlideRule Offline
Senior Member
 		Posts: 1,542
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
(08-20-2019 10:28 PM)twdeckard Wrote:  There are other hp41 routines that are rumored to be in AMSAT libraries but I've never surfaced them.

An extract from AMSAT Orbit magazine (JAN-FEB/1983 pg. 19) …
"Calculator Program Orders
The AMSAT Software Exchange address listed previously handles only programs for microcomputer systems. Orders for and inquiries about programs for calculators such as HP-41C should be directed to: AMSAT Calculator Program Library, John Montague, W0RUE, Box 541, Willenie, MN 55090."

BEST!
SlideRule
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08-21-2019, 02:29 AM
Post: #4
twdeckard Offline
Member
 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
Thanks! Its not far from me in space, but pretty far in time. I'll stuff an envelop in the time machine and see what happens.

Todd
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08-21-2019, 07:30 AM (This post was last modified: 08-21-2019 07:32 AM by Ángel Martin.)
Post: #5
Ángel Martin Offline
Senior Member
 		Posts: 1,448
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
In case you want to test it, this program is included in the LATLON module available in the CL Library, with id# = "LTLN". The program label is LBL "SATRACK".

Stay tuned for a couple of new compilation ROMS including programs from several papers contributed by SlideRule.
Slow train coming... but here at last!
"To live or die by your own sword one must first learn to wield it aptly."
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08-21-2019, 11:45 AM
Post: #6
twdeckard Offline
Member
 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
(08-21-2019 07:30 AM)Ángel Martin Wrote:  In case you want to test it, this program is included in the LATLON module available in the CL Library, with id# = "LTLN". The program label is LBL "SATRACK".

Greetings Angel! I would very much like to experiment with it. I do not have a CL, can you point me to the original FOCAL?

Best
Todd
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08-21-2019, 12:11 PM
Post: #7
twdeckard Offline
Member
 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
Greetings Angel,

Unless you have it readily at hand I may be able to fish for myself.

I downloaded LATLON.ROM from Mr. Dalrymple's site and converted it to .raw and .txt with the most excellent utilities available on Mr. Furlow's site but at first blush it doesn't contain SATRACK? This evening I will experiment.

Todd
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08-21-2019, 11:27 PM
Post: #8
twdeckard Offline
Member
 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
I had to use Free42 (also excellent) as the .raw file had muitiple ends.

I love the fact that there are still experts and tools for this platform.

I am going to reactivate the original project and I will also graft the TLE parser onto this routine.

Code:

"\x00SATRACK"  ;".SATRACK"
XEQ 04
STO 00
CF 12
"TIME  AZIMUTH"
>"  ELEVATION"
AVIEW
LBL 05
XEQ 01
FIX 02
60
/
RCL 12
HR
+
RND
FIX 00
24
MOD
INT
10
X>Y?
>" "
ARCL Y
>":"
LASTX
FRC
60
*
X<Y?
>"0"
ARCL X
RCL 08
X=0?
>"*"
X#0?
>" "
RCL 13
RCL 17
RCL 09
-
SIN
STO 06
X<> L
COS
RCL 15
*
RCL 04
*
RCL 14
RCL 13
*
+
STO 05
RCL 14
*
-
RCL 15
/
RCL 05
ACOS
SIN
STO 09
/
ACOS
RCL 06
SIGN
+
360
MOD
XEQ 08
>"     "
RCL 05
RCL 01
-
RCL 09
/
ATAN
XEQ 06
GTO 05
LBL E
XEQ 04
STO 00
"GROUND TRACK"
AVIEW
CF 12
ADV
"TIME   LAT"
>"   LONG   RNG"
AVIEW
LBL 03
XEQ 01
FIX 00
XEQ 02
FIX 01
RCL 07
XEQ 08
RCL 09
XEQ 08
RCL 01
ACOS
D-R
RCL 19
*
0.1
%
XEQ 06
GTO 03
LBL 01
FIX 06
1
RCL 08
RCL 03
/
-
PI
*
STO 06
ENTER
LBL 00
CLX
RCL 06
R-D
RCL 02
P-R
1
-
STO 07
CLX
RCL 06
-
+
RND
RCL 07
/
ST- 06
X#0?
GTO 00
RCL 06
R-D
COS
RCL 02
-
RCL 07
/
ACOS
RCL 00
SIGN
*
STO 05
RCL 10
*
XEQ 07
RCL 00
-
RCL 00
3.989
/
+
RCL 11
*
360
MOD
STO 09
1
RCL 02
RCL 05
COS
*
-
RCL 03
PI
/
2
ENTER
3
/
Y^X
/
RCL 21
/
1
RCL 02
X^2
-
/
STO 01
CLA
RCL 08
RTN
LBL 08
>" "
LBL 02
RND
ENTER
ABS
X=Y?
>" "
100
X>Y?
>" "
SQRT
X>Y?
>" "
ARCL Z
RTN
LBL 04
FIX 00
SF 12
CF 29
"ORBIT"
PROMPT
ARCL X
AVIEW
ADV
ENTER
X<> 20
-
RCL 03
*
3
/
ENTER
X<> 11
+
360
MOD
X<> 11
15
/
RCL 12
HR
*
24
MOD
HMS
STO 12
RCL 03
RCL 10
MOD
RCL 03
-
STO 00
RCL 18
LBL 07
1
P-R
X<>Y
CHS
RCL 16
*
STO 13
ASIN
STO 07
COS
STO 04
/
ACOS
RCL 07
SIGN
*
RTN
LBL 06
XEQ 02
RCL Z
X>0?
AVIEW
RCL 08
RCL 10
+
STO 00
RCL 03
X<Y?
STOP
END


