Eclipses

Eclipses for the HP-41

Overview

1°) Program#1
2°) Program#2 ( lower accuracy )
3°) Eclipses+Phases of the Moon #1
4°) Phases of the Moon+Eclipses #2

-Programs #1 & #2 calculate the date & time of a Solar or a Lunar eclipse.
-The type of the eclipse is also determined: Partial, Annular, Total or Hybrid ( also called Annular-Total ) for a Solar eclipse
and Partial or Total, Umbral or Penumbral for a Lunar eclipse.
-The magnitude is also returned.

-The first routine is valid a few centuries around J2000 with an accuracy of the order of a few minutes for the time of maximum eclipse.
-For the second and third programs, the accuracy is about 5 minutes over the time span [1900,2100]
-Program #4 has an accuracy of a few minutes for dates between 1000 and 3000 ( at least )

1°) Program#1

Data Registers: R00 thru R15: temp

R04 = 0 for a Solar eclipse R03 = m' R10 = gamma
R04 = 1 for a Lunar eclipse R09 = m

For a Solar eclipse, gamma = the least "distance" from the center of the Earth to the axis of the Moon's shadow ( unit = Earth's radius )
For a Lunar eclipse, gamma = the least "distance" from the center of the Moon to the axis of the Earth's shadow ( unit = Earth's radius )

Flag: F02 is set to indicate a Hybrid ( solar ) eclipse.
Subroutines: "J0" & "DT" ( cf "Julian & Gregorian Calendars for the HP-41" ) or "J1" & "D1" or "J2" & "D2"

-R06 contains an integer that is even for a Solar eclipse and odd for a Lunar eclipse.
-One is added to R06 until the HP-41 finds an eclipse.

-Line 07 may be replaced by FLOOR
-Line 178 is a three-byte GTO 01
-Lines 322 & 324: FLOOR and FRC2 are 2 M-Code routines listed in "A Few M-Code Routines for the HP-41"
but lines 322 to 326 may be replaced by INT LASTX FRC X<0? DSE Y FRC 24 ST* Y MOD

01 LBL "ECLIPSE"
02 DEG
03 XEQ "J0"
04 14.7652944
05 STO 05
06 /
07 INT
08 STO 06
09 GTO 00
10 LBL 01
11 ISG 06
12 LBL 00
13 .36
14 RCL 06
15 195.33525
16 *
17 160.71
18 +
19 STO 04
20 SIN
21 ABS
22 X>Y?
23 GTO 01
24 CF 02
25 125
26 RCL 06
27 .782
28 *
29 -
30 SIN
31 37
32 /
33 ST- 04
34 RCL 06
35 14.55268
36 *
37 2.55
38 +
39 STO 01
40 SIN
41 2070
42 *
43 RCL 01
44 ST+ X
45 STO 14
46 SIN
47 24
48 *
49 +
50 RCL 06
51 192.90847
52 *
53 201.56
54 +
55 STO 00
56 RCL 01

57 +
58 STO 12
59 SIN
60 73
61 *
62 -
63 RCL 00
64 RCL 01
65 -
66 STO 13
67 SIN
68 67
69 *
70 +
71 1
72 RCL 06
73 E6
74 /
75 -
76 STO 15
77 *
78 RCL 00
79 SIN
80 392
81 *
82 -
83 RCL 00
84 ST+ X
85 STO 11
86 SIN
87 116
88 *
89 +
90 RCL 04
91 ST+ X
92 STO 02
93 SIN
94 118
95 *
96 +
97 RCL 04
98 COS
99 STO 03
100 *
101 RCL 14
102 COS
103 20
104 *
105 RCL 01
106 COS
107 48
108 *
109 -
110 RCL 12
111 COS
112 60

113 *
114 -
115 RCL 13
116 COS
117 41
118 *
119 +
120 RCL 15
121 *
122 RCL 00
123 COS
124 3299
125 *
126 -
127 52207
128 +
129 RCL 04
130 SIN
131 *
132 +
133 1
134 RCL 03
135 ABS
136 208
137 /
138 -
139 *
140 STO 10
141 ABS
142 STO 07
143 RCL 01
144 COS
145 46
146 *
147 RCL 15
148 *
149 59
150 +
151 RCL 00
152 COS
153 182
154 *
155 -
156 RCL 11
157 COS
158 4
159 *
160 +
161 RCL 12
162 COS
163 5
164 *
165 -
166 STO 08
167 15433
168 +

