## Sunday, November 26, 2023

### DM42/HP 42S: Most Probable Position

DM42/HP 42S:  Most Probable Position

Introduction

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

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.   The program MPP requires the four variables to be entered in L, λ, Hc, and H0 to be entered in DDMM.m format (see the Instructions section).

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.  (negative is towards, positive is away)

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

To exit the program, press (EXIT).

DM42/HP 42S/Free42/Plus Code:  Most Probable Position

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

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

94 EXITALL

95 .END.

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

Eddie

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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