(50g) Week day / Season begin / Mean / True ecliptic / Julian Day / Astron Nutation

[Gil]

HP49-50G

Just changed the title, as the prog calculates also the week day (Sunday = 0, Monday = 1,..., Saturday = 6) for arg yyyy.mmdd, with year >= -4713.

To calculate Earth axial tilt,
indicate

year.mmdd (stack level 2)
H.mmss (stack level 1).

Then press
—>epsilon.

Note
EPSILON.0 is the mean ecliptic,
whereas EPSILON is the true ecliptic value, which takes into account the nutation.

Accurateness
is within 0.01", according to Astronomical Algorithms, from Jean Meeus.

Apparently, most figures published in Internet give approximate or wrong values, in particular regarding the arctic circle (90 - mean/real axial tilt).
Please then check with professional astronomical application before using it on a large scale.

Season beginning
was included here,
accurateness within 60".

Juste give for that :
yyyy SEASON

Commentaries or corrections welcome.

Regards, Gil

[Gil]

Here are the codes.

—>epsilon
\<< "
2 Inputs
:
. 
y.mmdd

. 
h.mmsss 
[in TD]
" DROP DEG \->T \->D \->M \->M\180 \->F \->\GW \->\GD\165 \->\Ge0 \->\GD\Ge \Ge0 \GD\Ge HMS+ DUP '\Ge' STO "\Ge.True D.mmss" \->TAG
\>>


—>T
\<< \->JD + 2451545 - 36525 / \->NUM DUP 'T' STO "T" \->TAG
\>>

—>D
\<< '297.85036+445267.11148*T-.0019142*T^2+T^3/189474' \->NUM 360 MOD \->HMS DUP 'D' STO "D D.mmss" \->TAG
\>>

—>M
\<< '357.52772+35999.05034*T-.0001603*T^2-T^3/300000.' \->NUM 360 MOD \->HMS DUP 'M' STO "M D.mmss" \->TAG
\>>

—>M'
\<< '134.96298+477198.867398*T+.0086972*T^2+T^3/56250' \->NUM 360 MOD \->HMS DUP 'M\180' STO "M\180 D.mmss" \->TAG
\>>

—>F
\<< '93.27191+483202.017538*T-.0036825*T^2+T^3/327270' \->NUM 360 MOD \->HMS DUP 'F' STO "F D.mmss" \->TAG
\>>

—>GW
\<< '125.04452-1934.136261*T+.0020708*T^2+T^3/450000.' \->NUM 360 MOD \->HMS DUP '\GW' STO "\GW D.mmss" \->TAG
\>>


—>¥
\<< D HMS\-> M HMS\-> M\180 HMS\-> F HMS\-> \GW HMS\-> \-> D M M\180 F \GW
\<< 0 1 63
FOR i D T22A { i 1 } GET * M T22A { i 2 } GET * + M\180 T22A { i 3 } GET * + F T22A { i 4 } GET * + \GW T22A { i 5 } GET * + SIN T22A { i 6 } GET T22A { i 7 } GET T * + * +
NEXT 10000 / DUP '\GD\165' STO "\GD\165.Nut.Long s.ss" \->TAG
\>>
\>>

T22A
[[ 0 0 0 0 1 -171996 -174.2 92025 8.9 ]
[ -2 0 0 2 2 -13187 -1.6 5736 -3.1 ]
[ 0 0 0 2 2 -2274 -.2 977 -.5 ]
[ 0 0 0 0 2 2062 .2 -895 .5 ]
[ 0 1 0 0 0 1426 -3.4 54 -.1 ]
[ 0 0 1 0 0 712 .1 -7 0 ]
[ -2 1 0 2 2 -517 1.2 224 -.6 ]
[ 0 0 0 2 1 -386 -.4 200 0 ]
[ 0 0 1 2 2 -301 0 129 -.1 ]
[ -2 -1 0 2 2 217 -.5 -95 .3 ]
[ -2 0 1 0 0 -158 0 0 0 ]
[ -2 0 0 2 1 129 .1 -70 0 ]
[ 0 0 -1 2 2 123 0 -53 0 ]
[ 2 0 0 0 0 63 0 0 0 ]
[ 0 0 1 0 1 63 .1 -33 0 ]
[ 2 0 -1 2 2 -59 0 26 0 ]
[ 0 0 -1 0 1 -58 -.1 32 0 ]
[ 0 0 1 2 1 -51 0 27 0 ]
[ -2 0 2 0 0 48 0 0 0 ]
[ 0 0 -2 2 1 46 0 -24 0 ]
[ 2 0 0 2 2 -38 0 16 0 ]
[ 0 0 2 2 2 -31 0 13 0 ]
[ 0 0 2 0 0 29 0 0 0 ]
[ -2 0 1 2 2 29 0 -12 0 ]
[ 0 0 0 2 0 26 0 0 0 ]
[ -2 0 0 2 0 -22 0 0 0 ]
[ 0 0 -1 2 1 21 0 -10 0 ]
[ 0 2 0 0 0 17 -.1 0 0 ]
[ 2 0 -1 0 1 16 0 -8 0 ]
[ -2 2 0 2 2 -16 .1 7 0 ]
[ 0 1 0 0 1 -15 0 9 0 ]
[ -2 0 1 0 1 -13 0 7 0 ]
[ 0 -1 0 0 1 -12 0 6 0 ]
[ 0 0 2 -2 0 11 0 0 0 ]
[ 2 0 -1 2 1 -10 0 5 0 ]
[ 2 0 1 2 2 -8 0 3 0 ]
[ 0 1 0 2 2 7 0 -3 0 ]
[ -2 1 1 0 0 -7 0 0 0 ]
[ 0 -1 0 2 2 -7 0 3 0 ]
[ 2 0 0 2 1 -7 0 3 0 ]
[ 2 0 1 0 0 6 0 0 0 ]
[ -2 0 2 2 2 6 0 -3 0 ]
[ -2 0 1 2 1 6 0 -3 0 ]
[ 2 0 -2 0 1 -6 0 3 0 ]
[ 2 0 0 0 1 -6 0 3 0 ]
[ 0 -1 1 0 0 5 0 0 0 ]
[ -2 -1 0 2 1 -5 0 3 0 ]
[ -2 0 0 0 1 -5 0 3 0 ]
[ 0 0 2 2 1 -5 0 3 0 ]
[ -2 0 2 0 1 4 0 0 0 ]
[ -2 1 0 2 1 4 0 0 0 ]
[ 0 0 1 -2 0 4 0 0 0 ]
[ -1 0 1 0 0 -4 0 0 0 ]
[ -2 1 0 0 0 -4 0 0 0 ]
[ 1 0 0 0 0 -4 0 0 0 ]
[ 0 0 1 2 0 3 0 0 0 ]
[ 0 0 -2 2 2 -3 0 0 0 ]
[ -1 -1 1 0 0 -3 0 0 0 ]
[ 0 1 1 0 0 -3 0 0 0 ]
[ 0 -1 1 2 2 -3 0 0 0 ]
[ 2 -1 -1 2 2 -3 0 0 0 ]
[ 0 0 3 2 2 -3 0 0 0 ]
[ 2 -1 0 2 2 -3 0 0 0 ]]

—>GD\Ge
\<< D HMS\-> M HMS\-> M\180 HMS\-> F HMS\-> \GW HMS\-> \-> D M M\180 F \GW
\<< 0 1 63
FOR i D T22A { i 1 } GET * M T22A { i 2 } GET * + M\180 T22A { i 3 } GET * + F T22A { i 4 } GET * + \GW T22A { i 5 } GET * + COS T22A { i 8 } GET T22A { i 9 } GET T * + * +
NEXT 100000000 / DUP '\GD\Ge' STO 10000 * "\GD\Ge.Nut.Obl s.ss" \->TAG
\>>
\>>

—>Ge0
\<< T 100 / \-> U '-4680.93*U-1.55*U^2+1999.25*U^3-51.38*U^4-249.67*U^5-39.05*U^6+7.12*U^7+27.87*U^8+5.79*U^9+2.45*U^10' \->NUM 10000 / 23.2621448 + DUP '\Ge0' STO "\Ge0.Mean D.mmss" \->TAG
\>>

