hp41programs

Satellites The Satellites of Jupiter for the HP-41

Overview

-This program calculates the coordinates x and y of the 4 greatest satellites of Jupiter ( Io , Europe , Ganymede , Callisto ), as seen from the Earth.
-The x-axis coincides with the equator of the planet, the y-axis is the planet's rotation axis.
-Jupiter is the origin and x , y are measured in units of Jupiter's equatorial radius. ( the polar radius of Jupiter is 0.933 )

Data Registers: R00 = the number of days since 01/01/2000 0h ET

R01 = x₁ ; R03 = x₂ ; R05 = x₃ ; R07 = x₄
R02 = y₁ ; R04 = y₂ ; R06 = y₃ ; R08 = y₄ and R09 = - sin D_E where D_E is the planetocentric declination of the Earth.

Satellite 1 = Io ; Satellite 2 = Europe ; Satellite 3 = Ganymede ; Satellite 4 = Callisto.

Flags: F01 F02 F03 F04

-Flag nn is set when the distance Earth-Satellite n is shorter than the distance Earth-Jupiter:
-This is useful to distinguish inferior conjunctions from superior conjunctions.

Subroutine: -none if you have a Time-module
"J0" otherwise.( cf for instance "Julian & Gregorian Calendars for the HP-41" )

-If you don't have a Time-module, replace lines 07 to 09 by XEQ "J0" +
-If you don't have an X-Functions module, replace lines 60-61 by CF 01 CF 02 CF 03 CF 04

01 LBL "IEGC"
02 DEG
03 HR
04 24
05 /
06 X<>Y
07 1.012
08 DDAYS
09 -
10 STO 00
11 .9856
12 *
13 3
14 -
15 STO 01
16 SIN
17 1.92
18 *
19 RCL 01
20 ST+ X
21 SIN
22 50
23 /
24 +
25 RCL 00
26 12.036
27 /
28 RCL 00
29 896
30 /
31 7
32 -
33 SIN
34 3
35 /
36 STO 02
37 ST+ Z
38 -
39 20
40 +
41 STO 03
42 SIN
43 5.56
44 *
45 RCL 03
46 ST+ X
47 SIN
48 6

49 /
50 +
51 STO 09
52 -
53 RCL 00
54 .902518
55 *
56 +
57 65.66
58 +
59 STO 04
60 CLX
61 X<> F
62 1
63 RCL 01
64 COS
65 60
66 /
67 -
68 5209
69 RCL 03
70 COS
71 252
72 *
73 -
74 RCL 03
75 ST+ X
76 COS
77 6
78 *
79 -
80   E3
81 /
82 STO 05
83 X^2
84 LASTX
85 R^
86 *
87 ST+ X
88 RCL 04
89 COS
90 *
91 -
92 X<>Y
93 X^2
94 +
95 SQRT
96 STO 07

97 /
98 RCL 04
99 SIN
100 *
101 ASIN
102 STO 08
103 LASTX
104 RCL 00
105 12.035
106 /
107 56.3
108 +
109 RCL 02
110 -
111 RCL 09
112 ST- 08
113 +
114 STO 06
115 COS
116 *
117 2.22
118 *
119 RCL 06
120 20.8
121 +
122 SIN
123 3.12
124 *
125 -
126 RCL 06
127 32.5
128 -
129 COS
130 RCL 05
131 RCL 07
132 ST- Y
133 /
134 *
135 1.3
136 *
137 -
138 SIN
139 STO 09
140 368
141 LN
142 RCL 00
143 RCL 07
144 173

145 /
146 -
147 STO 07
148 101.291633
149 *
150 52.24
151 -
152 RCL 08
153 +
154 STO 03
155 3
156 *
157 RCL 07
158 50.234518
159 *
160 19.4
161 -
162 RCL 08
163 +
164 STO 05
165 ST+ X
166 -
167 180
168 +
169 STO 01
170 RCL 03
171 -
172 ST+ X
173 STO 06
174 COS
175 41
176 /
177 -
178 STO 02
179 RCL 06
180 SIN
181 .47
182 *
183 ST+ 01
184 9.4
185 RCL 03
186 RCL 05
187 -
188 ST+ X
189 STO 06
190 COS
191 5
192 D-R

193 *
194 -
195 STO 04
196 RCL 06
197 SIN
198 2.9
199 LN
200 *
201 ST+ 03
202 859
203 D-R
204 RCL 07
205 50.31048
206 *
207 54
208 -
209 STO 06
210 COS
211 46
212 /
213 -
214 X<> 06
215 SIN
216 6
217 /
218 ST+ 05
219 26.37
220 RCL 07
221 21.48798
222 *
223 214.07
224 +
225 RCL 08
226 +
227 X<> 07
228 21.56923
229 *
230 76.6
231 +
232 STO 08
233 COS
234 11
235 D-R
236 *
237 -
238 RCL 08
239 SIN
240 .84

241 *
242 RCL 07
243 +
244 X<>Y
245 P-R
246 X>0?
247 SF 04
248 RCL 09
249 *
250 STO 08
251 X<>Y
252 STO 07
253 RCL 05
254 RCL 06
255 P-R
256 X>0?
257 SF 03
258 RCL 09
259 *
260 STO 06
261 X<>Y
262 STO 05
263 RCL 03
264 RCL 04
265 P-R
266 X>0?
267 SF 02
268 RCL 09
269 *
270 STO 04
271 X<>Y
272 STO 03
273 RCL 01
274 RCL 02
275 P-R
276 X>0?
277 SF 01
278 RCL 09
279 *
280 STO 02
281 X<>Y
282 STO 01
283 END

( 453 bytes / SIZE 010 )

STACK	INPUTS	OUTPUTS
Y	Date	y₁
X	hh.mnss ( ET )	x₁

Example1: Find the configuration of the 4 Galilean satellites of Jupiter on 1992 December 16 at 0h UT = 0h00m59s ET

12.161992 ENTER^ ( if your HP-41 is in MDY format )
0.0059 XEQ "IEGC"

and 31 seconds later x₁ = -3.45
X<>Y y₁ = 0.21

RCL 03 >>>> x₂ = 7.45 RCL 05 >>>> x₃ = 1.24 RCL 07 >>>> x₄ = 7.09
RCL 04 >>>> y₂ = 0.25 RCL 06 >>>> y₃ = 0.65 RCL 08 >>>> y₄ = 1.10

-Flags F01 F02 F03 F04 are set but it's not particularly useful here!

Example2: Find the configuration of the Galilean satellites of Jupiter on 1984 September 20 at 6h34m ET

     20.091984 ENTER^
       6.34            R/S                 yields    x₁ = 0.00
                         X<>Y                          y₁ = 0.20

RCL 03 >>>> x₂ = -8.08 RCL 05 >>>> x₃ = 14.97 RCL 07 >>>> x₄ = -4.95
RCL 04 >>>> y₂ = -0.16 RCL 06 >>>> y₃ = -0.01 RCL 08 >>>> y₄ = -0.86

-Since F01 is set , Io is in transit over Jupiter's disk because its distance to the planet's center is significantly inferior to 1.

Notes:

-If you use "J0" , dates must be keyed in 1992.1216 and 1984.0920
-The accuracy is of the order of 0.1 ( but x-values are more accurate than y-values )
-The reference below also provides a high-accuracy method.

Reference:

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