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

[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