Attached File(s)
.pdf  satellite track.pdf (Size: 416.08 KB / Downloads: 31)
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11-05-2021, 07:42 AM
Post: #9
Ángel Martin Offline
Senior Member
 		Posts: 1,448
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
(08-21-2019 11:27 PM)twdeckard Wrote:  I am going to reactivate the original project and I will also graft the TLE parser onto this routine.

It's been a while... so i was wondering if you had a chance to look int this projext since? Pls. update us on the progress...

I noticed strange code lines in the INPSTA routine. There are inputs of value pairs (say a,b) but only the second value (b) is stored in a data register R30, R31 and R39. As this is done repeated times all the ä) values entered are lost due to stack overflow... I suppose this wasn't intended?

Cheers,
ÁM
"To live or die by your own sword one must first learn to wield it aptly."
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11-23-2021, 09:08 PM (This post was last modified: 11-23-2021 09:13 PM by twdeckard.)
Post: #10
twdeckard Offline
Member
 		Posts: 105
Joined: Dec 2013
RE: (41C) Tracking Satellites in Elliptical Orbits
Greetings Angel,

thank you for your gracious follow up. I never made much progress on the project. All my energy was squandered on the Arduino driven antenna rotor drive and alas that is quite dusty as well.

Here is an early test:

https://www.youtube.com/watch?v=VG5L5oP2...j_&index=4

Here is the unit running in sky survey mode:

https://www.youtube.com/watch?v=3rMM7kyH..._&index=14

The telescope provided quite some amusement for my neighbor across the street when I teased him that based on the 300K noise I was picking up was throwing off my survey of the cosmic background radiation and probably a sign of some alien presence -- an elaborate aluminum foil ET appeared in his window a few days later.

Here is an actual attempt at a contact over an amateur radio satellite. This one was funny. There are several attempts that worked.

https://www.youtube.com/watch?v=O5nFwU_w...j_&index=3

You are correct the INPUTSTA is flawed. Early in the projects I generally "rough" in the application to see if it will even fit in the mighty HP41 calculator before I really dive in.

Here was the last variant of the code but again, I never carried it across the finish line. Thank you for your inquiry -- I really enjoy the forum and the community.

