This program was first published in the HP41C Users' Library Solutions: Games by HewlettPackard and is used here by permission.
This program is supplied without representation or warranty of any kind. HewlettPackard Company 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.
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 freefalling 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 timeindependent, the program has to convert the desired "deltat" 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 introducedyou will still be on exactly the correct orbitbut 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 HP41C
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. 



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 . . . . . .
LINE KEYS 01 LBL "ORBIT" Initialize 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 Thrust 19 69 20 * 21 R^ 22 RCL 00 23 X<=Y? 24 X<>Y No greater than 7 gees 25 RDN 26 X<=Y? 27 X<>Y 28 RDN 29 ST 00 30 PR 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 Compute new orbit 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 7 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 Free fall 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 / g 108 RCL 12 109 * 110 2 111 / 112 RCL 04 113 X<>Y 114  115 RCL 12 116 * 117 RCL 01 118 + 119 RP 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 LBL 06 145 X<>Y 146 X!=0? 147 FIX 7 148 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 PR 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 2 Output 175 ADV 176 "A=" 177 RCL 01 178 RCL 11 179  180 X<0? 181 CLX 182 ARCL X 183 " M" 184 AVIEW Altitude 185 STOP 186 "=" 187 RCL 02 188 1 189 PR 190 RP 191 ARCL Y 192 AVIEW Longitude 193 STOP 194 "V=" 195 ARCL 13 196 " M/S" Velocity 197 AVIEW 198 STOP 199 "V=" 200 ARCL 14 Angle from horizon 201 AVIEW 202 STOP 203 "F=" 204 ARCL 00 Fuel 205 AVIEW 206 STOP 207 GTO 10 208 LBL 21 209 RDN 210 RDN Vector sums 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 RP 237 STO 01 238 X<>Y 239 ST+ 02 240 LBL 00 241 RCL 04 242 RCL 05 243 RP 244 STO 13 245 X<>Y 246 GTO 20 247 LBL 22 248 ST 01 Impact 249 3 250 * 251 RCL 04 252 X^2 253 + 254 ABS 255 SQRT 256 CHS 257 STO 04 258 GTO 00 259 .END.
R00 Fuel R01 Ri R02 i R03 Gm R04 Vr R05 Ve R06 E R07 1 R08 Ko R09 e R10 ' R11 surface R12 t R13 V R14 _{v}
05 Used
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