(42S/DM42/Free42/Plus42) Most Probable Position

[Eddie W. Shore]

The program MPP calculates an adjusted latitude (+N, -S) and adjusted longitude (+W, -E) of an observer:

* The latitude and longitude of the observer's dead reckoning.
* The computed altitude and azimuth (N = 0°, E = 90°, S = 180°, W = 270°).
* The height of the sextant held by the observer.

The most probable position is calculated by:

Calculated latitude:

LAT* = L - (Hc - H0) × cos(Z)

Calculated longitude:

LON* = λ - ( (H0 - Hc) × sin(Z) ÷ cos(L) )

where

L = dead reckoning latitude
λ = dead reckoning longitude
Hc = computed altitude of the celestial object
Z = zenith of the celestial object
H0 = correct sextant height

L, λ, Hc, H0 are customarily entered in degrees-minutes or degrees-minutes-seconds format.

Instructions

Soft menu items are enclosed in parenthesis.

1. Enter the longitude and latitude in DDMM.m format. DD represents decimal degrees, MM represents the integer part of minutes, and .m represents the fractional part of minutes.

Examples:

Enter 52°00' as 5200.

Enter 17°16.56' as 1716.56.

Enter the longitude, press [ENTER], enter the latitude, then press (LA/LO). North longitude is positive, west latitude is positive.

2. Enter the altitude of the reference object (star, planet, sun, other celestial object) in DDMM.m format, press [ENTER], the object's zenith in degrees, then press (HC/Z).

3. Enter the correct sextant height in DDMM.m format, press (>H0). The altitude intercept (Hc - H0) is displayed in miles.

4. Press (CALC) to get the computed latitude (LAT*), press [ R/S ] to get the computed longitude (LNG*).

To exit the program, press (EXIT).

Code:

00 { 234-Byte Prgm }
01▸LBL "MPP"
02 DEG
03 "MOST PROBABLE"
04 AVIEW
05 PSE
06 "POSITION, HP 65"
07 AVIEW
08 PSE
09 "DDMM.m, +N, +W"
10 AVIEW
11 PSE
12▸LBL 30
13 "LA/LO"
14 KEY 1 XEQ 21
15 "HC/Z"
16 KEY 2 XEQ 22
17 ">H0"
18 KEY 3 XEQ 23
19 "CALC"
20 KEY 4 XEQ 24
21 "EXIT"
22 KEY 6 XEQ 26
23 MENU
24▸LBL 00
25 STOP
26 GTO 00
27▸LBL 21
28 XEQ 31
29 STO 07
30 X<>Y
31 XEQ 31
32 STO 02
33 GTO 30
34▸LBL 22
35 STO 05
36 X<>Y
37 XEQ 31
38 STO 04
39 GTO 30
40▸LBL 23
41 XEQ 31
42 STO 06
43 RCL 04
44 X<>Y
45 -
46 STO 01
47 XEQ 32
48 GTO 30
49▸LBL 31
50 →HMS
51 100
52 ÷
53 →HR
54 RTN
55▸LBL 32
56 →HMS
57 100
58 ×
59 →HR
60 RTN
61▸LBL 24
62 RCL 02
63 RCL 05
64 COS
65 RCL× 01
66 -
67 STO 03
68 XEQ 32
69 "LAT*="
70 ARCL ST X
71 AVIEW
72 STOP
73 RCL 07
74 RCL 05
75 SIN
76 RCL× 01
77 RCL 02
78 COS
79 ÷
80 +
81 1
82 →REC
83 →POL
84 X<>Y
85 STO 08
86 XEQ 32
87 "LNG*="
88 ARCL ST X
89 AVIEW
90 PSE
91 GTO 30
92▸LBL 26
93 CLMENU
94 EXITALL
95 .END.

Download: https://drive.google.com/file/d/1Jrs14guVv3wuYEMuFRYDq4N3MGHrICxL/view?usp=sharing


Example

Data Given:
Latitude: 30°44' N
Longitude: 128°36' W
Computed Altitude of star: 21°40'
Azimuth of the star: 61°
Corrected Sextant: 19°32'

Enter:
3044 ENTER 12836 (LA/LO)
2140 ENTER 61 (HC/Z)
1932 (>H0)

(CALC)
LAT*=2941.57 (29°41.57' N)
LNG*=13046.25 (130°46.25' W)


Source

Hewlett Packard. "NAV 1-20A: MOST PROBABLE POSITION" HP-65 Navigation Pac 1 1974. pp. 64-65, 137