49 50 Ver6.09.hp Geodesic distance & Earth Euclidean distance calculator, bearing

[Gil]

For HP49-HP50, programs to calculate exact distances (error less than 0.5 mm) on the earth surface.

Last version; 6.08, January 7th 2024.

Copy the file-directory ending by .doc or by .hp.

Inside are two programs:
1) P1P2—> (indirect method/problem)
2) P1—>P2 (direct method/problem)

Both programs give very accurate answers, for example the calculated distance is exact to 0.5 mm.

Let's assume you have two points P1 and P2 on the earth geoid.

1) To get the shortest distance between them, enter the following known 4 "objects" in the stack: lat1 and lon1 in the stack, for the 1st point P1, then for the 2nd point P2 lat2 and lon2 again in the stack, all of them in the format DD.mmsssss (be careful, not decimal degrees or radians).

Then press P1P2—>

After a few seconds you get the distance s, the forward azimuth alpha12 (initial bearing) and the backward azimuth alpha21.

2) The direct method/problem: you enter the coordinates of P1 in then stack, i. e. lat1 and lon2, then enter the chosen distance s in meters and the forward azimuth alpha12 (initial bearing) in DD.mmsssss.

Then press P1—>P2.

After a few seconds you get the coordinates of the new point P2, i.e. lat2 and lon2, as well as the backward azimuth alpha 21.

Iterations are made according to Vincenty's formulae.
Be careful: in this version of the indirect method/problem, the program P1P2—> might not find a solution for (near) antipodal points P1/P2; but those are special, rare cases.

You can change the radius a and b according to your preferred geoid; just modify the values in both programs P1P2—> and P1—>P2 and choose always meters (and not km or other units).

All "degrees" results are given in DD.mmssss, so that you can check the results of one program directly entering those found values for the other program.

Remarks are welcome.

Gil