—>delta.T
\<< \-> t
\<< t 2005 < t 2050 > OR
IF
THEN "Form.NOT.avail"
ELSE t 2000 - 't' STO '62.92+.32217*t+.005589*t^2' EVAL 2 RND "\GDT(s)=TAI-TUC" \->TAG
END
\>>
\>>

—>JD
\<< "
2 Inputs
:
. 
y.mmddd

. 
h.mmsss 
[in TD]
" DROP STD DUP2 SWAP 0 0 \-> h.mmsss date A B
\<< date IP date FP 100 * ABS DUP FP 100 * SWAP IP SWAP \-> y m d
\<<
IF m 2 \<=
THEN y 1 - 'y' STO m 12 + 'm' STO
END y 100 / IP 'A' STO
IF date 1582.1004 \<=
THEN 0
ELSE 2 A - A 4 / IP +
END 'B' STO 365.25 y 4716 + * IP 30.6001 m 1 + * IP + d + B + 1524.5 - h.mmsss 12 \>=
IF
THEN .5 + "JD" \->TAG h.mmsss 12 -
ELSE IP "JD" \->TAG h.mmsss 12 +
END HMS\-> 24 / "+JD" \->TAG
\>>
\>>
\>>

JD—>
\<< "
2 Inputs
:

 
. 
JD 
IP!


. 
JD 
FP!


" DROP STD DUP2 \-> Z F
\<< .5 F + DUP FP 'F' STO 'Z' STO+ 0 0 0 0 0 0 0 0 0 0 \-> \Ga A B C D E m d y s
\<<
IF Z 2291161 <
THEN Z
ELSE Z 1867216.25 - 36524.25 / IP '\Ga' STO Z 1 + \Ga + \Ga 4 / IP -
END 'A' STO A 1524 + 'B' STO B 122.1 - 365.25 / IP 'C' STO 365.25 C * IP 'D' STO B D - 30.6001 / IP 'E' STO B D - 30.6001 E * IP - IP 'd' STO
IF E 14 <
THEN E 1 -
ELSE E 13 -
END 'm' STO m 2 >
IF
THEN C 4716 -
ELSE C 4715 -
END 'y' STO y SIGN 's' STO y ABS 'y' STO y m 100 / + d 10000 / + s * "y.mmddd" \->TAG F 24 * \->HMS "+ TD h.mmss" \->TAG
\>>
\>>
\>>

SEASON
\<< \-> y
\<< y -1000 < y 3000 > OR "Not very accurate" 1 IFTE DEG y 1000. /
[[ 485 ]
[ 203 ]
[ 199 ]
[ 182 ]
[ 156 ]
[ 136 ]
[ 77 ]
[ 74 ]
[ 70 ]
[ 58 ]
[ 52 ]
[ 50 ]
[ 45 ]
[ 44 ]
[ 29 ]
[ 18 ]
[ 17 ]
[ 16 ]
[ 14 ]
[ 12 ]
[ 12 ]
[ 12 ]
[ 9 ]
[ 8 ]]
[[ 324.96 ]
[ 337.23 ]
[ 342.08 ]
[ 27.85 ]
[ 73.14 ]
[ 171.52 ]
[ 222.54 ]
[ 296.72 ]
[ 243.58 ]
[ 119.81 ]
[ 297.17 ]
[ 21.02 ]
[ 247.54 ]
[ 325.15 ]
[ 60.93 ]
[ 155.12 ]
[ 288.79 ]
[ 198.04 ]
[ 199.76 ]
[ 95.39 ]
[ 287.11 ]
[ 320.81 ]
[ 227.73 ]
[ 15.45 ]]
[[ 1934.136 ]
[ 32964.467 ]
[ 20.186 ]
[ 445267.112 ]
[ 45036.886 ]
[ 22518.443 ]
[ 65928.934 ]
[ 3034.906 ]
[ 9037.513 ]
[ 33718.147 ]
[ 150.678 ]
[ 2281.226 ]
[ 29929.562 ]
[ 31555.956 ]
[ 4443.417 ]
[ 67555.328 ]
[ 4562.452 ]
[ 62894.029 ]
[ 31436.921 ]
[ 14577.848 ]
[ 31931.756 ]
[ 34777.259 ]
[ 1222.114 ]
[ 16859.074 ]] 0 { } { } { } { } \-> Y A B C JDE0 T W \GD\Gl S
\<<
IF y 1000 \<=
THEN '1721139.29189+365242.1374*Y+.06134*Y^2+.00111*Y^3-.00071*Y^4' EVAL '1721233.25401+365241.72562*Y-.05323*Y^2+.00907*Y^3+.00025*Y^4' EVAL '1721325.70455+365242.49558*Y-.11677*Y^2-.00297*Y^3+.00074*Y^4' EVAL '1721414.39987+365242.88257*Y-.00769*Y^2-.00933*Y^3-.00006*Y^4' EVAL
ELSE Y 2 - 'Y' STO '2451623.80984+365242.37404*Y+.05169*Y^2-.00411*Y^3-.00057*Y^4' EVAL '2451716.56767+365241.62603*Y+.00325*Y^2+.00888*Y^3-.0003*Y^4' EVAL '2451810.21715+365242.01767*Y-.11575*Y^2+.00337*Y^3+.00078*Y^4' EVAL '2451900.05952+365242.74049*Y-.06223*Y^2-.00823*Y^3+.00032*Y^4' EVAL
END 4 \->LIST 'JDE0' STO 1 4
FOR i T JDE0 i GET 2451545 - 36525 / + 'T' STO W T i GET 35999.373 * 2.47 - + 'W' STO \GD\Gl 1 .0334 W i GET COS * + .0007 W i GET 2 * COS * + + '\GD\Gl' STO S 0 1 24
FOR j A j GET B j GET C j GET T i GET * + COS * +
NEXT + 'S' STO JDE0 i GET S i GET .00001 * \GD\Gl i GET / + DUP IP SWAP FP JD\-> 4 ROLL 4 ROLL DROP2 2 \->LIST
NEXT
\>>
\>> 5 ROLL DUP 1 == DROPN
\>>

Regards,
Gil

[Gil]

HP49-50G
Version 4
2 programs :
- SEASON begin
- Earth axial tilt.

- SEASON
Give chosen year with four digits like yyyy
Then press SEASON

- Earth axial tilt
Indicate
year.mmdd (stack level 2) [example 2921.0131 ENTER]
H.mmss (stack level 1) [for 0 a.m., put 0 ENTER]
Then press
—>epsilon.

This Version 4 includes different astronomical theories:
- 80 for IAU 1980
- 86 for Laskar 1986
- 00 for IAU Series 2000B
- 03 for IAU 2006, P03 model
if you want to check some published results like the ones given by on-line calculators
such as
http://www.neoprogrammics.com/nutations/...980_2000b/
that uses a mix of 80/03/06, though since 2006 IAU2006 recommends to use P03 model, in particular for epsilon_mean (and not Laskar's 10-degrees polynom).

