Can you help me with this problem, it's driving me insane?

Question

The Earth rotates eastward at speed s=500m/s at equator. Airplane flies in due west direction along equator at speed v=s=500m/s wrt earth.

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When I do this problem in the frame of refence rotating with the earth, then:

forces acting on the plane are:
gravity mg (downwards)
centrifugal force mω²R = ms²/R (upwards)
airlift F (upwards)

dynamic equation for the airplane is
ma = F - mg + ms²/R
Accleration a is centripetal accleration:
a = -v²/R (minus signifies downward direction)
Final equation for airlift:
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F = m(g - 2s²/R)
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But when I consider this problem in inertial frame of reference, the airplane is at rest, and I get simply
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F = mg
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Answer 1

I don't think there is any centrifugal force acting on the plane per se. Gravity provides the centripetal force which results in circular motion.

The dynamic equation should be
ma = -mv²/R = F - mg
where a = acceleration in +ve r direction

For the plane flying on the opposite direction to the earth, the absolute speed in space is zero.
So F - mg = 0
F = mg

Answer 2

Inertially the plane is at rest but neither the Earth nor its atmosphere is, so the aero lift equation applies. And at 1800 km/hr it'll apply a lot! You're right that the centrifugal term vanishes.

Answer 3

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Answer 4

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http://www.groupsrv.com/science/about266577-0.html