Helmert’s Equation

Description

by Dr. D.G. Simpson, http://www.pgccphy.net/1030/software.html

Given the latitude θ (in degrees) and the elevation H (in meters), this program uses Helmert’s equation to find the acceleration due to gravity g.
To run the program, enter:

0.025928 STO . 1
9.80616 STO . 2
6.9 EEX 5 STO . 3
3.086 EEX 6 STO . 4

θ ENTER H f A

where θ is in degrees and H is in meters. The program returns the acceleration due to gravity g in m/s2.
After running the program, the calculator will be set to degrees mode.

Example:
Let θ = 38.898°, H = 53 m. Enter the above program, then type:

38.898 ENTER 53 f A

The program returns g = 9.80052 m/s2.

Program Resources

Labels

Name Description
 A Helmert’s Equation

Storage Registers

Name Description
.0 2 x Theta
.1 0.025928
.2 9.80616
.3 6.9 x10^-5
.4 3.086 x 10^-6

Program

Line Display Key Sequence
000
001 42,21,11 f LBL A
002 43 7 g DEG
003 34 x↔y
004 2 2
005 20 ×
006 44 .0 STO . 0
007 24 COS
008 45 .1 RCL . 1
009 20 ×
010 45 .2 RCL . 2
011 34 x↔y
012 30
013 45 .0 RCL . 0
014 24 COS
015 43 11 g
016 45 .3 RCL . 3
017 20 ×
018 40 +
019 34 x↔y
020 45 .4 RCL . 4
021 20 ×
022 30
023 43 32 g RTN