The Museum of HP Calculators

Orbital Lander for the HP-41C/CV/CX

This program is Copyright © HP and is used here by permission. It was originally printed in the Games Solution Book. This program was entered and uploaded by Tony Duell. The documentation was entered by Dave Hicks. The Barcode for this program was provided by Brian Ward.

This program is supplied without representation or warranty of any kind. Tony Duell, Hewlett Packard 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 simulates a Lunar Excursion Module in orbit 100 km above the surface of the moon. The object is to execute a soft landing (velocity less than 5m/sec, at an angle not more than 5° from vertical) given a limited supply of fuel. On each move, you have the option of either free-falling for a specified period of time, or applying a specified thrust during a specified time period. Thrust is calculated and applied from your input of change in velocity over a given amount of time in a given direction from 0° to +/-180°. Your velocity will not actually change by this amount, of course, since gravity is also acting. You are not allowed to apply a thrust of greater than 7 Gees (69m/sec/sec of time period). If you run out of fuel, your thrust will be reduced to the fuel supply on hand. Thereafter, any thrust value you provide will be automatically changed to zero. When you pass zero altitude (i.e., land or crash), the program will calculate and display your velocity at impact. (Note to skilled pilots: try also to land at 0° longitude.)

Because the orbital equations are time-independent, the program has to convert the desired "delta-t" into a variable the equations can work with. This conversion process is not completely accurate, but the only error it introduces is that the actual duration of the jump may be slightly different from the one you specify. No positional error is introduced--you will still be on exactly the correct orbit--but you will find yourself at a slightly different point along that orbit. For example, a 2000 second jump along the initial orbit will take you almost a third of the way around the moon, but the conversion approximation will be about 10 percent shorter than an actual 2000 second jump.

Variable Conventions:

Important: The altitude (A) is from the surface of the moon, not the center.

The angle of velocity (V) is given from horizontal, with 0° being forward and 90° straight up.

Thrust angles also follow V conventions. 180° is a retrofire.

Note: Requires 1 Memory Module on HP-41C

Instructions

 Step Instructions Input Data/Units Keys Output Data/Units 1 Enter program 2 Initialize [XEQ] ORBIT 3 *Mission status: altitude A= longitude [R/S] = velocity [R/S] V= angle of flight [R/S] V= fuel remaining [R/S] F= 4 To free fall: key in number of seconds. Go to step 3 for outputs. n [A] Go to step 3 for outputs. 5 To fire rockets: key in total change in V dV(m/s) [ENTER] key in angle of thrust (deg) [ENTER] key in number of seconds for total burn n (sec) [B] Go to step 3 for outputs. When A=0.00, you are down. * Continuing [R/S]will repeat status.

Example

```   Keystrokes:          Display:
[XEQ] [ALPHA]
SIZE [ALPHA] 015
[XEQ] [ALPHA]
ORBIT [ALPHA]           A=100000.00 M  (altitude)
[R/S]                   =0.00        (longitude)
[R/S]                   V=1631.77 M/S  (velocity)
[R/S]                   V=0.00        (angle from horizontal)
[R/S]                   F=2,000.00     (fuel)
1000 [A]                A=99,957.06 M
[R/S]                   =55.65
[R/S]                   V=1,631.80 M/S
[R/S]                   V= 0.00
[R/S]                   F=2,000.00
For 10 seconds apply 7 gravities as retrofire
69 [ENTER] 10 [X]
180 [ENTER]
10 [B]                  A=99,908.77 M
[R/S]                   =55.95
[R/S]                   V=941.88 M/S
[R/S]                   V=-0.59
[R/S]                   F=1,310.00
200 [A]                 A=78,392.28 M
[R/S]                   =61.89
[R/S]                   V=974.77 M/S
[R/S]                   V=-12.14
[R/S]                   F=1,310.00
.                        .
.                        .
.                        .
```

How to get this Program to your Calculator (via HP-IL, disk, wand, and fingers)
Display the Program Barcode (.pdf) for printing and scanning

