The Museum of HP Calculators

Equinoxes and Solstices for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-The following program calculates the times of the equinoxes and solstices.
-The accuracy is of the order of 5 minutes over the time span +1000 , +3000.
-The results are given in Ephemeris Time.

Program Listing

Data Register:   R00: temp
Flags: /
Subroutine:   "DT" ( cf "Phases of the Moon for the HP-41 )
                        none if you have a Time Module

01 LBL "EQSOL"
02 DEG
03 365242374
04 STO 00
05 X<> Z
06   E3
07 /
08 2
09 -
10 ENTER^
11 ENTER^
12 GTO IND T
13 LBL 01
14 4
15 *
16 CHS
17 52
18 +
19 *
20 RCL 00
21 +
22 *
23 79310
24 GTO 12
25 LBL 02
26 9
27 *
28 3
29 +
30 *
31 RCL 00
32 748
33 -
34 +
35 *
36 172068
37 GTO 12
38 LBL 03
39 3
40 *
41 118
42 -
43 *
44 RCL 00
45 356
46 -
47 +
48 *
49 265717
50 GTO 12
51 LBL 04
52 8
53 *
54 CHS
55 62
56 -
57 *
58 RCL 00
59 366
60 +
61 +
62 *
63 355560
64 LBL 12
65 +
66 .1
67 %
68 STO Y
69 365250
70 /
71 STO 00
72 329645
73 *
74 23
75 -
76 COS
77 202
78 RCL 00
79 *
80 18
81 -
82 COS
83 +
84 20
85 *
86 19341
87 RCL 00
88 *
89 35
90 -
91 COS
92 49
93 *
94 +
95 4452671
96 RCL 00
97 *
98 22
99 +
100 COS
101 18
102 *
103 +
104 450369
105 RCL 00
106 *
107 73
108 +
109 COS
110 16
111 *
112 +
113 225184
114 RCL 00
115 *
116 9
117 -
118 COS
119 14
120 *
121 -
122   E4
123 /
124 +
125 INT
126 LASTX
127 FRC
128 X<0?
129 DSE Y
130 ""                    ( TEXT 0 or another NOP instruction like LBL 00 .... )
131 24
132 ST* Y
133 MOD
134 HMS
135 X<>Y
136 XEQ "DT"      ( Line 136 may be replaced by     1.012   X<>Y   DATE+    if you have a Time Module )
137 END

( 241 bytes / SIZE 001 )

      STACK        INPUTS      OUTPUTS

           Y         YYYY        hh.mnss

           X             k YYYY.MNDD

where YYYY = year

and k = 1 for the spring equinox k = 3 for the autumn equinox
k = 2 for the summer solstice k = 4 for the winter solstice

Example: Find the times of the eqinoxes and solstices of the year 2004

2004 ENTER^
1 XEQ "EQSOL" >>>> 2004.0320 X<>Y 6.5040 ( 2004 March 20 at 6h50m40s ET )

2004 ENTER^
2 R/S >>>> 2004.0621 X<>Y 0.5823 ( 2004 June 21 at 0h58m23s ET )

2004 ENTER^
3 R/S >>>> 2004.0922 X<>Y 16.3013 ( 2004 September 22 at 16h30m13s ET )

2004 ENTER^
4 R/S >>>> 2004.1221 X<>Y 12.4146 ( 2004 December 21 at 12h41m46s ET )

-Subtract about 1 minute to get the result in Universal Time in 2004
and round to the nearest minute.

Reference: Jean Meeus , "Astronomical Algorithms" - Willmann-Bell - ISBN 0-943396-35-2

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