169 RCL 06
170 2
171 MOD
172 STO 04
173 140
174 *
175 +
176 -
177 X>0?
178 GTO 01
179 CHS
180 STO 03
181 RCL 04
182 X=0?
183 GTO 00
184 10128
185 RCL 07
186 -
187 RCL 08
188 -
189 5450
190 ST/ 03
191 /
192 STO 09
193 GTO 02
194 LBL 00
195 RCL 07
196 9972
197 X>Y?
198 SF 02
199 RCL 08
200 ABS
201 +
202 X>Y?
203 GTO 00
204 CLX
205 X<> 03
206 5461
207 RCL 08
208 ST+ X
209 +
210 /
211 STO 09
212 GTO 02
213 LBL 00
214 RCL 07
215 E4
216 /
217 X^2
218 SIGN
219 ENTER^
220 STO 03
221 LASTX
222 -
223 X<0?
224 CLX

225 SQRT
226 46.4
227 *
228 RCL 08
229 X<Y?
230 X<0?
231 CF 02
232 X<>Y
233 5461
234 ST- Z
235 -
236 /
237 X>Y?
238 STO 03
239 STO 09
240 LBL 02
241 RCL 01
242 SIN
243 1721
244 RCL 04
245 6
246 *
247 +
248 *
249 RCL 13
250 SIN
251 73
252 *
253 +
254 RCL 12
255 SIN
256 50
257 *
258 -
259 RCL 14
260 SIN
261 21
262 *
263 +
264 RCL 01
265 RCL 11
266 +
267 SIN
268 6
269 *
270 +
271 RCL 15
272 *
273 4075
274 RCL 04
275 10
276 *
277 -
278 RCL 00
279 SIN
280 *

281 -
282 RCL 11
283 SIN
284 161
285 *
286 +
287 RCL 02
288 SIN
289 97
290 *
291 -
292 RCL 00
293 RCL 02
294 -
295 SIN
296 23
297 *
298 -
299 RCL 00
300 RCL 02
301 +
302 SIN
303 12
304 *
305 +
306 RCL 00
307 RCL 11
308 +
309 SIN
310 4
311 *
312 -
313 55977
314 +
315 E4
316 ST/ 10
317 /
318 RCL 05
319 RCL 06
320 *
321 +
322 FLOOR
323 LASTX
324 FRC2
325 24
326 *
327 HMS
328 X<>Y
329 XEQ "DT"
330 RCL 03
331 RCL 09
332 R^
333 R^
334 END

( 505 bytes / SIZE 016 )

STACK	INPUTS	OUTPUTS
T	/	m'
Z	/	m
Y	/	HH.MNSS
X	yyyy.mndd	YYYY.MNDD

where yyyy.mndd is an approximate date

YYYY.MNDD is the date of the eclipse
HH.MNSS is the time of maximum eclipse

For a Lunar Eclipse:

m = magnitude of the umbral eclipse m , m' > 1 for a total eclipse, if m < 0 there is no umbral eclipse
m' = magnitude of the penumbral eclipse m , m' < 1 for a partial eclipse

For a Solar Eclipse:

m = magnitude of the eclipse m > 1 for a total or hybrid eclipse m < 1 for a partial eclipse

         m' = 0   for a partial eclipse
         m' = 1   for an annular eclipse
         m' = m for a total or hybrid eclipse                F02 will be set for a hybrid eclipse

Example1:

   2008.0701 XEQ "ECLIPSE"   >>>>   2008.0801                     --- Execution time = 39s ---
                                                    RDN       10.2230
                                                    RDN         1.0193
                                                    RDN         1.0193                           and flag F02 is clear

-So, there is a Total Solar eclipse on 2008/08/01 at 10h23mn TT and its magnitude = 1.019

-You also have R04 = 0 to confirm that it is a Solar eclipse.

-And R10 = gamma = 0.8315 , therefore, the eclipse is visible in the northern hemisphere

-If R10 < 0 the eclipse is visible in the southern hemisphere
-If R10 is small ( compared to 1 ), the eclipse is visible from equatorial regions.

