I maybe wrong and maybe I am missing the point, but isn't this a fairly easy task?
Using just those three formulas:
I can't check your students sheet as its not available anymore, but for the distance on the orthodrome at least I get the very same result as the site you try to duplicate.
To perfectly duplicate the values this site gives back when you choose "ball" you have to set the earth radius to 6378.137 km as this seems to be the value used at that site. Its not the mean value usually taken to make a sphere the same volume as the geoid but this value is the radius at the equator according to the ellipsoid GRS 80 resp. WGS84 from the year 1979.
In the map below I also draw the orthodrome of the two points, the great circle they are lying on. Of course it does not appear as a straight line in the Mercator map.
Sorry to return again on the subject. I want to clarify that the angles by me used (latitude and longitude) are those commonly used in analysis, geometry and electromagnetism and illustrated in octant here depicted below. Certainly I have not referred to the conventions of the art navigation or similar. (The z axis coincides with the terrestrial axis.)
You didn't use geographical coordinates as needed, so this explains the wrong results you got.
It furthermore explains your confusion about the North-South, East-West selectors, which you unfortunately had disabled in your last version. I don't know any Russian at either all but the meaning was clear from the context if you think of geographical coordinates - those selectors had to be there (and they are, too, on the site, Valery had linked to and which he is trying to imitate) . They do not do any harm - they just change the sign if needed (if South or West is selected) and have nothing to do with degree vs. radian. Valery just displayed the results in degrees (which makes much sense in this context).
So I guess your picture of the earth is just a static one and is not dynamically showing the entered locations as the Mercator plot does finally (this was the main work and its still unsatisfactory).
I was not able to find a decent set of continent border data to make a 3D earth plot showing the locations and connections. Maybe some day when I am really bored I'll download a set of KML data and extract the coordinates - but then, probably not.
Thank you, Werner for your kind response. Certainly, I have considered the angles in radians, already present in the worksheet of Valery. My graphics, no claim, they are sketches made with Paint. The verification of the measurement of distances can be done with "Google Earth", I'm sure you certainly know (here, in my country, it is very common) and from which I have drawn the image of the globe with a simple keyboard print. What I mind is the correctness of the calculations resulting from geometrical considerations in space. Not knowing the Russian language, I tried to translate with google translator the fundamental astronomical four directions north south east west, associated with the radio button, but I did not find the correspondence, even with abbreviations. I had guessed, but I preferred to proceed. The answers that I generally do, are the proofs that need, as such, more and corrections. But I think that, since it's only recently that I try to participate in discussions it happens that, as you know, when something starts, the output can have a transitory with "ups and downs" dangerous, which then dampen. It would not be wise, for me, to continue down this road.
