The Museum of HP Calculators

The Satellites of Jupiter for the HP-41

This program is by Jean-Marc Baillard and is used here by permission.

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

-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 "Phases of the Moon for the HP-41" )

001 LBL "IEGC"
002 DEG
003 HR
004 24
005 /
006 X<>Y
007 1.012               if you don't have a Time-module, replace lines 07 to 09 by XEQ "J0"   +
008 DDAYS
009 -
010 STO 00
011 .9856
012 *
013 3
014 -
015 STO 01
016 SIN
017 1.92
018 *
019 RCL 01
020 ST+ X
021 SIN
022 50
023 /
024 +
025 RCL 00
026 12.036
027 /
028 RCL 00
029 896
030 /
031 7
032 -
033 SIN
034 3
035 /
036 STO 02
037 ST+ Z
038 -
039 20
040 +
041 STO 03
042 SIN
043 5.56
044 *
045 RCL 03
046 ST+ X
047 SIN
048 6
049 /
050 +
051 STO 09
052 -
053 RCL 00
054 .902518
055 *
056 +
057 65.66
058 +
059 STO 04
060 CLX               if you don't have an X-Functions module, replace lines 60-61 by
061 X<> F            CF 01 CF 02 CF 03 CF 04
062 1
063 RCL 01
064 COS
065 60
066 /
067 -
068 5209
069 RCL 03
070 COS
071 252
072 *
073 -
074 RCL 03
075 ST+ X
076 COS
077 6
078 *
079 -
080   E3
081 /
082 STO 05
083 X^2
084 LASTX
085 R^
086 *
087 ST+ X
088 RCL 04
089 COS
090 *
091 -
092 X<>Y
093 X^2
094 +
095 SQRT
096 STO 07
097 /
098 RCL 04
099 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: Jean Meeus "Astronomical Algorithms" Willmann-Bell ISBN 0-943396-35-2

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