>>>> To search for the next eclipse, simply press XEQ 01 without disturbing R05 & R06

-Here, it yields in 34 seconds:              2008.0816
                                               RDN       21.1117
                                               RDN         0.8012
                                               RDN         1.8307

-Thus, there is a Lunar eclipse on 2008/08/16 at 21h11mn TT
-This eclipse is an umbral one ( m > 0 ) and its magnitude is m = 0.801

Example2:

     2013.1101   R/S   >>>>    2013.1103
                                 RDN         12.4713
                                 RDN           1.0078
                                 RDN           1.0078              and flag F02 is set

-So, there will be a Hybrid ( Annular/Solar ) eclipse on 2013/11/03 at 12h47mn TT and its magnitude = 1.008

Example3:

     2001.1225   R/S   >>>>    2001.1230
                                  RDN        10.3049
                                  RDN        -0.1241
                                  RDN         0.8846

-There was a Lunar eclipse on 2001/12/30 at 10h31mn TT
-Since m < 0 , it was not an umbral eclipse but a penumbral one and its magnitude was 0.885

Example4:

     2001.1201   R/S   >>>>    2001.1214
                                  RDN        20.5339
                                  RDN          0.9832
                                  RDN          1.0000               flag F02 is clear

-Since m' = 1 and m < 1 , there was an Annular Solar eclipse on 2001/12/14 at 20h54mn TT magnitude = 0.983

Notes:

-There is no ambiguity between Solar and Lunar eclipses after seeing registers Z and T
-But in order to get a clearer information, you could replace lines 330 to 333 by

"LUNAR" RCL 04 X=0? "SOLAR" CLX RCL 03 RCL 09 R^ R^ AVIEW

-Other lines may of course be added so that the HP-41 displays the exact type of the eclipse, but it will cost several extra bytes...

-More periodic terms can be found in reference [1] to get the time of maximum eclipse with a better accuracy.
-I've also neglected several secular terms that should be added to seek eclipses that occurred more than 2 or 3 centuries ago.

2°) Program#2

-In order to save bytes, we can round some coefficients and use less terms ( and a few "tricks" )

Data Registers: R00 thru R14: temp

R04 = 0 for a Solar eclipse R03 = m' R10 = gamma
R04 = 1 for a Lunar eclipse R09 = m

Flag: F02 is set to indicate a Hybrid ( solar ) eclipse.
Subroutines: "J0" & "DT" ( cf "Julian & Gregorian Calendars for the HP-41" ) or "J1" & "D1" or "J2" & "D2"

-Line 153 is a three-byte GTO 01
-Lines 268 to 272 may be replaced by INT LASTX FRC X<0? DSE Y FRC 24 ST* Y MOD

01 LBL "ECL"
02 DEG
03 XEQ "J0"
04 14.7652944
05 STO 05
06 /
07 INT
08 STO 06
09 GTO 00
10 LBL 01
11 ISG 06
12 LBL 00
13 .36
14 RCL 06
15 195.33525
16 *
17 372
18 SQRT
19 -
20 STO 04
21 SIN
22 ABS
23 X>Y?
24 GTO 01
25 CF 02
26 RCL 06
27 14.55268
28 *
29 13
30 LN
31 +
32 STO 01
33 SIN
34 207
35 *
36 RCL 06
37 192.90847
38 *
39 465
40 SQRT
41 +
42 STO 00
43 SIN
44 39
45 *
46 +
47 RCL 00

48 ST+ X
49 STO 11
50 SIN
51 RCL 04
52 ST+ X
53 STO 02
54 SIN
55 +
56 11.7
57 *
58 +
59 RCL 01
60 ST+ X
61 STO 14
62 SIN
63 ST+ X
64 +
65 RCL 00
66 RCL 01
67 +
68 STO 12
69 SIN
70 RCL 00
71 RCL 01
72 -
73 STO 13
74 SIN
75 -
76 7
77 *
78 +
79 RCL 04
80 COS
81 STO 03
82 *
83 5221
84 RCL 01
85 COS
86 5
87 *
88 -
89 RCL 14
90 COS
91 ST+ X
92 +
93 RCL 00
94 COS

95 330
96 *
97 +
98 RCL 12
99 COS
100 6
101 *
102 +
103 RCL 13
104 COS
105 4
106 *
107 -
108 RCL 04
109 SIN
110 *
111 +
112 RCL 03
113 ABS
114 208
115 /
116 1
117 -
118 *
119 STO 10
120 ABS
121 STO 07
122 5.9
123 RCL 00
124 COS
125 18
126 *
127 +
128 RCL 01
129 COS
130 9
131 *
132 RCL 11
133 COS
134 +
135 RCL 12
136 COS
137 +
138 2
139 /
140 +
141 STO 08