Code:
; SATTRK 
; DERIVED ENTIRELY FROM PLAN-13 BY J.R. Miller G3RUH
; REQUIRES 41CX WITH ADVANTAGE ROM 
;
; REGISTERS AND MNEMONICS BELOW:
; 
00      4^TMP        ; 00-13 ALSO SCRATCH SPACE FOR ADV SOLVE FUNCTION
01    4^TMP
02    4^TMP
03    4^TMP        
04    4^SX        ; DAMN YOU ADVANTAGE ROM, VECTORS ON Rn+1 BOUNDARIES
05    4^SY
06    4^SZ
07    4^OX
08    4^OY
09    4^OZ
10     4^VOx
11    4^VOy
12    4^VOz
13    4^RX
14    4^RY
15     4^RZ
16    4ELAPST        ; (COMPUTED) ELAPSED TIME (DAYS) SINCE EPOCH [EPTIME] 
17    4CURORB        ; (COMPUTED) CURRENT ORBIT NUMBER
18     4OBJECT        ; (INPUT) SATELLITE OBJECT BEING TRACKED
19    1EPYEAR        ; (TLE) EPOCH YEAR                 1:19-20        
20    2EPTIME        ; (TLE) EPOCH TIME                    1:21-32
21    3INCLIN        ; (TLE) ORBITAL INCLINATION             2:09-16        
22    2R.A.A.N    ; (TLE) ORBITAL RIGHT ASCENSION OF ASCEND. NODE 2:27-33
23    4ECCENT        ; (TLE) ORBITAL ECCENTRICITY
24    2PERIGE        ; (TLE) ORBITAL PERIGEE             2:35-42
25    2MEANAN        ; (TLE) ORBITAL MEAN ANOMOLY             2:44-51
26    3MMDOT1        ; (TLE) ORBITAL ANGULAR MOMENTUM         1:34-43
27    3MMDOT2        ; (TLE) ORBITAL ANGULAR MOMENTUM RATE         1:45-52
28    4DECAYR        ; (TLE) ORBITAL DECAY RATE             1:54-61
29    1ORBITN        ; (TLE) ORBIT NUMBER                
30    6OBSLAT        ; (INPUT) OBSERVERS LATITUDE
31    6OBSLON        ; (INPUT) OBSERVERS LONGITUDE
32    4LAMBDA        ; (COMPUTED) LAMBDA
33    1SATRNG        ; (COMPUTED) SATELLITE RANGE
34    4DOPPLR        ; (COMPUTED) DOPPLER CORRECTION
35    6SATLAT        ; (COMPUTED) SATELLITE LATITUDE        
36    6SATLON        ; (COMPUTED) SATELLITE LONGITUDE
37    1AZIMUT        ; (COMPUTED) SATELLITE AZIMUTH
38    1ELEVAT        ; (COMPUTED) SATELLITE ELEVATION    
39    1OBSHGT        ; (INPUT) OBSERVERS HEIGHT
40     4MEANAT        ; (COMPUTED) MEAN ANOMOLY AT TIME T
41    4KD        ; (COMPUTED) LINEAR DRAG TERM             
42    4KDP        ; (COMPUTED) LINEAR DRAG TERM
;
;
; EXTENDED MEMORY FILES
;
; ISS        ALPHA        TWO-LINE-ELEMENTS
; SATREG    ALPHA        REGISTER MNEMONICS
;
; ENTRY POINTS
;
;SATTRK    SATELLITE TRACKING PROGRAM HP41
;DISTLE    DISPLAY TLE STORED IN EXTENDED MEMORY
;GETTLE    READ ORBITAL PARAMETERS FROM TLE IN EM
;KEPLER    COMPUTE LAMBDA 
;SATPOS    COMPUTE SATELLITE LATITUDE AND LONGITUDE
;AZELEV    COMPUTE AZIMUTH AND ELEVATION
;SATRNG    COMPUTE RANGE TO SATELLITE
;DOPPLR    COMPUTE DOPPLER SHIFT
;OUTPUT AZIMUTH AND ELEVATION
;EVRY20    ACTIVATE TIMER ROUTINE TO COMPUTE AND DISPLAY EVERY TWENTY SECONDS
;UPDATE COMPUTE SATPOS, AZIMUTH AND ELEVATION
;NEXT24    AZIMUTH AND ELEVATION OVER NEXT 24 HOURS
;NEXT12 AZIMUTH AND ELEVATION OVER NEXT 12 HOURS
;DISPLA    PRINT OUT REGISTERS WITH MNEMONICS
;DEORBI END PROGRAM
; 
LBL "PLAN13"
000.04201 
CLRGX            ; CLEAR REGISTERS
"A"            ; CLEAR EXTENDED MEMORY FILES
XEQ 40
"B"
XEQ 40
"C" 
XEQ 40
"D" 
XEQ 40
"RAAN"
XEQ 40
"IN"
XEQ 40
XEQ INPSTA        ; PROMPT FOR OBJECT, OBS LAT/LON/HGT
GTO a            ; ** TEMPORARY SKIP TLE FOR DEBUG