Here are the codes:

"'
SEASON
'"
"<< -> y
<< y -1000 < y 3000 > OR \"Not very accurate\" 1 IFTE DEG y 1000. /
[[ 485 ]
[ 203 ]
[ 199 ]
[ 182 ]
[ 156 ]
[ 136 ]
[ 77 ]
[ 74 ]
[ 70 ]
[ 58 ]
[ 52 ]
[ 50 ]
[ 45 ]
[ 44 ]
[ 29 ]
[ 18 ]
[ 17 ]
[ 16 ]
[ 14 ]
[ 12 ]
[ 12 ]
[ 12 ]
[ 9 ]
[ 8 ]]
[[ 324.96 ]
[ 337.23 ]
[ 342.08 ]
[ 27.85 ]
[ 73.14 ]
[ 171.52 ]
[ 222.54 ]
[ 296.72 ]
[ 243.58 ]
[ 119.81 ]
[ 297.17 ]
[ 21.02 ]
[ 247.54 ]
[ 325.15 ]
[ 60.93 ]
[ 155.12 ]
[ 288.79 ]
[ 198.04 ]
[ 199.76 ]
[ 95.39 ]
[ 287.11 ]
[ 320.81 ]
[ 227.73 ]
[ 15.45 ]]
[[ 1934.136 ]
[ 32964.467 ]
[ 20.186 ]
[ 445267.112 ]
[ 45036.886 ]
[ 22518.443 ]
[ 65928.934 ]
[ 3034.906 ]
[ 9037.513 ]
[ 33718.147 ]
[ 150.678 ]
[ 2281.226 ]
[ 29929.562 ]
[ 31555.956 ]
[ 4443.417 ]
[ 67555.328 ]
[ 4562.452 ]
[ 62894.029 ]
[ 31436.921 ]
[ 14577.848 ]
[ 31931.756 ]
[ 34777.259 ]
[ 1222.114 ]
[ 16859.074 ]] 0 { } { } { } { } -> Y A B C JDE0 T W GDGl S
<<
IF y 1000 <=
THEN '1721139.29189+365242.1374*Y+.06134*Y^2+.00111*Y^3-.00071*Y^4' EVAL '1721233.25401+365241.72562*Y-.05323*Y^2+.00907*Y^3+.00025*Y^4' EVAL '1721325.70455+365242.49558*Y-.11677*Y^2-.00297*Y^3+.00074*Y^4' EVAL '1721414.39987+365242.88257*Y-.00769*Y^2-.00933*Y^3-.00006*Y^4' EVAL
ELSE Y 2 - 'Y' STO '2451623.80984+365242.37404*Y+.05169*Y^2-.00411*Y^3-.00057*Y^4' EVAL '2451716.56767+365241.62603*Y+.00325*Y^2+.00888*Y^3-.0003*Y^4' EVAL '2451810.21715+365242.01767*Y-.11575*Y^2+.00337*Y^3+.00078*Y^4' EVAL '2451900.05952+365242.74049*Y-.06223*Y^2-.00823*Y^3+.00032*Y^4' EVAL
END 4 ->LIST 'JDE0' STO 1 4
FOR i T JDE0 i GET 2451545 - 36525 / + 'T' STO W T i GET 35999.373 * 2.47 - + 'W' STO GDGl 1 .0334 W i GET COS * + .0007 W i GET 2 * COS * + + 'GDGl' STO S 0 1 24
FOR j A j GET B j GET C j GET T i GET * + COS * +
NEXT + 'S' STO JDE0 i GET S i GET .00001 * GDGl i GET / + DUP IP SWAP FP JD-> 4 ROLL 4 ROLL DROP2 2 ->LIST
NEXT
>>
>> 5 ROLL DUP 1 == DROPN
>>"


"'
->Ge
'"
"<< \"
2 Inputs
:
. 
y.mmdd

. 
h.mmsss 
[in TD]

\" DROP DEG ->T ->L80 ->L00 ->L18080 ->L18000 ->F80 ->F00 ->D80 ->D00 ->GW80 ->GW00 ->GD16580 ->GD16500 ->GeGm80 ->GeGm86 ->GeGm03 ->GDGe80 ->GDGe00 ->Ge80 ->Ge86.80 ->Ge86.00 ->Ge03.00 GeGm03 \"
GeGm
03^o180s\" ->TAG GDGe00 10000 * \"
GDGe
00[s]\" ->TAG
>>"

"'JD->'"
"<< \"
2 Inputs
:

 
. 
JD 
IP!


. 
JD 
FP!


\" DROP STD DUP2 -> Z F
<< .5 F + DUP FP 'F' STO 'Z' STO+ 0 0 0 0 0 0 0 0 0 0 -> Ga A B C D E m d y s
<<
IF Z 2291161 <
THEN Z
ELSE Z 1867216.25 - 36524.25 / IP 'Ga' STO Z 1 + Ga + Ga 4 / IP -
END 'A' STO A 1524 + 'B' STO B 122.1 - 365.25 / IP 'C' STO 365.25 C * IP 'D' STO B D - 30.6001 / IP 'E' STO B D - 30.6001 E * IP - IP 'd' STO
IF E 14 <
THEN E 1 -
ELSE E 13 -
END 'm' STO m 2 >
IF
THEN C 4716 -
ELSE C 4715 -
END 'y' STO y SIGN 's' STO y ABS 'y' STO y m 100 / + d 10000 / + s * \"y.mmddd\" ->TAG F 24 * ->HMS \"+ TD h.mmss\" ->TAG
>>
>>
>>"

"'
->JD
'"
"<< \"
2 Inputs
:
. 
y.mmddd

. 
h.mmsss 
[in TD]
\" DROP STD DUP2 SWAP 0 0 -> h.mmsss date A B
<< date IP date FP 100 * ABS DUP FP 100 * SWAP IP SWAP -> y m d
<<
IF m 2 <=
THEN y 1 - 'y' STO m 12 + 'm' STO
END y 100 / IP 'A' STO
IF date 1582.1004 <=
THEN 0
ELSE 2 A - A 4 / IP +
END 'B' STO 365.25 y 4716 + * IP 30.6001 m 1 + * IP + d + B + 1524.5 - h.mmsss 12 >=
IF
THEN .5 + \"JD\" ->TAG h.mmsss 12 -
ELSE IP \"JD\" ->TAG h.mmsss 12 +
END HMS-> 24 / \"+JD\" ->TAG
>>
>>
>>"

"'
->GDT
'"
"<< -> t
<< t 2005 < t 2050 > OR
IF
THEN \"Form.NOT.avail\"
ELSE t 2000 - 't' STO '62.92+.32217*t+.005589*t^2' EVAL 2 RND \"GDT(s)=TAI(TD)-TUC\" ->TAG
END
>>
>>"

"
'->T
'"
"<< ->JD + DUP 'JD' STO \"JD\" ->TAG DUP 2451545 - 36525 / ->NUM DUP 'T' STO \"T\" ->TAG
>>"

"'
->L80
'"
"<< '134.96298+477198.867398*T+.0086972*T^2+T^3/56250' ->NUM 360 MOD ->HMS DUP 'L80' STO \"L80^o's\" ->TAG
>>"

"'
->L00
'"
"<< '(485868.249036+1717915923*T+.2178*T+31.8792*T^2+.051635*T^3-.0002447*T^4)/3600' ->NUM 360 MOD ->HMS DUP 'L00' STO \"L00^o's\" ->TAG
>>"

"'
->L18080
'"
"<< '357.52772+35999.05034*T-.0001603*T^2-T^3/300000.' ->NUM 360 MOD ->HMS DUP 'L18080' STO \"L18080^o's\" ->TAG
>>"

"'
->L18000
'"
"<< '(1287104.79305+129596581*T+.0481*T-.5532*T^2+.000136*T^3-.00001149*T^4)/3600.' ->NUM 360 MOD ->HMS DUP 'L18000' STO \"L18000^o's\" ->TAG
>>"

"'
->F80
'"
"<< '93.27191+483202.017538*T-.0036825*T^2+T^3/327270' ->NUM 360 MOD ->HMS DUP 'F80' STO \"F80^o's\" ->TAG
>>"

"'
->F00
'"
"<< '(335779.526232+1739527262*T+.8478*T-12.7512*T^2-.001037*T^3+.00000417*T^4)/3600' ->NUM 360 MOD ->HMS DUP 'F00' STO \"F00^o's\" ->TAG
>>"

"'
->D80
'"
"<< '297.85036+445267.11148*T-.0019142*T^2+T^3/189474' ->NUM 360 MOD ->HMS DUP 'D80' STO \"D80^o's\" ->TAG
>>"

"'
->D00
'"
"<< '(1072260.70369+1602961601*T+.209*T-6.3706*T^2+.006593*T^3-.00003169*T^4)/3600' ->NUM 360 MOD ->HMS DUP 'D00' STO \"D00^o's\" ->TAG
>>"

"'
->GW80'"
"<< '125.04452-1934.136261*T+.0020708*T^2+T^3/450000.' ->NUM 360 MOD ->HMS DUP 'GW80' STO \"GW80^o's\" ->TAG
>>"

"'
->GW00
'"
"<< '(450160.398036-6962890.5431*T+7.4722*T^2+.007702*T^3-.00005939*T^4)/3600' ->NUM 360 MOD ->HMS DUP 'GW00' STO \"GW00^o's\" ->TAG
>>"

