Originally Posted by Shadoko
Hope I didn't make errors there and this could help!
One small point - the satellite can't see the full earth disc! Why, because it is too close.
Use 35786km as Earth to Satellite distance, and 6371km as Earth radius. The right-angle triangle with 35786+6371 as side'c', 6371 as side 'a', will when solved for side 'b' provide a max distance of 41672.8km. Solving for satellite beam center to max angle (half beam) will provide 8.69°.
Using the above will show quickly that the 90° elevation at the Equator is correct, but the satellite doesn't see the poles.
Enough said, and I'm sure you'll go back and make the necessary changes.
As a help, check
post #3929
Also
post #5965 will show the earth - satellite elevation angles for some possible positions.
The so-called 'ping' times are of course the time taken for the receipt of the return of the aircraft's ICAO unique ID when polled by the satellite on an hourly basis - divided by 2 and converted to distance allowing for any latency/aircraft SATCOM through time. That timing creates the distance and ultimately the arc position on the earth's surface. The initial 'ping' was most likely at 1611UTC when the STATCOM system was powered up during the pre-flight checks.