## Saturday, June 3, 2017

### HP 20S and HP 21S Great Circle

HP 20S and HP 21S Great Circle

The following program calculates the distance between two places on Earth (or any other planet) given the coordinates latitude (λ, east is positive) and longitude (ϕ, north is positive).

Inputs:
R1:  longitude 1, R2:  latitude 1
R4:  longitude 2, R5:  latitude 2
Enter the coordinates in DD.MMSSSS.

R1, R4: ϕ1, ϕ2;   R2, R5:  λ1, λ2

Distance, in miles, is stored in R0.  Degrees mode is set.

Formula:

distance = acos( sin ϕ1 * sin ϕ2 + cos ϕ1 * cos ϕ2 * cos (λ2 – λ1) )* 3958.75 * π/180

On the HP 20S and HP 21S, can multiply by π/180 by executing the >RAD function.

HP 20S and HP 21S Program:  Great Circle

 STEP CODE KEY 01 61, 41, A LBL A 02 61, 23 DEG 03 22, 1 RCL 1 04 51, 54 >HR 05 21, 1 STO 1 06 23 SIN 07 55 * 08 22, 4 RCL 4 09 51, 54 >HR 10 21, 4 STO 4 11 23 SIN 12 75 + 13 22, 1 RCL 1 14 24 COS 15 55 * 16 22, 4 RCL 4 17 24 COS 18 55 * 19 33 ( 20 22, 2 RCL 2 21 51, 54 >HR 22 21, 2 STO 2 23 65 - 24 22, 5 RCL 5 25 51, 54 >HR 26 21, 5 STO 5 27 34 ) 28 24 COS 29 74 = 30 51, 24 ACOS 31 55 * 32 3 3 33 9 9 34 5 5 35 8 8 36 73 . 37 7 7 38 5 5 39 74 = 40 61, 55 >RAD 41 21, 0 STO 0 42 61, 26 RTN

Example 1:
Los Angeles to Rome:
Los Angeles (ϕ1 = 34°13’, λ1 = -118°15’)
Rome (ϕ2 = 41°15’, λ2 = 12°30’)
Result:  6322.2196 mi

Example 2:
Dublin to Las Vegas:
Dublin (ϕ1 = 53°20’52”, λ1 = -6°15’35”)
Las Vegas (ϕ2 = 36°10’30”, λ2 = -115°08’11”)
Result:  4938.7520 mi

Eddie

This blog is property of Edward Shore, 2017.