XEQ GETTLE         ; PARSE TLE FILE IN EM
LBL a
XEQ **TEST
GTO b            ; TEMPORARY SKIP TLE DISPLAY FOR DEBUG
XEQ DISTLE        ; DISPLAY TWO LINE ELEMENTS
LBL b
XEQ *ECFENU        ; TRANSFORM MATRIX GEOCENTRIC TO LOCAL CARTESIAN    
XEQ *RADIUS        ; COMPUTE EARTH RADIUS WGS-84 AND SET UP OBS X,Y,Z CALCULATION
XEQ *OBSXYZ        ; COMPUTE OBSERVERS X,Y,Z COORDINATES        
XEQ *OBSVEL        ; COMPUTE OBSERVERS VELOCITY
;
; DEBUG VERSION ONLY PERFORMS CALCULATION         
; ONCE AND USES CURRENT SYSTEM TIME
;
XEQ *MA+ORB        ; COMPUTE CURRENT ORBIT NUMBER             
XEQ *SOLVEA        ; SOLVE KEPLERS EQUATION
XEQ *CELEST        ; [C] = [RAAN]*[IN]*[AP]        
XEQ *SATCEL        ; COMPUTE SATELLITE CELESTIAL COORDINATES
XEQ *SATGEO        ; COMPUTE SATELLITE GEOCENTRIC COORDINATES
XEQ *^RANGE        ; COMPUTE RANGE VECTOR
XEQ *AZIELE        ; COMPUTE AZIMUTH ELEVATION
STOP
;
; READ TWO LINE ELEMENTS FROM EM FILE NAMED IN [OBJECT] 
;
LBL "GETTLE"
0.000
CLA
ARCL 18
SEEKPTA
19
0.0017018
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
2000
ST+ 19
20
0.019031
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
21
1.007015
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
22
1.016024
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
23
1.025032
XEQ 20            ; <*GETEL>
>"."
-1
AROT            ; LEADING DECIMAL PRESUMED
RDN
XEQ 30            ; <*PARSE>
24
1.033041
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
25
1.042050
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
26
0.032042
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
27
0.043051
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
28
0.052060
XEQ 20            ; <*GETEL>
XEQ 30            ; <*PARSE>
RTN
LBL "*GETEL"
LBL 20
CLA
ARCL 18
SEEKPTA
GETREC
RTN
LBL "*PARSE"
LBL 30
FRC
1000
*
ENTER
INT
X<>Y
FRC
1000
*
X<>Y
-
2
+
42
XEQ "SC"        ; FROM PPC, SUBSTITUTE CHARACTER
ANUM            ; USED TO INSERT NON-NUMERIC TERMINATOR IN ALPHA 
STO IND T        ; TO PARSE NUMBERS FROM TWO LINE ELEMENTS
RTN
LBL "SC"
X<>Y
AROT
-1
AROT
RDN
ATOX
CLX
RDN
X<>Y
XTOA
X<>Y
CHS
AROT
CHS
X<>Y
RTN
;
; PROMPT FOR SATELLITE OBJECT AND OBSERVER COORDINATES
; DEBUG HARD CODED FOR INTERNATIONAL SPACE STATION AND EN34FV 
;
LBL "INPSTA"            
ISS
ASTO 18
44.885077         ; ARLINGTON CT
55.21            ; TEST LATITUDE IN PLAN13    
STO 30
-93.551546        ; ARLINGTON CT
.06            ; TEST LONGITUDE IN PLAN13
STO 31
800            ; ARLINGTON CT
79            ; TEST HEIGHT IN PLAN13
STO 39
RTN
LBL "SATPOS"
RTN
LBL "AZELEV"
RTN
LBL "SATRNG"
RTN
LBL "*SATGEO"
RTN
LBL "*^RANGE"
RTN
LBL "*AZIELE"
RTN
LBL "OUTPUT"
RTN
LBL "NEXT24"
RTN
LBL "NEXT12"
RTN
LBL 40            ; DELETE EM FILE NAMED IN ALPHA
SF 25
PURFL
RTN
LBL "DISTLE"        ; NOTE: CREATE A COMMON SUBROUTINE TO PRINT MNEUMONICS
018.02901
XEQ 36
RTN
LBL "DISALL"
000.03501
XEQ 36
RTN
LBL 36
STO 00
LBL 46
RCL 00
INT
XEQ 47
ISG 00
GTO 46
RTN
LBL 47
"SATREG"
SEEKPTA
GETREC
+":"
RCL IND X
ATOX
ASTO Z
X<>Y
FIX 0
XEQ IND Y
AVIEW
RTN
LBL 48
ARCL X
RTN
LBL 49
FIX 0
ARCL X
RTN
LBL 50
FIX 1
ARCL X
RTN
LBL 51
LBL 52
FIX 2
ARCL X
RTN
LBL 53
CLK24
FIX 4
ATIME24
RTN
LBL 54
FIX 4
HMS
ATIME24
RTN