"'
->GD16580
'"
"<< D80 HMS-> L18080 HMS-> L80 HMS-> F80 HMS-> GW80 HMS-> -> D L180 L F GW
<< 0 1 63
FOR i D T80 { i 1 } GET * L180 T80 { i 2 } GET * + L T80 { i 3 } GET * + F T80 { i 4 } GET * + GW T80 { i 5 } GET * + SIN T80 { i 6 } GET T80 { i 7 } GET T * + * +
NEXT 100000000 / DUP 'GD16580' STO 10000 * \"GD16580[s]\" ->TAG
>>
>>"

"'
->GD16500
'"
"<< DEG L00 HMS-> L18000 HMS-> F00 HMS-> D00 HMS-> GW00 HMS-> -> L L180 F D GW
<< 0 1 77
FOR i L 'T00' { i 1 } GET * L180 'T00' { i 2 } GET * + F 'T00' { i 3 } GET * + D 'T00' { i 4 } GET * + GW 'T00' { i 5 } GET * + DUP COS 'T00' { i 8 } GET * SWAP SIN 'T00' { i 6 } GET 'T00' { i 7 } GET T * + * + +
NEXT 100000000000 / DUP 'GD16500' STO 10000 * \"GD16500[s]\" ->TAG
>>
>>"

"'
->GeGm80
'"
"<< '-46.815*T-.00059*T^2+.001813*T^3' ->NUM 3600 / ->HMS 23.2621448 HMS+ DUP 'GeGm80' STO \"GeGm80^o180s\" ->TAG
>>"

"'
->GeGm86
'"
"<< T 100 / -> U '-4680.93*U-1.55*U^2+1999.25*U^3-51.38*U^4-249.67*U^5-39.05*U^6+7.12*U^7+27.87*U^8+5.79*U^9+2.45*U^10' ->NUM 3600 / ->HMS 23.2621448 HMS+ DUP 'GeGm86' STO \"GeGm86^o180s\" ->TAG
>>"

"'
->GeGm03
'"
"<< '84381.406-46.836769*T-.0001831*T^2+.0020034*T^3-.000000576*T^4-.0000000434*T^5' 3600. / ->NUM ->HMS DUP 'GeGm03' STO \"GeGm03^o180s\" ->TAG
>>"

"'
->GDGe80
'"
"<< D80 HMS-> L18080 HMS-> L80 HMS-> F80 HMS-> GW80 HMS-> -> D L180 L F GW
<< 0 1 63
FOR i D T80 { i 1 } GET * L180 T80 { i 2 } GET * + L T80 { i 3 } GET * + F T80 { i 4 } GET * + GW T80 { i 5 } GET * + COS T80 { i 8 } GET T80 { i 9 } GET T * + * +
NEXT 10000 / 3600 / ->HMS DUP 'GDGe80' STO 10000 * \"GDGe80[s]\" ->TAG
>>
>>"

"'
->GDGe00
'"
"<< DEG L00 HMS-> L18000 HMS-> F00 HMS-> D00 HMS-> GW00 HMS-> -> L L180 F D GW
<< 0 1 77
FOR i L 'T00' { i 1 } GET * L180 'T00' { i 2 } GET * + F 'T00' { i 3 } GET * + D 'T00' { i 4 } GET * + GW 'T00' { i 5 } GET * + DUP SIN 'T00' { i 11 } GET * SWAP COS 'T00' { i 9 } GET 'T00' { i 10 } GET T * + * + +
NEXT 100000000000 / DUP 'GDGe00' STO 10000 * \"GDGe00[s]\" ->TAG
>>
>>"

"'
->Ge80
'"
"<< GeGm80 GDGe80 HMS+ DUP 'Ge80' STO \"Ge80^o180s\" ->TAG
>>"

"'
->Ge86.80
'"
"<< GeGm86 GDGe80 HMS+ DUP 'Ge86.80' STO \"Ge86.80^o180s\" ->TAG
>>"

"'
->Ge86.00
'"
"<< GeGm86 GDGe00 HMS+ DUP 'Ge86.00' STO \"Ge86.00^o180s\" ->TAG
>>"

"'
->Ge03.00
'"
"<< GeGm03 GDGe00 HMS+ DUP 'Ge03.00' STO \"
Ge
03.00^o180s\" ->TAG
>>"

"'
EXPL
'"
"<< \"L : GmAnom Moon
L': GmAnom Sun
F : GmArg Lat Moon
D:GmElongMoon from Sun
GD165:Nutat in Longitude
GDGe:Nutat in Obliquity
GW:GmLongAscendNode Moon
80:IAU1980 00:IAU2000B
86:LASKAR1986 03:P2003\" 1 DISP 7 FREEZE
>>"

"'
T80
'"
"[[ 0 0 0 0 1 -171996 -174.2 92025 8.9 ]
[ -2 0 0 2 2 -13187 -1.6 5736 -3.1 ]
[ 0 0 0 2 2 -2274 -.2 977 -.5 ]
[ 0 0 0 0 2 2062 .2 -895 .5 ]
[ 0 1 0 0 0 1426 -3.4 54 -.1 ]
[ 0 0 1 0 0 712 .1 -7 0 ]
[ -2 1 0 2 2 -517 1.2 224 -.6 ]
[ 0 0 0 2 1 -386 -.4 200 0 ]
[ 0 0 1 2 2 -301 0 129 -.1 ]
[ -2 -1 0 2 2 217 -.5 -95 .3 ]
[ -2 0 1 0 0 -158 0 0 0 ]
[ -2 0 0 2 1 129 .1 -70 0 ]
[ 0 0 -1 2 2 123 0 -53 0 ]
[ 2 0 0 0 0 63 0 0 0 ]
[ 0 0 1 0 1 63 .1 -33 0 ]
[ 2 0 -1 2 2 -59 0 26 0 ]
[ 0 0 -1 0 1 -58 -.1 32 0 ]
[ 0 0 1 2 1 -51 0 27 0 ]
[ -2 0 2 0 0 48 0 0 0 ]
[ 0 0 -2 2 1 46 0 -24 0 ]
[ 2 0 0 2 2 -38 0 16 0 ]
[ 0 0 2 2 2 -31 0 13 0 ]
[ 0 0 2 0 0 29 0 0 0 ]
[ -2 0 1 2 2 29 0 -12 0 ]
[ 0 0 0 2 0 26 0 0 0 ]
[ -2 0 0 2 0 -22 0 0 0 ]
[ 0 0 -1 2 1 21 0 -10 0 ]
[ 0 2 0 0 0 17 -.1 0 0 ]
[ 2 0 -1 0 1 16 0 -8 0 ]
[ -2 2 0 2 2 -16 .1 7 0 ]
[ 0 1 0 0 1 -15 0 9 0 ]
[ -2 0 1 0 1 -13 0 7 0 ]
[ 0 -1 0 0 1 -12 0 6 0 ]
[ 0 0 2 -2 0 11 0 0 0 ]
[ 2 0 -1 2 1 -10 0 5 0 ]
[ 2 0 1 2 2 -8 0 3 0 ]
[ 0 1 0 2 2 7 0 -3 0 ]
[ -2 1 1 0 0 -7 0 0 0 ]
[ 0 -1 0 2 2 -7 0 3 0 ]
[ 2 0 0 2 1 -7 0 3 0 ]
[ 2 0 1 0 0 6 0 0 0 ]
[ -2 0 2 2 2 6 0 -3 0 ]
[ -2 0 1 2 1 6 0 -3 0 ]
[ 2 0 -2 0 1 -6 0 3 0 ]
[ 2 0 0 0 1 -6 0 3 0 ]
[ 0 -1 1 0 0 5 0 0 0 ]
[ -2 -1 0 2 1 -5 0 3 0 ]
[ -2 0 0 0 1 -5 0 3 0 ]
[ 0 0 2 2 1 -5 0 3 0 ]
[ -2 0 2 0 1 4 0 0 0 ]
[ -2 1 0 2 1 4 0 0 0 ]
[ 0 0 1 -2 0 4 0 0 0 ]
[ -1 0 1 0 0 -4 0 0 0 ]
[ -2 1 0 0 0 -4 0 0 0 ]
[ 1 0 0 0 0 -4 0 0 0 ]
[ 0 0 1 2 0 3 0 0 0 ]
[ 0 0 -2 2 2 -3 0 0 0 ]
[ -1 -1 1 0 0 -3 0 0 0 ]
[ 0 1 1 0 0 -3 0 0 0 ]
[ 0 -1 1 2 2 -3 0 0 0 ]
[ 2 -1 -1 2 2 -3 0 0 0 ]
[ 0 0 3 2 2 -3 0 0 0 ]
[ 2 -1 0 2 2 -3 0 0 0 ]]"