142 1543
143 +
144 RCL 06
145 2
146 MOD
147 STO 04
148 14
149 *
150 +
151 -
152 X>0?
153 GTO 01
154 CHS
155 STO 03
156 RCL 04
157 X=0?
158 GTO 00
159 1013
160 RCL 07
161 -
162 RCL 08
163 -
164 545
165 ST/ 03
166 /
167 STO 09
168 GTO 02
169 LBL 00
170 RCL 07
171 997.2
172 X>Y?
173 SF 02
174 RCL 08
175 ABS
176 +
177 X>Y?
178 GTO 00
179 CLX
180 X<> 03
181 546
182 RCL 08
183 ST+ X
184 +
185 /
186 STO 09
187 GTO 02
188 LBL 00

189 RCL 07
190 E3
191 /
192 X^2
193 SIGN
194 ENTER^
195 STO 03
196 LASTX
197 -
198 22
199 *
200 X<0?
201 CLX
202 SQRT
203 RCL 08
204 X<Y?
205 X<0?
206 CF 02
207 X<>Y
208 546
209 ST- Z
210 -
211 /
212 X>Y?
213 STO 03
214 STO 09
215 LBL 02
216 RCL 01
217 SIN
218 86
219 *
220 RCL 11
221 SIN
222 8
223 *
224 +
225 RCL 02
226 SIN
227 5
228 *
229 -
230 RCL 00
231 RCL 02
232 -
233 SIN
234 +
235 RCL 14

236 SIN
237 +
238 ST+ X
239 RCL 00
240 SIN
241 407
242 *
243 +
244 RCL 13
245 SIN
246 7
247 *
248 -
249 RCL 12
250 SIN
251 5
252 *
253 +
254 RCL 00
255 RCL 02
256 +
257 SIN
258 -
259 5598
260 +
261 E3
262 ST/ 10
263 /
264 RCL 05
265 RCL 06
266 *
267 +
268 FLOOR
269 LASTX
270 FRC2
271 24
272 *
273 HMS
274 X<>Y
275 XEQ "DT"
276 RCL 03
277 RCL 09
278 R^
279 R^
280 END

( 401 bytes / SIZE 015 )

-The instructions are identical, for example:

   2008.0701 XEQ "ECL"   >>>>   2008.0801                     --- Execution time = 35s ---
                                            RDN       10.2424
                                            RDN         1.0191
                                            RDN         1.0191                           and flag F02 is clear

So, there is a Total Solar eclipse on 2008/08/01 at 10h24mn TT and its magnitude = 1.019

R10 = gamma = 0.8335 , therefore, the eclipse is visible in the northern hemisphere.

Notes:

-With respect to Solar eclipses over the interval [ 1900 , 2100 ] the type of the eclipse is correctly found
except on 1935/01/05 where the partial eclipse - magnitude = 0.001 - is not found at all!
and on 1948/05/09: there was an annular eclipse - magnitude = 0.9999 - whereas "ECL" gives a hybrid eclipse - magnitude = 1.0002.

-Three more bytes can be saved if you delete lines 213-212-194
-In this case, the HP-41 will return m' = 1 for annular, hybrid and total Solar eclipses

3°) Eclipses + Phases of the Moon

-We can combine "ECL" and "PHASE" to reduce space memory.
-The phases of the Moon are usually defined by the difference between the longitudes of the Moon and the Sun ( 0° 90° 180° 270° )
-In the following routine, we use another definition i-e when the illuminated fraction of the Moon's disk equals 0 , 1/2 , 1 , 1/2
-Thus - unlike the standard definition - the instant of a Solar eclipse is identical to the instant of the New Moon
( likewise for a Lunar eclipse and a Full Moon ) which is perhaps more logical...

Data Registers: R00 = M'-180° where M' = Moon's mean anomaly R05 = 7.382647 R08 = 1000 u ( u = radius of the umbral cone )

                               R01 = M             where M = Sun's mean anomaly                   R06 = 4k                    R09 = 0 for New Moon or Full Moon
                               R02 = 2F            where F = Moon's argument of latitude        R07 = phase               R09 = 1 for First Quarter or Last Quarter
                               R03 = m'                               R10 = m
                               R04 = F-180°, gamma          R11 = 2M'   R12 = M'+M-180°   R13 = M'-M-180°   R14 = 2M       R15 = 1000 | gamma |

Flag: F02 is set to indicate a Hybrid ( solar ) eclipse.
Subroutines: "J0" & "DT" ( cf "Julian & Gregorian Calendars for the HP-41" ) or "J1" & "D1" or "J2" & "D2"