LBL *RAAN        ; CREATE ROTATION ABOUT Z OF RAAN
"RAAN"
RCL 22            ; [RAAN]
XEQ *ROTZ        
RTN
LBL *IN0        ; CREATE ROTATION ABOUT X OF INCLINATION              
"IN"
RCL 21            ; [INCL]
XEQ *ROTX        
RTN
LBL *AP            ; CREATE ROTATION ABOUT Z OF ARGUMENT OF PERIGEE 
"AP"
RCL 24            ; [PERIGEE]
XEQ ROTZ
RTN
LBL *CELEST        ; ORBITAL PLANE TO CELESTIAL COORDINATE TRANSFORMATION
3.003
"C"
MATDIM
"B"
MATDIM
XEQ "*RAAN"
XEQ "*IN0"
"RAAN,IN,B"
M*M
"RAAN"
XEQ 40
"IN"
XEQ 40
XEQ "*AP"
"B,AP,C"
M*M            ; [C] = [RAAN]*[IN]*[AP]
"AP"
XEQ 40
"B"
XEQ 40
RTN    
;
; TRANSFORMATION FROM EAST NORTH UP TO EARTH CENTERED EARTH FIXED COORDINATES
;
; clockwise rotation over east-axis by angle (90-phi) to align up-axis with z-axis
; 
; clockwise rotation over z-axis by angle (90+lambda) to align east axis with x-axis
; 
; >>>>>USING THIS INSTEAD R3(PI)*R2(PHI-PI/2)*R3(LAMBDA-PI)
; 
; http://gis.stackexchange.com/questions/82998/trasformation-from-ecef-to-enu
;
LBL "*ECFENU"        ;
3.003
ENU
MATDIM
"C"
MATDIM
-90
"A"
XEQ "*ROT3"
RCL 30
90
-
"B"
XEQ "*ROT2"
"A,B,C"
M*M
"A"
PURFL
"B" 
PURFL
RCL 31
180
-
"D"
XEQ "*ROT3"
"C,D,ENU"
M*M
"C"
PURFL
"D"
PURFL 
RTN
; ENU MATRIX DOES NOT LOOK CORRECT
;
; TEST RESULTS
; Ux=0.6127688125485028
; Uy=0.0006416902235684213
; Uz=0.7902619632764536
; 
; Ex=-0.001047197341936584
; Ey=0.9999994516887132
; Ez=0
; 
; Nx=-0.7902615299668996
; Ny=-0.0008275602273766885
; Nz=0.6127691485367431
;
;
; A*B=ENU (-LAT,-LON)
;
; 1:1= 0.79026=Uz   1:2= 0.00064=Uy  1:3= 0.61277=Ux
; 2:1= 0.61277=Nz   2:2=-0.00083=Ny  2:3=-0.79026=Nx
; 3:1= 0.00000=Ez   3:2= 1.00000=Ey  3:3=-0.00105=Ex
;
; 1:1= 0.79026=Uz   2:1= 0.61277=Nz  3:1= 0.00000=Ez
; 1:2= 0.00064=Uy   2:2=-0.00083=Ny  3:2= 1.00000=Ey
; 1:3= 0.61277=Ux   2:3=-0.79026=Nx  3:3=-0.00105=Ex
;

