Moon's Nodes

Passages of the Moon through the Nodes for the HP-41

Overview

-This program takes an approximate date and returns the time when the Moon passes at the ascending or the descending node of its orbit ( Moon's latitude = 0 ).
-The accuracy is about 5 minutes over the interval [1900,2100]

Data Registers: R00 thru R04: temp ( R04 is an even integer for the ascending node or an odd integer for the descending node )
Flags: /
Subroutines: "J0" & "DT" ( cf "Julian & Gregorian Calendars for the HP-41" ) or "J1" & "D1" or "J2" & "D2"

-Line 07 may be replaced by the M-Code routine FLOOR
-Lines 120 to 128 may be replaced by FLOOR LASTX FRC2 24 *

01 LBL "MNODE"
02 DEG
03 XEQ "J0"
04 13.6061104
05 STO 03
06 /
07 INT
08 STO 04
09 331.73736
10 *
11 7.28
12 +
13 STO 02
14 ST+ X
15 RCL 04
16 177.76374
17 *
18 38.38
19 +
20 STO 00
21 -
22 SIN
23 RCL 00
24 SIN
25 472
26 *
27 -
28 RCL 00

29 RCL 02
30 -
31 SIN
32 87
33 *
34 +
35 RCL 00
36 RCL 02
37 +
38 SIN
39 RCL 04
40 13.4102
41 *
42 17.4
43 +
44 STO 01
45 RCL 02
46 -
47 SIN
48 +
49 8
50 *
51 +
52 RCL 00
53 RCL 01
54 +
55 RCL 02
56 -

57 SIN
58 4
59 *
60 +
61 RCL 00
62 ST+ X
63 SIN
64 LASTX
65 RCL 02
66 -
67 SIN
68 +
69 RCL 01
70 RCL 02
71 +
72 SIN
73 +
74 RCL 01
75 RCL 00
76 -
77 SIN
78 +
79 RCL 01
80 SIN
81 +
82 RCL 02
83 ST+ X
84 SIN

85 +
86 RCL 02
87 SIN
88 55
89 *
90 -
91 3
92 *
93 +
94 RCL 00
95 RCL 01
96 +
97 SIN
98 RCL 02
99 2
100 /
101 SIN
102 -
103 RCL 04
104 .72
105 *
106 56
107 +
108 SIN
109 +
110 ST+ X
111 +
112 20662

113 +
114 E3
115 /
116 RCL 03
117 RCL 04
118 *
119 +
120 INT
121 LASTX
122 FRC
123 X<0?
124 DSE Y
125 FRC
126 24
127 ST* Y
128 MOD
129 HMS
130 X<>Y
131 XEQ "DT"
132 RCL 04
133 2
134 MOD
135 X>0?
136 CHS
137 X=0?
138 SIGN
139 END

( 215 bytes / SIZE 005 )

STACK	INPUTS	OUTPUTS
Z	/	HH.MNSS
Y	/	YYYY.MNDD
X	yyyy.mndd	+/-1

X-output = +1 for a passage at the ascending node
X-output = -1 for a passage at the descending node

Examples:

   2008.0825   XEQ "MNODE" >>>>         1                          ---Execution time = 20s---
                                                   RDN    2008.0912
                                                   RDN        18.2530

-The Moon passes through the ascending node on 2008/09/12 at 18h25m TT

   2008.0915          R/S               >>>>       -1
                                                   RDN   2008.0925
                                                   RDN       16.2137

-The Moon passes through the descending node on 2008/09/25 at 16h22m TT

Reference:

[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell - ISBN 0-943396-61-1

hp41programs

Passages of the Moon through the Nodes for the HP-41