Program Listing

```LINE  KEYS
01 LBL "ORBIT"
02 SF 27
03 CLRG
04 CF 05
05 2000
06 STO 00
07 1839000
08 STO 01
09 4.89663 E12
10 STO 03
11 1631.765625
12 STO 05
13 1739000
14 STO 11
15 0
16 GTO 01
17 LBL B
18 STO 12
19 69
20 *
21 R^
22 RCL 00
23 X<=Y?
24 X<>Y
25 RDN
26 X<=Y?
27 X<>Y
28 RDN
29 ST- 00
30 P-R
31 ST+ 05
32 RCL 05
33 9
34 X>Y?
35 GTO 21
36 R^
37 ST+ 04
38 LBL 01
39 RCL 04
40 X^2
41 RCL 05
42 X^2
43 +
44 2
45 /
46 RCL 03
47 RCL 01
48 /
49 -
50 STO 06
51 RCL 01
52 RCL 05
53 *
54 STO 07
55 X^2
56 RCL 03
57 /
58 STO 08
59 *
60 2
61 *
62 RCL 03
63 /
64 1
65 +
66 SQRT
67 STO 09
68 RCL 08
69 RCL 01
70 /
71 1
72 -
73 RCL 09
74 /
75 FIX 07
76 RND
77 ACOS
78 RCL 04
79 RCL 05
80 *
81 X>0?
82 SF 05
83 RDN
84 FS?C 05
85 CHS
86 RCL 02
87 +
88 360
89 MOD
90 STO 10
91 RCL 12
92 LBL A
93 STO 12
94 0
95 ENTER
96 ENTER
97 RCL 05
98 9
99 X>Y?
100 GTO 21
101 RDN
102 RCL 12
103 *
104 RCL 03
105 RCL 01
106 X^2
107 /
108 RCL 12
109 *
110 2
111 /
112 RCL 04
113 X<>Y
114 -
115 RCL 12
116 *
117 RCL 01
118 +
119 R-P
120 RDN
121 ST+ 02
122 RCL 08
123 RCL 09
124 RCL 02
125 RCL 10
126 -
127 COS
128 *
129 1
130 +
131 /
132 STO 01
133 RCL 03
134 X<>Y
135 /
136 RCL 06
137 +
138 2
139 *
140 SQRT
141 STO 13
142 RCL 01
143 *
144 RCL 07
145 X<>Y
146 /
147 FIX 07
148 RND
149 ACOS
150 RCL 07
151 RCL 02
152 RCL 10
153 -
154 SIN
155 *
156 X<0?
157 SF 05
158 RDN
159 FS?C 05
160 CHS
161 LBL 20
162 STO 14
163 RCL 13
164 P-R
165 STO 05
166 RDN
167 STO 04
168 RCL 01
169 RCL 11
170 -
171 X<0?
172 GTO 22
173 LBL 10
174 FIX 02
176 "A="
177 RCL 01
178 RCL 11
179 -
180 X<0?
181 CLX
182 ARCL X
183 " M"
184 AVIEW
185 STOP
186 "="  ;"\0D="
187 RCL 02
188 1
189 P-R
190 R-P
191 ARCL Y
192 AVIEW
193 STOP
194 "V="
195 ARCL 13
196 " M/S"
197 AVIEW
198 STOP
199 "V="  ;"V\0D="
200 ARCL 14
201 AVIEW
202 STOP
203 "F="
204 ARCL 00
205 AVIEW
206 STOP
207 GTO 10
208 LBL 21
209 RDN
210 RDN
211 2
212 /
213 CHS
214 RCL 05
215 +
216 RCL 12
217 *
218 X<>Y
219 RCL 03
220 RCL 01
221 X^2
222 /
223 RCL 12
224 *
225 -
226 ST+ 04
227 2
228 /
229 CHS
230 RCL 04
231 +
232 RCL 12
233 *
234 RCL 01
235 +
236 R-P
237 STO 01
238 X<>Y
239 ST+ 02
240 LBL 00
241 RCL 04
242 RCL 05
243 R-P
244 STO 13
245 X<>Y
246 GTO 20
247 LBL 22
248 ST- 01
249 3
250 *
251 RCL 04
252 X^2
253 +
254 ABS
255 SQRT
256 CHS
257 STO 04
258 GTO 00
259 END
```