-If you prefer the standard definitions for the New Moon and Full Moon,

    add   SF 10                                        after line 304
    add   X<0? FS? 10 FS? 30 CHS    after line 42
    add   CF 10                                       after line 13

-If you prefer the standard definitions for the First and Last Quarters,
replace line 93 by - and lines 83 to 86 by 3
-Lines 103 to 111 may be replaced by FLOOR LASTX FRC2 24 *
-Line 242 is a three-byte GTO 10

01 LBL "PHASE"
02 XEQ 05
03 INT
04 STO 06
05 4
06 MOD
07 STO 07
08 2
09 MOD
10 STO 09
11 XEQ 06
12 XEQ 07
13 STO 04
14 LBL 08
15 RCL 09
16 221
17 *
18 407
19 +
20 RCL 00
21 SIN
22 *
23 RCL 01
24 SIN
25 172
26 *
27 +
28 RCL 09
29 7
30 *
31 16
32 -
33 RCL 11
34 SIN
35 *
36 -
37 RCL 09
38 9
39 *
40 5
41 -
42 ST+ X
43 RCL 02
44 SIN
45 *
46 +
47 RCL 09
48 ST+ X
49 7
50 -
51 RCL 13
52 SIN
53 *
54 +
55 RCL 09
56 7
57 *
58 5
59 +

60 RCL 12
61 SIN
62 *
63 +
64 RCL 14
65 SIN
66 RCL 00
67 RCL 02
68 -
69 SIN
70 +
71 ST+ X
72 +
73 RCL 00
74 RCL 02
75 +
76 SIN
77 RCL 09
78 ST+ X
79 1
80 -
81 *
82 +
83 RCL 00
84 COS
85 9
86 +
87 RCL 07
88 2
89 -
90 RCL 09
91 *
92 *
93 +
94 5598
95 +
96 E3
97 ST/ 04
98 /
99 RCL 05
100 RCL 06
101 *
102 +
103 INT
104 LASTX
105 FRC
106 X<0?
107 DSE Y
108 FRC
109 24
110 ST* Y
111 MOD
112 HMS
113 X<>Y
114 XEQ "DT"
115 RCL 07
116 RTN
117 LBL "ECL"
118 XEQ 05

119 2
120 /
121 INT
122 ST+ X
123 STO 06
124 GTO 00
125 LBL 10
126 2
127 ST+ 06
128 LBL 00
129 .36
130 XEQ 06
131 SIN
132 ABS
133 X>Y?
134 GTO 10
135 CF 02
136 RCL 06
137 4
138 MOD
139 STO 07
140 CLX
141 STO 09
142 XEQ 07
143 SIN
144 207
145 *
146 RCL 14
147 SIN
148 ST+ X
149 +
150 RCL 00
151 SIN
152 39
153 *
154 +
155 RCL 11
156 SIN
157 RCL 02
158 SIN
159 +
160 11.7
161 *
162 +
163 RCL 12
164 SIN
165 RCL 13
166 SIN
167 -
168 7
169 *
170 +
171 RCL 04
172 COS
173 STO 03
174 *
175 5221
176 RCL 01
177 COS

178 5
179 *
180 -
181 RCL 14
182 COS
183 ST+ X
184 +
185 RCL 00
186 COS
187 330
188 *
189 +
190 RCL 12
191 COS
192 6
193 *
194 +
195 RCL 13
196 COS
197 4
198 *
199 -
200 RCL 04
201 SIN
202 *
203 +
204 RCL 03
205 ABS
206 208
207 /
208 1
209 -
210 *
211 STO 04
212 ABS
213 STO 15
214 5.9
215 RCL 00
216 COS
217 18
218 *
219 +
220 RCL 01
221 COS
222 9
223 *
224 RCL 11
225 COS
226 +
227 RCL 12
228 COS
229 +
230 2
231 /
232 +
233 STO 08
234 1543
235 +
236 RCL 07

237 7
238 *
239 +
240 -
241 X>0?
242 GTO 10
243 CHS
244 STO 03
245 RCL 07
246 X=0?
247 GTO 00
248 1013
249 RCL 15
250 -
251 RCL 08
252 -
253 545
254 ST/ 03
255 /
256 STO 10
257 GTO 09
258 LBL 00
259 RCL 15
260 997.2
261 X>Y?
262 SF 02
263 RCL 08
264 ABS
265 +
266 X>Y?
267 GTO 00
268 CLX
269 X<> 03
270 546
271 RCL 08
272 ST+ X
273 +
274 /
275 STO 10
276 GTO 09
277 LBL 00
278 RCL 15
279 E3
280 /
281 X^2
282 SIGN
283 ENTER^
284 STO 03
285 LASTX
286 -
287 22
288 *
289 X<0?
290 CLX
291 SQRT
292 RCL 08
293 X<Y?
294 X<0?
295 CF 02

