Watching Planes Approaching an Airport – never seen on the horizon

I was thinking about how airplanes would approach an airport and how they should look if on a globe.  I was looking at various sites that talk about when a commercial airline (flying at 30,000 feet) starts it’s decent.  At about 300 miles out the plane will start descending at about 500 feet per minute.   If you could look 200 miles out with a powerful enough telescope, the horizon would equal about 5.6 miles.  In other words no airplane could be seen since at that distance since 5.6 miles is the highest a plane normally flies.
With that descent time, a plane would reach ground in just under 1 hour.  It would be assumed that the cruising speed would also decrease since the average speed is about 500 miles per hour.  Assuming that the average speed during decent is about 300 miles per hour and 500 feet is dropped per minute then at what distance should the plane be visible?
After 30 minutes the plane will have dropped 15,000 feet (2.84 miles) and be 30 minutes out and 150 miles from the airport.  Again, if you could look out that far with a telescope the plane would be at or below the horizon.  Over the next 15 minutes the plan would drop another 7500 feet and be 75 miles out.   At that point the plan should still be at or below the horizon.  Over the next 7.5 minutes the plane would drop 3750 feet and be 37.5 miles out and 937.5 feet above the ground.  Again, the plan would not be visible.  Over the proceeding 3.75 minutes, the plane would be 18.75 miles out and 234 feet above the ground and still not visible.  However, it is mostly likely that the decent and speed would be throttle to match the runway so the final few miles one would finally allow the plane to appear at the horizon.  So what we would see would be the plane shoot upward from the horizon and then rapidly drop down.
Of course this is an extreme example to demonstrate the idea.  But the point it that if you watch airplanes approach airports they are always very high in the sky and slowly descend over time.  They never shoot up from the horizon.  What we do see is planes ascending or descending but never appear at the horizon.
If someone was to film airplanes as they approach the airport,  I can pretty much guarantee that not a single plan will shoot up from the horizon and then curve downwards toward the airport.
On another note, whenever you see jet streams they are always straight.  At plane at 30,000 feet will be visible for a shot period of time before it starts curving towards the horizon.  They should have a curve in them.  No ones sees that either.

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