"'
T00
'"
"[[ 0 0 0 0 1 -172064161 -174666 33386 92052331 9086 15377 ]
[ 0 0 2 -2 2 -13170906 -1675 13696 5730336 -3015 -4587 ]
[ 0 0 2 0 2 -2276413 -234 2796 978459 -485 1374 ]
[ 0 0 0 0 2 2074554 207 -698 -897492 470 -291 ]
[ 0 1 0 0 0 1475877 -3633 11817 73871 -184 -1924 ]
[ 0 1 2 -2 2 -516821 1226 -524 224386 -677 -174 ]
[ 1 0 0 0 0 711159 73 -872 -6750 0 358 ]
[ 0 0 2 0 1 -387298 -367 380 200728 18 318 ]
[ 1 0 2 0 2 -301461 -36 816 129025 -63 367 ]
[ 0 -1 2 -2 2 215829 -494 111 -95929 299 132 ]
[ 0 0 2 -2 1 128227 137 181 -68982 -9 39 ]
[ -1 0 2 0 2 123457 11 19 -53311 32 -4 ]
[ -1 0 0 2 0 156994 10 -168 -1235 0 82 ]
[ 1 0 0 0 1 63110 63 27 -33228 0 -9 ]
[ -1 0 0 0 1 -57976 -63 -189 31429 0 -75 ]
[ -1 0 2 2 2 -59641 -11 149 25543 -11 66 ]
[ 1 0 2 0 1 -51613 -42 129 26366 0 78 ]
[ -2 0 2 0 1 45893 50 31 -24236 -10 20 ]
[ 0 0 0 2 0 63384 11 -150 -1220 0 29 ]
[ 0 0 2 2 2 -38571 -1 158 16452 -11 68 ]
[ 0 -2 2 -2 2 32481 0 0 -13870 0 0 ]
[ -2 0 0 2 0 -47722 0 -18 477 0 -25 ]
[ 2 0 2 0 2 -31046 -1 131 13238 -11 59 ]
[ 1 0 2 -2 2 28593 0 -1 -12338 10 -3 ]
[ -1 0 2 0 1 20441 21 10 -10758 0 -3 ]
[ 2 0 0 0 0 29243 0 -74 -609 0 13 ]
[ 0 0 2 0 0 25887 0 -66 -550 0 11 ]
[ 0 1 0 0 1 -14053 -25 79 8551 -2 -45 ]
[ -1 0 0 2 1 15164 10 11 -8001 0 -1 ]
[ 0 2 2 -2 2 -15794 72 -16 6850 -42 -5 ]
[ 0 0 -2 2 0 21783 0 13 -167 0 13 ]
[ 1 0 0 -2 1 -12873 -10 -37 6953 0 -14 ]
[ 0 -1 0 0 1 -12654 11 63 6415 0 26 ]
[ -1 0 2 2 1 -10204 0 25 5222 0 15 ]
[ 0 2 0 0 0 16707 -85 -10 168 -1 10 ]
[ 1 0 2 2 2 -7691 0 44 3268 0 19 ]
[ -2 0 2 0 0 -11024 0 -14 104 0 2 ]
[ 0 1 2 0 2 7566 -21 -11 -3250 0 -5 ]
[ 0 0 2 2 1 -6637 -11 25 3353 0 14 ]
[ 0 -1 2 0 2 -7141 21 8 3070 0 4 ]
[ 0 0 0 2 1 -6302 -11 2 3272 0 4 ]
[ 1 0 2 -2 1 5800 10 2 -3045 0 -1 ]
[ 2 0 2 -2 2 6443 0 -7 -2768 0 -4 ]
[ -2 0 0 2 1 -5774 -11 -15 3041 0 -5 ]
[ 2 0 2 0 1 -5350 0 21 2695 0 12 ]
[ 0 -1 2 -2 1 -4752 -11 -3 2719 0 -3 ]
[ 0 0 0 -2 1 -4940 -11 -21 2720 0 -9 ]
[ -1 -1 0 2 0 7350 0 -8 -51 0 4 ]
[ 2 0 0 -2 1 4065 0 6 -2206 0 1 ]
[ 1 0 0 2 0 6579 0 -24 -199 0 2 ]
[ 0 1 2 -2 1 3579 0 5 -1900 0 1 ]
[ 1 -1 0 0 0 4725 0 -6 -41 0 3 ]
[ -2 0 2 0 2 -3075 0 -2 1313 0 -1 ]
[ 3 0 2 0 2 -2904 0 15 1233 0 7 ]
[ 0 -1 0 2 0 4348 0 -10 -81 0 2 ]
[ 1 -1 2 0 2 -2878 0 8 1232 0 4 ]
[ 0 0 0 1 0 -4230 0 5 -20 0 -2 ]
[ -1 -1 2 2 2 -2819 0 7 1207 0 3 ]
[ -1 0 2 0 0 -4056 0 5 40 0 -2 ]
[ 0 -1 2 2 2 -2647 0 11 1129 0 5 ]
[ -2 0 0 0 1 -2294 0 -10 1266 0 -4 ]
[ 1 1 2 0 2 2481 0 -7 -1062 0 -3 ]
[ 2 0 0 0 1 2179 0 -2 -1129 0 -2 ]
[ -1 1 0 1 0 3276 0 1 -9 0 0 ]
[ 1 1 0 0 0 -3389 0 5 35 0 -2 ]
[ 1 0 2 0 0 3339 0 -13 -107 0 1 ]
[ -1 0 2 -2 1 -1987 0 -6 1073 0 -2 ]
[ 1 0 0 0 2 -1981 0 0 854 0 0 ]
[ -1 0 0 1 0 4026 0 -353 -553 0 -139 ]
[ 0 0 2 1 2 1660 0 -5 -710 0 -2 ]
[ -1 0 2 4 2 -1521 0 9 647 0 4 ]
[ -1 1 0 1 1 1314 0 0 -700 0 0 ]
[ 0 -2 2 -2 1 -1283 0 0 672 0 0 ]
[ 1 0 2 2 1 -1331 0 8 663 0 4 ]
[ -2 0 2 2 2 1383 0 -2 -594 0 -2 ]
[ -1 0 0 0 2 1405 0 4 -610 0 2 ]
[ 1 1 2 -2 2 1290 0 0 -556 0 0 ]]"

Below
Other format with missing special characters.
Note : very often the missing character is an arrow, the epsilon (Greek e), the omega (Greek W) or the delta (Greek d).

