"I happened to read AAPT periodical "Interactions" (April 2008). There was an open forum letter stating that weightlessness should not be confused with zero- or microgravity. The letter made a distinction between the airplane flying a parabolic path (zero-gravity flight) and the space station following a circular orbit around the earth.
It was explained how in the space station "centrifugal force, due to inertia, equal and opposite gravity makes people and things orbit weightless". On the hand, the aeroplane is flying a parabolic path "that does not resist the force of gravity on the passenger and they are weightless but accelerating toward the earth due to gravity".
I have thought that both cases are equivalent from the point of view of relativity theory: the vehicles execute essentially free motion in gravitational field. Hence, the gravitational field in the frame of the vehicles is very nearly zero in both cases.
Or am I missing something here?
Regards,
Antti "
I think, both cases are absolutely equivalent with respect to the gravity force measured within a station or a falling plane. In both cases the object is in a state of a free fall. In both cases there is locally no gravity force on a point test mass within a freely falling object. Circular (or elliptical, for that matter) orbit is only a very special case of a free fall in which the falling object does not hit the attracting center because of its finely tuned transverse (orbital) velocity.
The same result can be described by using a concept of inertial force observed in any accelerated reference frame. In such a description we say that inertial force balances the gravity force. The centrifugal force in circular motion is merely a special case of an inertial force. If we consider just a freely falling elevator, there is no centrifugal force in it, but there is an inertial force. In all three cases the inertial force is mg, just as the gravity force, and in all three cases it is exactly opposite to the gravity force (assuming no additional instantaneous velocity of a test mass m relative to the falling object, be it an elevator, plane or space station).
The description using the inertial force is less preferable in all these cases since the inertial force is in all its properties locally indistinguishable from the gravity force produced by matter (the equivalence principle), except for the different boundary conditions (it does not disappear at infinity). Therefore it is better to just say that there is no gravity force on a freely falling object (another aspect of the same principle).
On the other hand, the absence of gravity force within a freely falling system does not mean absence of gravity as such. There is always an irreducible tidal effect, which can be observed and measured within a sufficiently large station. Geometrically, the spacetime curvature remains non-zero within a freely falling object in a field produced by a lump of matter, and this is also irrespective of the form of the orbit it follows.