LBL *ROTX        ;         |  1     0     0     | 
STO 00            ;        |                    |        
3.003            ; Rx(T) =     |  0  COS(T) -SIN(T) |    
MATDIM            ;         |                    |
0            ;         |  0  SIN(T)  COS(T) |
MSIJ
1
MSC+    ; MSR+    ; OOOPS
0
MSC+    ; MSR+
MSC+    ; MSR+
MSC+     ; MSR+
RCL 00
ENTER
SIN
X<>Y
COS
MSC+    ; MSR+
X<>Y
MSC+     ; MSR+
0
MSC+     ; MSR+
RDN
CHS
MSC+    ; MSR+
X<>Y
MS
RTN            ; VERIFIED 9/17/16


LBL *ROTZ        ;        | COS(T) -SIN(T)  0  |
STO 00            ;        |                    |    
3.003            ; Rz(T) =       | SIN(T)  COS(T)  0  |
MATDIM            ;        |                    |    
0            ;        |   0       0     1  |
MSIJ
RCL 00
ENTER
SIN
X<>Y
COS
MSC+    ;    MSR+
X<>Y
MSC+    ;    MSR+
0
MSC+    ;    MSR+
RDN
CHS
MSC+    ;    MSR+
X<>Y
MSC+    ;    MSR+
0
MSC+    ;    MSR+
MSC+    ;    MSR+
MSC+    ;    MSR+
1
MS
RTN            ; VERIFIED 9/17/2016

LBL *ROTY        ;        | COS(T)   0   SIN(T) |
STO 00            ;        |                     |
3.003            ; Ry(T) =       |    0     1     0    |
MATDIM            ;         |                     |
0            ;               |-SIN(T)   0   COS(T) |
MSIJ
RCL 00
ENTER
SIN
X<>Y
COS
MSC+
0
MSC+
X<>Y
MSC+
X<>Z
MSC+
1
MSC+
RDN
MSC+
X<>Z
MSC+
RDN
MS
RTN

LBL *ROT1        ;         |  1     0     0     | 
STO 00            ;        |                    |        
3.003            ; R1(T) =     |  0  COS(T)  SIN(T) |    
MATDIM            ;         |                    |
0            ;         |  0 -SIN(T)  COS(T) |
MSIJ
1
MSC+    ;
0
MSC+    ; 
MSC+    ; 
MSC+     ; 
RCL 00
ENTER
SIN
CHS
X<>Y
COS
MSC+    ; 
X<>Y    
MSC+     ; 
0
MSC+     ; 
RDN
CHS
MSC+    ; 
X<>Y
MS
RTN    

LBL *ROT3        ;        | COS(T)  SIN(T)  0  |
STO 00            ;        |                    |    
3.003            ; R3(T) =       | -SIN(T) COS(T)  0  |
MATDIM            ;        |                    |    
0            ;        |   0       0     1  |
MSIJ
RCL 00
ENTER
SIN
CHS
X<>Y
COS
MSC+    ;    
X<>Y
MSC+    ;
0
MSC+    ;    
RDN
CHS
MSC+    ;    
X<>Y
MSC+    ;    
0
MSC+    ;    
MSC+    ;    
MSC+    ;    
1
MS
RTN
;
;
;            
LBL *ROT2        ;        | COS(T)   0   -SIN(T) |
STO 00            ;        |                      |
3.003            ; R2(T) =       |    0     1     0     |
MATDIM            ;         |                      |
0            ;               |SIN(T)   0   COS(T)   |
MSIJ
RCL 00
ENTER
SIN
;;  CHS
X<>Y
COS
MSC+
0
MSC+
X<>Z
MSC+
X<>Z
MSC+
1
MSC+
RDN
MSC+
X<>Z
CHS
MSC+
X<>Z
MSC+
RDN
MS
RTN

;
; RE = 6378.137
; RP = 6256.752
;
; D  = SQRT(RE*RE*CL*CL + RP*RP*SL*SL)
; Rx = RE*RE/D + HT: Rz = RP*RP/D + HT
;
LBL *RADIUS
6378.137        ; RADIUS OF EARTH AT EQUATOR 
X^2            ; X=XX
STO 07            ; [OX]
STO 08            ; [OY]
6256.752        ; RADIUS OF EARTH THRU POLES 
X^2            ; 
STO 09            ; [OZ]          
RCL 30            ; [OBSLAT]
COS
X^2
RCL 07
*
RCL 30
SIN
X^2
RCL 09
+
SQRT
ST/ 07
ST/ 08
ST/ 09
RCL 40            ; [OBSHGT]
1000
/
ST+ 07            ; [OX]
ST+ 08            ; [OY]
ST+ 09            ; [OZ]
RTN
LBL *OBSXYZ
"ENU"
3.001
MSIJ
MRR+            ; UX
ST* 07            ; OPOS,X
MRR+            ; UY
ST* 08            ; OPOS,Y
MRR+            ; UZ
ST* 09            ; OPOS,Z
RTN
LBL *OBSVEL
RCL 08
STO 10
RCL 07
STO 11
CLX
STO 12
PI                 ; ERROR!!! CALC IN DEGREES
2 
* 
365.2421874 
/ 
/ 
ST* 11 
* 
+ 
86400 
ST* 11 
CHS 
ST* 10 
RTN 
; Calculate Satellite Position at DN,TN
; T  = (DN - DE) + (TN-TE) Elapsed T since epoch, days