F80
« *T^2+T^3/327270' NUM 360 MOD HMS DUP 'F80' STO "F80°'s" TAG
»


F00
« '(335779.526232+1739527262*T+.8478*T-12.7512*T^2-.001037*T^3+.00000417*T^4)/3600' NUM 360 MOD HMS DUP 'F00' STO "F00°'s" TAG
»



D80
« '297.85036+445267.11148*T-.0019142*T^2+T^3/189474' NUM 360 MOD HMS DUP 'D80' STO "D80°'s" TAG
»


D00
« '(1072260.70369+1602961601*T+.209*T-6.3706*T^2+.006593*T^3-.00003169*T^4)/3600' NUM 360 MOD HMS DUP 'D00' STO "D00°'s" TAG
»


80
« '125.04452-1934.136261*T+.0020708*T^2+T^3/450000.' NUM 360 MOD HMS DUP '80' STO "80°'s" TAG
»



00
« '(450160.398036-6962890.5431*T+7.4722*T^2+.007702*T^3-.00005939*T^4)/3600' NUM 360 MOD HMS DUP '00' STO "00°'s" TAG
»



›¥80
« D80 HMS L´80 HMS L80 HMS F80 HMS 80 HMS  D L´ L F 
« 0 1 63
FOR i D T80 { i 1 } GET * L´ T80 { i 2 } GET * + L T80 { i 3 } GET * + F T80 { i 4 } GET * +  T80 { i 5 } GET * + SIN T80 { i 6 } GET T80 { i 7 } GET T * + * +
NEXT 100000000 / DUP '›¥80' STO 10000 * "›¥80[s]" TAG
»
»


›¥00
« DEG L00 HMS L´00 HMS F00 HMS D00 HMS 00 HMS  L L´ F D 
« 0 1 77
FOR i L 'T00' { i 1 } GET * L´ 'T00' { i 2 } GET * + F 'T00' { i 3 } GET * + D 'T00' { i 4 } GET * +  'T00' { i 5 } GET * + DUP COS 'T00' { i 8 } GET * SWAP SIN 'T00' { i 6 } GET 'T00' { i 7 } GET T * + * + +
NEXT 100000000000 / DUP '›¥00' STO 10000 * "›¥00[s]" TAG
»
»



“µ80
« '-46.815*T-.00059*T^2+.001813*T^3' NUM 3600 / HMS 23.2621448 HMS+ DUP '“µ80' STO "“µ80°´s" TAG
»



“µ86
« T 100 /  U '-4680.93*U-1.55*U^2+1999.25*U^3-51.38*U^4-249.67*U^5-39.05*U^6+7.12*U^7+27.87*U^8+5.79*U^9+2.45*U^10' NUM 3600 / HMS 23.2621448 HMS+ DUP '“µ86' STO "“µ86°´s" TAG
»


“µ03
« '84381.406-46.836769*T-.0001831*T^2+.0020034*T^3-.000000576*T^4-.0000000434*T^5' 3600. / NUM HMS DUP '“µ03' STO "“µ03°´s" TAG
»



›“80
« D80 HMS L´80 HMS L80 HMS F80 HMS 80 HMS  D L´ L F 
« 0 1 63
FOR i D T80 { i 1 } GET * L´ T80 { i 2 } GET * + L T80 { i 3 } GET * + F T80 { i 4 } GET * +  T80 { i 5 } GET * + COS T80 { i 8 } GET T80 { i 9 } GET T * + * +
NEXT 10000 / 3600 / HMS DUP '›“80' STO 10000 * "›“80[s]" TAG
»
»



›“00
« DEG L00 HMS L´00 HMS F00 HMS D00 HMS 00 HMS  L L´ F D 
« 0 1 77
FOR i L 'T00' { i 1 } GET * L´ 'T00' { i 2 } GET * + F 'T00' { i 3 } GET * + D 'T00' { i 4 } GET * +  'T00' { i 5 } GET * + DUP SIN 'T00' { i 11 } GET * SWAP COS 'T00' { i 9 } GET 'T00' { i 10 } GET T * + * + +
NEXT 100000000000 / DUP '›“00' STO 10000 * "›“00[s]" TAG
»
»



“80
« “µ80 ›“80 HMS+ DUP '“80' STO "“80°´s" TAG
»



“86.80
« “µ86 ›“80 HMS+ DUP '“86.80' STO "“86.80°´s" TAG
»



“86.00
« “µ86 ›“00 HMS+ DUP '“86.00' STO "“86.00°´s" TAG
»



“03.00
« “µ03 ›“00 HMS+ DUP '“03.00' STO "
“
03.00°´s" TAG
»


EXPL
« "L : µAnom Moon
L': µAnom Sun
F : µArg Lat Moon
D:µElongMoon from Sun
ݴ:Nutat in Longitude
›“:Nutat in Obliquity
:µLongAscendNode Moon
80:IAU1980 00:IAU2000B
86:LASKAR1986 03:P2003" 1 DISP 7 FREEZE
»


T80
[[ 0 0 0 0 1 -171996 -174.2 92025 8.9 ]
[ -2 0 0 2 2 -13187 -1.6 5736 -3.1 ]
[ 0 0 0 2 2 -2274 -.2 977 -.5 ]
[ 0 0 0 0 2 2062 .2 -895 .5 ]
[ 0 1 0 0 0 1426 -3.4 54 -.1 ]
[ 0 0 1 0 0 712 .1 -7 0 ]
[ -2 1 0 2 2 -517 1.2 224 -.6 ]
[ 0 0 0 2 1 -386 -.4 200 0 ]
[ 0 0 1 2 2 -301 0 129 -.1 ]
[ -2 -1 0 2 2 217 -.5 -95 .3 ]
[ -2 0 1 0 0 -158 0 0 0 ]
[ -2 0 0 2 1 129 .1 -70 0 ]
[ 0 0 -1 2 2 123 0 -53 0 ]
[ 2 0 0 0 0 63 0 0 0 ]
[ 0 0 1 0 1 63 .1 -33 0 ]
[ 2 0 -1 2 2 -59 0 26 0 ]
[ 0 0 -1 0 1 -58 -.1 32 0 ]
[ 0 0 1 2 1 -51 0 27 0 ]
[ -2 0 2 0 0 48 0 0 0 ]
[ 0 0 -2 2 1 46 0 -24 0 ]
[ 2 0 0 2 2 -38 0 16 0 ]
[ 0 0 2 2 2 -31 0 13 0 ]
[ 0 0 2 0 0 29 0 0 0 ]
[ -2 0 1 2 2 29 0 -12 0 ]
[ 0 0 0 2 0 26 0 0 0 ]
[ -2 0 0 2 0 -22 0 0 0 ]
[ 0 0 -1 2 1 21 0 -10 0 ]
[ 0 2 0 0 0 17 -.1 0 0 ]
[ 2 0 -1 0 1 16 0 -8 0 ]
[ -2 2 0 2 2 -16 .1 7 0 ]
[ 0 1 0 0 1 -15 0 9 0 ]
[ -2 0 1 0 1 -13 0 7 0 ]
[ 0 -1 0 0 1 -12 0 6 0 ]
[ 0 0 2 -2 0 11 0 0 0 ]
[ 2 0 -1 2 1 -10 0 5 0 ]
[ 2 0 1 2 2 -8 0 3 0 ]
[ 0 1 0 2 2 7 0 -3 0 ]
[ -2 1 1 0 0 -7 0 0 0 ]
[ 0 -1 0 2 2 -7 0 3 0 ]
[ 2 0 0 2 1 -7 0 3 0 ]
[ 2 0 1 0 0 6 0 0 0 ]
[ -2 0 2 2 2 6 0 -3 0 ]
[ -2 0 1 2 1 6 0 -3 0 ]
[ 2 0 -2 0 1 -6 0 3 0 ]
[ 2 0 0 0 1 -6 0 3 0 ]
[ 0 -1 1 0 0 5 0 0 0 ]
[ -2 -1 0 2 1 -5 0 3 0 ]
[ -2 0 0 0 1 -5 0 3 0 ]
[ 0 0 2 2 1 -5 0 3 0 ]
[ -2 0 2 0 1 4 0 0 0 ]
[ -2 1 0 2 1 4 0 0 0 ]
[ 0 0 1 -2 0 4 0 0 0 ]
[ -1 0 1 0 0 -4 0 0 0 ]
[ -2 1 0 0 0 -4 0 0 0 ]
[ 1 0 0 0 0 -4 0 0 0 ]
[ 0 0 1 2 0 3 0 0 0 ]
[ 0 0 -2 2 2 -3 0 0 0 ]
[ -1 -1 1 0 0 -3 0 0 0 ]
[ 0 1 1 0 0 -3 0 0 0 ]
[ 0 -1 1 2 2 -3 0 0 0 ]
[ 2 -1 -1 2 2 -3 0 0 0 ]
[ 0 0 3 2 2 -3 0 0 0 ]
[ 2 -1 0 2 2 -3 0 0 0 ]]


