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.