296 X<>Y
297 546
298 ST- Z
299 -
300 /
301 X>Y?
302 STO 03
303 STO 10
304 LBL 09
305 XEQ 08
306 CLX
307 RCL 03
308 RCL 10
309 R^
310 R^
311 RTN
312 LBL 05
313 XEQ "J0"
314 7.3826472
315 STO 05
316 /
317 DEG
318 RTN
319 LBL 06
320 RCL 06
321 97.667626
322 *
323 372
324 SQRT
325 -
326 STO 02
327 STO 04
328 ST+ 02
329 RTN
330 LBL 07
331 RCL 06
332 96.454234
333 *
334 465
335 SQRT
336 +
337 STO 00
338 STO 11
339 STO 12
340 STO 13
341 ST+ 11
342 RCL 06
343 7.27634
344 *
345 13
346 LN
347 +
348 STO 01
349 STO 14
350 ST+ 12
351 ST- 13
352 ST+ 14
353 END

( 503 bytes / SIZE 016 )

STACK	INPUT	OUTPUT1(phase)	OUTPUT2(eclipse)
T	/	/	m'
Z	/	HH.MNSS	m
Y	/	YYYY.MNDD	HH.MNSS
X	yyyy.mndd	Phase	YYYY.MNDD

where yyyy.mndd is an approximate date and Phase = 0 , 1 , 2 , 3 for New Moon , First Quarter , Full Moon , Last Quarter.

YYYY.MNDD is the date of the phase or the eclipse
HH.MNSS is the time of the phase or the maximum eclipse

For a Lunar Eclipse:

m = magnitude of the umbral eclipse m , m' > 1 for a total eclipse, if m < 0 there is no umbral eclipse
m' = magnitude of the penumbral eclipse m , m' < 1 for a partial eclipse

For a Solar Eclipse:

m = magnitude of the eclipse m > 1 for a total or hybrid eclipse m < 1 for a partial eclipse

         m' = 0   for a partial eclipse
         m' = 1   for an annular eclipse
         m' = m for a total or hybrid eclipse                F02 will be set for a hybrid eclipse

Example1:

   2008.0801   XEQ "PHASE"   >>>>          0                                              --- Execution time = 17s ---
                                                  RDN    2008.0801
                                                  RDN        10.2424

So, there is a New Moon on 2008/08/01 at 10h24mn TT 10h16m16s TT with the standard definition

-Likewise,

   First Quarter on 2008/08/08 at 20h02m42 TT          20h21m17s TT   with the standard definition
   Full Moon   on   2008/08/16 at 21h12m38 TT          21h19m43s TT   with the standard definition
   Last Quarter on   2008/08/24 at 00h08m38 TT         23h52m45s TT on 2008/08/23 with the standard definition

Example2:

   2008.0701     XEQ "ECL"        >>>>   2008.0801                     --- Execution time = 39s ---
                                                    RDN       10.2424
                                                    RDN         1.0191
                                                    RDN         1.0191                           and flag F02 is clear

There is a Total Solar eclipse on 2008/08/01 at 10h24mn TT and its magnitude = 1.019

-You also have R07 = 0 to confirm that it is a Solar eclipse.

-And R04 = gamma = 0.8334 > 0 ( the eclipse is visible in the northern hemisphere )

-If R04 < 0 the eclipse is visible in the southern hemisphere
-If R04 is small ( compared to 1 ), the eclipse is visible from equatorial regions.

>>>> To search for the next eclipse, simply press XEQ 10 without disturbing R05 & R06

-Here, it yields:

                  2008.0816                            ( in 34 seconds )
       RDN       21.1238
       RDN        0.8045
       RDN        1.8328

Partial Lunar eclipse on 2008/08/16 at 21h13mn TT , magnitude in the umbra = 0.804

Note:

-Three bytes can be saved if you delete lines 302-301-283
-The HP-41 will then return m' = 1 for annular, hybrid and total Solar eclipses

4°) Phases of the Moon + Eclipses

-This routine calculates the phases of the Moon with the same - non-standard - definition as the 3rd program
-More secular terms have been used to produce an accuracy of about 5 minutes for dates between 1000 & 3000 and probably a little more...

