Editing Openai/6945b8b5-5788-8000-9352-d5062c255aa0 (section)

==== 3. Mathematical demonstration (no analogies) ====

Let:
* va=500v_a = 500va=500 mph (airspeed)
* ve=v_e =ve= Earth’s eastward rotational speed at that latitude
* d=d =d= distance between Land A and Land B

===== Eastbound flight (A → B): =====

vground=ve+vav_{ground} = v_e + v_avground=ve+va
===== Westbound flight (B → A): =====

vground=ve−vav_{ground} = v_e - v_avground=ve−va
❗ This is where your reasoning stops — but it only applies if the air is stationary in space, which it is not.

Now include atmospheric motion properly:

Let the air itself move eastward at vev_eve.

The plane moves ±500 mph relative to the air, not the ground.

So the ground-relative velocity becomes:

vground=(ve)+(±500)v_{ground} = (v_e) + (\pm 500)vground=(ve)+(±500)
But the destination land is also moving at vev_eve.

So relative speed between plane and destination is:

(ve±500)−ve=±500(v_e \pm 500) - v_e = \pm 500(ve±500)−ve=±500
✅ Same magnitude. Same travel time.

No contradiction. No impossibility.