T00
[[ 0 0 0 0 1 -172064161 -174666 33386 92052331 9086 15377 ]
[ 0 0 2 -2 2 -13170906 -1675 13696 5730336 -3015 -4587 ]
[ 0 0 2 0 2 -2276413 -234 2796 978459 -485 1374 ]
[ 0 0 0 0 2 2074554 207 -698 -897492 470 -291 ]
[ 0 1 0 0 0 1475877 -3633 11817 73871 -184 -1924 ]
[ 0 1 2 -2 2 -516821 1226 -524 224386 -677 -174 ]
[ 1 0 0 0 0 711159 73 -872 -6750 0 358 ]
[ 0 0 2 0 1 -387298 -367 380 200728 18 318 ]
[ 1 0 2 0 2 -301461 -36 816 129025 -63 367 ]
[ 0 -1 2 -2 2 215829 -494 111 -95929 299 132 ]
[ 0 0 2 -2 1 128227 137 181 -68982 -9 39 ]
[ -1 0 2 0 2 123457 11 19 -53311 32 -4 ]
[ -1 0 0 2 0 156994 10 -168 -1235 0 82 ]
[ 1 0 0 0 1 63110 63 27 -33228 0 -9 ]
[ -1 0 0 0 1 -57976 -63 -189 31429 0 -75 ]
[ -1 0 2 2 2 -59641 -11 149 25543 -11 66 ]
[ 1 0 2 0 1 -51613 -42 129 26366 0 78 ]
[ -2 0 2 0 1 45893 50 31 -24236 -10 20 ]
[ 0 0 0 2 0 63384 11 -150 -1220 0 29 ]
[ 0 0 2 2 2 -38571 -1 158 16452 -11 68 ]
[ 0 -2 2 -2 2 32481 0 0 -13870 0 0 ]
[ -2 0 0 2 0 -47722 0 -18 477 0 -25 ]
[ 2 0 2 0 2 -31046 -1 131 13238 -11 59 ]
[ 1 0 2 -2 2 28593 0 -1 -12338 10 -3 ]
[ -1 0 2 0 1 20441 21 10 -10758 0 -3 ]
[ 2 0 0 0 0 29243 0 -74 -609 0 13 ]
[ 0 0 2 0 0 25887 0 -66 -550 0 11 ]
[ 0 1 0 0 1 -14053 -25 79 8551 -2 -45 ]
[ -1 0 0 2 1 15164 10 11 -8001 0 -1 ]
[ 0 2 2 -2 2 -15794 72 -16 6850 -42 -5 ]
[ 0 0 -2 2 0 21783 0 13 -167 0 13 ]
[ 1 0 0 -2 1 -12873 -10 -37 6953 0 -14 ]
[ 0 -1 0 0 1 -12654 11 63 6415 0 26 ]
[ -1 0 2 2 1 -10204 0 25 5222 0 15 ]
[ 0 2 0 0 0 16707 -85 -10 168 -1 10 ]
[ 1 0 2 2 2 -7691 0 44 3268 0 19 ]
[ -2 0 2 0 0 -11024 0 -14 104 0 2 ]
[ 0 1 2 0 2 7566 -21 -11 -3250 0 -5 ]
[ 0 0 2 2 1 -6637 -11 25 3353 0 14 ]
[ 0 -1 2 0 2 -7141 21 8 3070 0 4 ]
[ 0 0 0 2 1 -6302 -11 2 3272 0 4 ]
[ 1 0 2 -2 1 5800 10 2 -3045 0 -1 ]
[ 2 0 2 -2 2 6443 0 -7 -2768 0 -4 ]
[ -2 0 0 2 1 -5774 -11 -15 3041 0 -5 ]
[ 2 0 2 0 1 -5350 0 21 2695 0 12 ]
[ 0 -1 2 -2 1 -4752 -11 -3 2719 0 -3 ]
[ 0 0 0 -2 1 -4940 -11 -21 2720 0 -9 ]
[ -1 -1 0 2 0 7350 0 -8 -51 0 4 ]
[ 2 0 0 -2 1 4065 0 6 -2206 0 1 ]
[ 1 0 0 2 0 6579 0 -24 -199 0 2 ]
[ 0 1 2 -2 1 3579 0 5 -1900 0 1 ]
[ 1 -1 0 0 0 4725 0 -6 -41 0 3 ]
[ -2 0 2 0 2 -3075 0 -2 1313 0 -1 ]
[ 3 0 2 0 2 -2904 0 15 1233 0 7 ]
[ 0 -1 0 2 0 4348 0 -10 -81 0 2 ]
[ 1 -1 2 0 2 -2878 0 8 1232 0 4 ]
[ 0 0 0 1 0 -4230 0 5 -20 0 -2 ]
[ -1 -1 2 2 2 -2819 0 7 1207 0 3 ]
[ -1 0 2 0 0 -4056 0 5 40 0 -2 ]
[ 0 -1 2 2 2 -2647 0 11 1129 0 5 ]
[ -2 0 0 0 1 -2294 0 -10 1266 0 -4 ]
[ 1 1 2 0 2 2481 0 -7 -1062 0 -3 ]
[ 2 0 0 0 1 2179 0 -2 -1129 0 -2 ]
[ -1 1 0 1 0 3276 0 1 -9 0 0 ]
[ 1 1 0 0 0 -3389 0 5 35 0 -2 ]
[ 1 0 2 0 0 3339 0 -13 -107 0 1 ]
[ -1 0 2 -2 1 -1987 0 -6 1073 0 -2 ]
[ 1 0 0 0 2 -1981 0 0 854 0 0 ]
[ -1 0 0 1 0 4026 0 -353 -553 0 -139 ]
[ 0 0 2 1 2 1660 0 -5 -710 0 -2 ]
[ -1 0 2 4 2 -1521 0 9 647 0 4 ]
[ -1 1 0 1 1 1314 0 0 -700 0 0 ]
[ 0 -2 2 -2 1 -1283 0 0 672 0 0 ]
[ 1 0 2 2 1 -1331 0 8 663 0 4 ]
[ -2 0 2 2 2 1383 0 -2 -594 0 -2 ]
[ -1 0 0 0 2 1405 0 4 -610 0 2 ]
[ 1 1 2 -2 2 1290 0 0 -556 0 0 ]]

Working example
January 1st, 2021, 0 Hour

Type
yyyy.mmdd ENTER H.mmsds ENTER
That is:
2021.0101 ENTER
0 ENTER
Then —>epsilon

You should get :
2021.0101
0
JD: 2459215.5*
T: .210006844627
L80°'s: 269.59303576
L00°'s: 269.59320244
L´80°'s: 357.342886373
L´00°'s: 357.34338291
F80°'s: 49.00099684
F00°'s: 49.00105768
D80°'s: 206.592894532
D00°'s: 206.592835096 :
Omega80°'s: 78.5145929153
Omegs00°'s: 78.5146055221 :
Delts¥80[s]: -16.154209453
Delta¥00[s]: -16.1620342527
Epsilonµ80°´s: 23.261161652
Epsilonµ86°´s: 23.2611617738
Epsilonµ03°´s: 23.2611569968
DeltaEpsilon 80[s]: 1.25832275817
DeltsEpsilon00[s]: 1.26469136991
Epsilon80°´s: 23.2612874843
Epsilon86.80°´s: 23.2612876061
Epsilon86.00°´s: 23.2612882429
Epsilon03.00°´s: 23.2612834659
Epsilonµ03°´s: 23.2611569968
DeltsEpsilon00[s]: 1.26469136991

*
Note*
To convert JD into a date + hour, don't use fraction.
Use instead integer part in stack line 2
and fraction part in stack line 1.
Then JD—>
Here 2459215 ENTER
0.5 ENTER
Then JD—>

Remarks welcome.

Regards,
Gil

[Gil]

HP49-50G
Here is the missing directory with all the programs.
Sorry.
Regards,
Gil

[Gil]

Version 5.
Just added the variable DATEH, a list representing the yyyy.mmdd and time requested for the —>epsilon calculation: if you clean the screen you might want to know the initial inputs

[Gil]

New Version 7

Calculates now also the day of the week.
0 stands for Sunday, 1 for Monday..., 6 for Saturday.

Give as single input:
yyyy.mmdd

and press —>WK.D

Works for year -4712 to "no limit" in the future.