Data Registers: R00 = 4.k R05 = 0 or 1 R10 = 2.F R15 = 7.38264721

                               R01 = m                 R06:   temp           R11 = 2.M'                      R16:    temp
                               R02 = m'                R07 = E                R12 = M'+M-180°
                               R03 = gamma         R08 = M' - 180°   R13 = M'-M-180°
                               R04 = phase           R09 = M               R14 = 2M

Flag: F02 is set to indicate a Hybrid ( solar ) eclipse.
Subroutines: "J0" & "DT" ( cf "Julian & Gregorian Calendars for the HP-41" ) or "J1" & "D1" or "J2" & "D2"

-Lines 108 to 116 may be replaced by FLOOR LASTX FRC2 24 *
-Line 247 is a three-byte GTO

01 LBL "PHASE"
02 XEQ 05
03 INT
04 STO 00
05 4
06 MOD
07 STO 04
08 XEQ 06
09 XEQ 07
10 LBL 08
11 RCL 00
12 2
13 MOD
14 STO 05
15 221
16 *
17 407
18 +
19 RCL 08
20 SIN
21 *
22 RCL 09
23 SIN
24 172
25 *
26 RCL 07
27 *
28 +
29 RCL 05
30 7
31 *
32 16
33 -
34 RCL 11
35 SIN
36 *
37 -
38 RCL 05
39 9
40 *
41 5
42 -
43 ST+ X
44 RCL 10
45 SIN
46 *
47 +
48 RCL 05
49 ST+ X
50 7
51 -
52 RCL 13
53 SIN
54 *
55 +
56 RCL 05
57 7
58 *
59 5
60 +
61 RCL 12

62 SIN
63 *
64 +
65 RCL 14
66 SIN
67 RCL 08
68 RCL 10
69 -
70 SIN
71 +
72 ST+ X
73 +
74 RCL 08
75 RCL 10
76 +
77 SIN
78 RCL 05
79 ST+ X
80 1
81 -
82 *
83 +
84 RCL 08
85 COS
86 9
87 +
88 RCL 04
89 2
90 -
91 RCL 05
92 *
93 *
94 +
95 5598
96 +
97 E3
98 ST/ 03
99 /
100 RCL 00
101 RCL 15
102 *
103 +
104 RCL 16
105 70
106 /
107 +
108 INT
109 LASTX
110 FRC
111 X<0?
112 DSE Y
113 FRC
114 24
115 ST* Y
116 MOD
117 HMS
118 X<>Y
119 XEQ "DT"
120 RCL 04
121 RTN
122 LBL "ECL"

123 XEQ 05
124 2
125 /
126 INT
127 1
128 -
129 ST+ X
130 STO 00
131 LBL 10
132 2
133 ST+ 00
134 .36
135 XEQ 06
136 SIN
137 ABS
138 X>Y?
139 GTO 10
140 CF 02
141 RCL 00
142 4
143 MOD
144 STO 04
145 XEQ 07
146 SIN
147 207
148 *
149 RCL 07
150 *
151 RCL 14
152 SIN
153 ST+ X
154 +
155 RCL 08
156 SIN
157 39
158 *
159 +
160 RCL 10
161 SIN
162 RCL 11
163 SIN
164 +
165 11.7
166 *
167 +
168 RCL 12
169 SIN
170 RCL 13
171 SIN
172 -
173 7
174 *
175 +
176 RCL 03
177 COS
178 STO 02
179 *
180 5221
181 RCL 09
182 COS
183 5

184 *
185 -
186 RCL 14
187 COS
188 ST+ X
189 +
190 RCL 08
191 COS
192 330
193 *
194 +
195 RCL 12
196 COS
197 6
198 *
199 +
200 RCL 13
201 COS
202 4
203 *
204 -
205 RCL 03
206 SIN
207 *
208 +
209 RCL 02
210 ABS
211 208
212 /
213 1
214 -
215 *
216 STO 03
217 ABS
218 STO 05
219 5.9
220 RCL 08
221 COS
222 18
223 *
224 +
225 RCL 09
226 COS
227 9
228 *
229 RCL 11
230 COS
231 +
232 RCL 12
233 COS
234 +
235 2
236 /
237 +
238 STO 06
239 1543
240 +
241 RCL 04
242 7
243 *
244 +

