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+--- Thread: (20S and 21S) Great Circle (/thread-8453.html)
(20S and 21S) Great Circle - Eddie W. Shore - 06-03-2017 08:42 PM
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
Code:
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 RTNExample 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
RE: (20S and 21S) Great Circle - Marcel - 06-03-2017 10:00 PM
Hi Eddie!
For an other planet, the user must change the numerical factor!!!.. the radius of the planet in miles or km.
Marcel
RE: (20S and 21S) Great Circle - Dieter - 06-04-2017 03:37 PM
(06-03-2017 10:00 PM)Marcel Wrote: For an other planet, the user must change the numerical factor!!!.. the radius of the planet in miles or km.
Since most planets are not perfect spheres there is not a single radius. For instance the WGS84 system (cf. GPS) works with an Earth radius of 6378,137 km in East-West direction and with 6356,7523 km for North-South.
Eddie's formula uses a constant radius of 3958,75 miles or 6371 km. This is a good choice that minimizes the error of the calculation (cf. here). Yet there still is a potential error of 0,5%. So the result should be rounded to at most three significant digits. For the given examples that's 6320 resp. 4940 miles.
A final hint: enter an angle, and 1 P→R simultaneously returns both sine (in Y) and cosine (in X).
Edit: this works on classic RPN calculators and probably cannot be used for the algebraic 20S and 21S.
Dieter