It uses the Julian day and the code is the following :
\<< "
1 Input
:

yyyy.mmdd

" DROP 0 \->JD DROP UNROT DROP2 2 + 7 MOD
\>>

Can be used with an ASN User Key, to get an answer from any place/Directory you are working on.
For instance, in my case:
\<< PATH \-> p
\<< HOME HOME1 EARTH EPHEM \->WK.D p EVAL
\>>
\>>

As usual copy the full file/directory ended by .doc and attached here into your (phone) HP49-50G calculator.

Regards,
Gil

[Gil]

Version #/label introduced.

Now this is the version Xe.

1)
Output for weekday improved with bugs fixed.

2)
JD conversion with calendar date "corrected" according to usual notion of calendar date :
no date of the format 0.mmdd is anymore admitted, as the year 0 has never existed.

Though now the negative years yyyy correspond to (yyyy+1) in Meus' Astronomical Algorithms (the strictly positive year remaining unchanged and 0.mmddd format, as mentioned, disappearing), for the rest the method employed to get JD or a calendar date follows rigorously the one proposed by Meeus in his book.

Two consequences:

a) Now JD=0 correspond to
date "-4713.0101, 12 h"
(Meeus: to date "-4712.0101, 12 h").

b) The day -1.1231 (December 31st, year -1)
is now followed, "more logically" (for most common users), by +1.0101 (January 1st, year +1).

A rough checking is made to check for non-allowed negative JD, dates before "-4713.0101, 12hours" or years=0.

3)
Introduction, on page 1.5 of the directory, of a preliminary version for the topical year calculation at an instant T.

[Gil]

Version Xf

New updated version of tropical year according to IMCCE paper published on September 2021, after VSOP2013 model.

[Gil]

The calculation for the tropical year was added recently to the directory.

An error relative to it was fixed up in this
new version Xi (the reference of which + date to be found on last page 10.5 of the directory).

The input and output for the tropical year (at page 1.5) are now saved on page 2.1 & 2.2 under names DAT.T (for Date T=Tropical) & TRP. YR.

On page 2.3, the input for the epsilon program (at page 1.6), is now labelled DAT.epsilon (and no more under name DATE.H).

As always, possible to find the Julian Day from (page 1.4) starting from "calendar date + fraction of day" and reverse (page 1.3).

Season and weekday calculation remain at the very beginning of the directory, at pages 1.1 & 1.2.

My thanks to Pascal Descamps of Institut de mécanique céleste et de calcul des éphémérides (IMCCE) for his readiness in forwarding me the formulae relative to tropical year, including its most up-to-date expression in connection with VSOP2013.

[Gil]

Added mean and apparent sideral time/angle
in this new version Xi2.

Code relative to sideral time/angle :
\<< "
2 Inputs
:
. 
y.mmdd

. 
h.mmsss 
[in TU ]
" DROP SWAP 0 \->T '8640184*T+.812866*T+.093104*T^2-.0000062*T^3' \->NUM 86400 MOD 3600 / \->HMS 6.415054841 HMS+ 4 ROLL DROP 5 ROLL DUP 5 ROLLD HMS\-> 1.00273790935 * \->HMS HMS+ 24 MOD "Green.MEAN.Sid h's" \->TAG 5 ROLL 5 ROLL \->\Ge 25 DROPN 5 ROLLD 5 ROLLD DUP \Ge80 COS \GD\16580 15 / * HMS+ "w/Theory 1980" \->TAG "Green.APP.Sid h's" SWAP 3 PICK \Ge03.00 COS \GD\16500 15 / * HMS+ "w/Theory 2000/03" \->TAG DUP2 6 PICK SWAP R\->C 'SID00' STO 5 PICK SWAP R\->C 'SID80' STO
\>>

[Gil]

Version Xi2b

Just used the command R->I to get rid of the decimal point by integers.

[Gil]

Version Xi2c

Suppression of a string for label output in —>WK.D.

Regards,
Gil

[Gil]

Correction
for present weekday calculation.

For the special case -4713.0101 (January 1 BCE),
the weekday calculated is correct,
but the date shown was induly transformed into -4713.0102.

—> Issue fixed up now.
—> Corresponding new code:

\<< "
1 Input
:

yyyy.mmdd


no year < -4713 !
" DROP DUP -4713.0101 == 1 0 IFTE \-> k
\<< .0001 k * - 0 \->JD ROT DROP2 2 + k - 7 MOD DUP { Sun Mon Tue Wed Thu Fri Sat } SWAP 1 + GET SWAP R\->I \->TAG k .0001 * ROT + "y.mmdd" \->TAG SWAP
\>>
\>>

The name of that program in Ephemerid Directory
was changed into —>WK2.D.
It is to be found at the very end of EPHEMERID Directory.

The reason:
A completely new program, using
mathematician John Conway
(died from Covid on 11 April 2020)
Doomsday algorithm,
was developed under the name —>WK.D.
The input is as in the previous program.
The pro: you don't need any more to calculate previously the Astronomical Julian Day; you can now enter any valid *date.
(*The year zero does not exist, as when you start something, the year in question is never zero, but year 1— though that non existing year zero in real life is used internally here for computing purposes —, December 31, year -1, being therefore followed by January 1, year +1
* as previously, the date after October 4 1582, Julian Calendar, is October 15,1582, Gregorian Calendar)
In other words dates before January 1st 4713 BCE are now allowed;
for instance -88888.0131 will return correctly Tuesday.

(See for checking:
https://keisan.casio.com/exec/system/1247132711)

The corresponding code — now corrected in bold —, for that completely new, unlimited program
—>WK.D:

\<< "
1 Input
:

yyyy.mmdd


any year,
even <-4713 !

\[]No Year 0
31.12 yr-1 follow. by
01.01 yr+1
\[]1582.1004 followed by
1582.1015 (Jul\->Greg)
" DROP "yyyy.mmdd" \->TAG DUP DUP IP SWAP FP ABS 100 * DUP FP 100 * SWAP IP ROT 100 / DUP IP SWAP FP 100 * DUP 0 \<= 1 0 IFTE + DUP2 SWAP 100 * + \-> d m Y y Yy
\<< y DUP 2 MOD 0 \=/ 11 0 IFTE + 2 / DUP 2 MOD 0 \=/ 11 0 IFTE + 7 SWAP 7 MOD - Yy 1582 < Yy 1582 == m 10 < AND OR Yy 1582 == m 10 == AND d 5 \<= AND OR
IF
THEN Y NEG 7 MOD Yy 4 MOD 0 == 1 0 IFTE
ELSE Y 4 MOD \-> YM
\<<
CASE YM 0 ==
THEN 2
END YM 1 ==
THEN 0
END YM 2 ==
THEN 5
END YM 3 ==
THEN 3
END
END
\>>
IF y 0 \=/
THEN y 4 MOD 0 == 1 0 IFTE
ELSE Yy 400 MOD 0 == 1 0 IFTE
END
END \-> ly
\<< + d
CASE m 1 ==
THEN 3 ly +
END m 2 ==
THEN 0 ly +
END m 3 ==
THEN 0
END m 4 ==
THEN 4
END m 5 ==
THEN 9
END m 6 ==
THEN 6
END m 7 ==
THEN 4
END m 8 ==
THEN 8
END m 9 ==
THEN 5
END m 10 ==
THEN 10
END m 11 ==
THEN 0
END 12
END - + 7 MOD DUP { Sun Mon Tue Wed Thu Fri Sat } SWAP 1 + GET SWAP R\->I \->TAG
\>>
\>>
\>>

Now all 1st of each month of each odd year from -4701 (BCE) to 4701 (ACE) give the same and correct results (weekdays) with both programs —>WK.D and —>WK2.D.

In fact, you could leave the version running via Julian Day calculation, as nowadays conventions for the months and their lengths are not to be found nor valid as such in the past.

The attached correct files should be
WKneuB.Doc
EPHEMERID.Ver.Xi3c.Doc (c and not b)

Should errors occurr, please inform me to check and correct the issue.

Regards,
Gil Campart

[Gil]

Version EPHEMERID.3Xi.d.hp
with .hp ending

[Gil]

New version 5d

For seasons begin (equinoxes and solstices), with full algorithms according to[b] abridged version VDOP1987 (using tables pages 418-421 of Jean Meeus Astronomical Algorithms.

Slight correction in subprogram —>LBR