245 -
246 X>0?
247 GTO 10
248 CHS
249 STO 02
250 RCL 04
251 X=0?
252 GTO 00
253 1013
254 RCL 05
255 -
256 RCL 06
257 -
258 545
259 ST/ 02
260 /
261 STO 01
262 GTO 09
263 LBL 00
264 RCL 05
265 997.2
266 X>Y?
267 SF 02
268 RCL 06
269 ABS
270 +
271 X>Y?
272 GTO 00
273 CLX
274 X<> 02
275 546
276 RCL 06
277 ST+ X
278 +
279 /
280 STO 01
281 GTO 09
282 LBL 00
283 RCL 05
284 E3
285 /
286 X^2
287 SIGN
288 STO 02
289 LASTX
290 -
291 22
292 *
293 X<0?
294 CLX
295 SQRT
296 RCL 06
297 X<Y?
298 X<0?
299 CF 02
300 X<>Y
301 546
302 ST- Z
303 -
304 /
305 STO 01

306 LBL 09
307 XEQ 08
308 CLX
309 RCL 02
310 RCL 01
311 R^
312 R^
313 RTN
314 LBL 05
315 XEQ "J0"
316 7.38264721
317 STO 15
318 /
319 DEG
320 RTN
321 LBL 06
322 RCL 00
323 97.667626
324 *
325 372
326 SQRT
327 -
328 STO 03
329 STO 10
330 ST+ 10
331 RTN
332 LBL 07
333 1
334 RCL 00
335 197 E4
336 /
337 -
338 STO 07
339 96.454234
340 RCL 00
341 ST* Y
342 47699
343 /
344 X^2
345 STO 16
346 +
347 465
348 SQRT
349 +
350 STO 08
351 STO 11
352 ST+ 11
353 STO 12
354 STO 13
355 RCL 00
356 7.276339
357 *
358 13
359 LN
360 +
361 STO 09
362 ST+ 12
363 ST- 13
364 STO 14
365 ST+ 14
366 END

( 527 bytes / SIZE 017 )

STACK	INPUT	OUTPUT1(phase)	OUTPUT2(eclipse)
T	/	/	m'
Z	/	HH.MNSS	m
Y	/	YYYY.MNDD	HH.MNSS
X	yyyy.mndd	Phase	YYYY.MNDD

where yyyy.mndd is an approximate date and Phase = 0 , 1 , 2 , 3 for New Moon , First Quarter , Full Moon , Last Quarter.

YYYY.MNDD is the date of the phase or the eclipse
HH.MNSS is the time of the phase or the maximum eclipse

For a Lunar Eclipse:

m = magnitude of the umbral eclipse m , m' > 1 for a total eclipse, if m < 0 there is no umbral eclipse
m' = magnitude of the penumbral eclipse m , m' < 1 for a partial eclipse

For a Solar Eclipse:

m = magnitude of the eclipse m > 1 for a total or hybrid eclipse m < 1 for a partial eclipse

         m' = 0   for a partial eclipse
         m' = 1   for an annular eclipse
         m' = m for a total or hybrid eclipse                F02 will be set for a hybrid eclipse

Examples:

   3000.0715   XEQ "PHASE"   >>>>         3                    ( Last Quarter )
                                                  RDN    3000.0716
                                                  RDN        21.5653           Note the difference with the standard definition of phases: 21h38m01s

   3000.1016   XEQ "ECL"   >>>>    3000.1019                Flag F02 is set, so we have a Hybrid ( Solar ) eclipse
                                              RDN        16.0807
                                              RDN     m = 1.0027              R03 = gamma = -0.2167
                                              RDN     m' = 1                      R04 = phase = 0 ( New Moon )

-The exact time is 16h10m16s and the exact m = 1.0049

-The instructions are identical to those of the program listed in §3, in particular:

>>>> To search for the next eclipse, simply press XEQ 10

-In the last example, it yields:

3000/11/04 RDN 5h44m53s RDN m = -0.4165 RDN m' = 0.5983 R03 = gamma = -1.2355 R04 = 2 ( Full Moon )

-Since m < 0 , there is no eclipse in the umbra: this Lunar eclipse is a penumbral one.

References:

[1] Jean Meeus - "Astronomical Algorithms" - Willmann-Bell - ISBN 0-943396-61-1
[2] Five Millennium Canon of Solar Eclipses: -1999 to +3000
[3] http://eclipse.gsfc.nasa.gov/LEcat/LEcatalog.html

hp41programs

Eclipses for the HP-41