LBL *MA+ORB
RCL 19                ; EPYEAR
1E6
/
1.01
+
DATE
DDAYS
RCL 20                ; EPTIME
INT
- 
TIME
24
/
RCL 20
FRC
-
+
STO 16                ; ELAPST SINCE EPOCH, DAYS
; DRAG COEFF = -2*M2/MM/3: (Angular momentum rate)/(Ang mom)  s^-1
RCL 27                ; MMDOT2 
-2
*
RCL 26                ; MMDOT1
/
3
/
*
; LINEAR DRAG TERMS KD = 1+4*DT:KDP= 1-7*DT
; Mean anomaly at YR,TN M = MA + MM*T*(1-3*DT)
STO 40                ; MEANAT
STO 41                ; KD
STO 42                ; KDP
4 
ST* 41                ; KD
-7
ST* 42                ; KDP
-3
ST* 40                ; MEANAT
1 
ST+ 41                ; KD
ST+ 42                ; KDP
ST+ 40                ; MEANAT
RCL 16                ; ELAPST
ST* 40                ; MEANAT
RCL 25                ; MMDOT1
ST* 40                ; MEANAT
RCL 24                ; MEANAN
ST+ 40                ; MEANAT
RCL 40                ; MEANAT
RTN
STOP
360
/
INT
ENTER
360
*
ST- 40                ; MEANAT
X<>Y
RCL 28                ; ORBITN
+
STO 17                ; CURORB
RTN

 2100 EA = M:                 REM Initial solution
 2110 REPEAT
 2120   C = COS(EA): S = SIN(EA): DNOM=1-EC*C
 2130   D = (EA-EC*S-M)/DNOM:   REM Change to EA for better solution
 2140   EA = EA - D:            REM by this amount
 2150 UNTIL ABS(D) < 1E-5:      REM Until converged

LBL *SOLVEA
RCL 40
STO 01
STO 02
"*KEPLE"
STO 06
XEQ SOL                ; IMPORTANT - MY HP41CX HAS BOTH MATH/STAT AND 
                ; ADVANTAGE.  REMOVE MATH MODULE WHEN ENTERING
                ; INSTRUCTION.  SHOULD BE XROM XX

                ; DISREGARD USING MATH SOL
RTN
LBL "*KEPLE"
;
;
LBL *KEPLER
;
;
; M = EA - EC*SIN(EA)
ENTER
SIN
X<>Y
RCL 23 ; ECCENTRICITY
*
-
RCL 40 ; MEANAT 
-
RTN
;
; ADVANTAGE <SOLVE> FUNCTION CONSUMES 13 REGISTERS
; MATH      <SOLVE> FUNCTION CONSUMES 7  REGISTERS
; NOTE: CHECK WHEN VECTORS COMPUTED
; 
;    RCL 41                ; [M]
;    STO 32                ; [LAMBDA]
;    
;    LBL 60
;    RCL 32                ; [LAMBDA]
;    RCL 32                ; [LAMBDA]
;    SIN
;    RCL 23                ; [ECCENT]
;    -
;    RCL 41
;    -
;    1
;    RCL 23                ; [ECCENT]
;    RCL 32                ; [LAMBDA]
;    COS
;    *
;    -
;    /
;    ST- 32                ; [LAMBDA]
;    ABS
;    1E-5
;    X>Y?
;    GTO 60
;    RTN
;
; Cambridge UK 52.2053? N, 0.1218? E
;
;
LBL **TEST
1990 
STO 19                ; EPYEAR
191.145409
STO 20                ; EPOTIM
59.9975
STO 21                ; INCLIN
146.4527
STO 22                ; RAAN
0.6986        
STO 23                ; ECCENT
231.0027
STO 24                ; PERIGE
43.2637 
STO 25                ; MEANAN
2.09695848
STO 26                ; MMDOT1
1E-8 
STO 27                ; MMDOT2
1585
STO 29                ; ORBITN
52.21
STO 30
0.06
STO 31
79
STO 39
RTN
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