The Museum of HP Calculators
The Museum of HP Calculators
This program was first published in the HP-41C Users' Library Solutions: Games by Hewlett-Packard and is used here by permission.
This program is supplied without representation or warranty of any kind. Hewlett-Packard 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 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
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Step |
Instructions |
Input Data/Units |
Keys |
Output Data/Units |
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1 |
Enter program |
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2 |
Initialize |
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[XEQ] ORBIT |
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3 |
*Mission status: altitude |
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A= |
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longitude |
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[R/S] |
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| velocity |
[R/S] |
V= |
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| angle of flight |
[R/S] |
V |
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| fuel remaining |
[R/S] |
F= |
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4 |
To free fall: key in number of seconds. Go to step 3 for outputs. |
n |
[A] |
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| Go to step 3 for outputs. | ||||
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5 |
To fire rockets: key in total change in V |
dV(m/s) |
[ENTER] |
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| key in angle of thrust |
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[ENTER] |
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key in number of seconds for total burn |
n (sec) |
[B] |
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| Go to step 3 for outputs. |
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When A=0.00, you are down. |
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* |
Continuing [R/S]will repeat status. |
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Keystrokes: Display: [XEQ] [ALPHA] SIZE [ALPHA] 015 [XEQ] [ALPHA] ORBIT [ALPHA] A=100000.00 M (altitude) [R/S]
LINE KEYS 01LBL "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
M" 184 AVIEW Altitude 185 STOP 186 "
R00 Fuel R01 Ri R02i R03 Gm R04 Vr R05 Ve R06 E R07 1 R08 Ko R09 e R10
05 Used
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