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My first thought was to use an accelerometer.

However, quoting from wikipedia,

an accelerometer at rest on the surface of the Earth will measure an acceleration g= 9.81 m/s2 straight upwards. By contrast, accelerometers in free fall (falling toward the center of the Earth at a rate of about 9.81 m/s2) will measure zero.

I'm assuming that the same accelerometer would measure zero in absence of any gravitational fields whatsoever too (say in outer space, away from all and any massive objects)

So an accelerometer can't distinguish between the two situations, then what can?

I think that the two situations aren't equivalent because in free fall, the kinetic energy of the object increases with time (i.e. there is a change in velocity due to acceleration), so there must be a way to distinguish between the two.

Can this be answered with Newtonian mechanics? If not, then is it a limitaion of Newtonian mechanics?

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No, it can't: free fall and zero gravity are the same thing. On that equivalence hangs the theory of General Relativity, in fact.

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  • $\begingroup$ How would you explain the I think that the two situations aren't equivalent because in free fall, the kinetic energy of the object increases with time (i.e. there is a change in velocity due to acceleration), so there must be a way to distinguish between the two.? $\endgroup$ – Peeyush Kushwaha Apr 5 '16 at 8:42
  • $\begingroup$ @PeeyushKushwaha: I'd 'explain' it by asking you to design an experiment, local to the body, which will distinguish between free-fall and absence of gravity. Well, it turns out that there is no such experiment (or none we know of I should say). The whole notion of kinetic energy is something which is only defined with respect to some other object: you can't locally measure your own kinetic energy because it is always zero. $\endgroup$ – tfb Apr 5 '16 at 8:54
  • $\begingroup$ @PeeyushKushwaha In general relativity, the acceleration we typically measure in free fall is referred to as "coordinate acceleration," and is not true acceleration. If the curvature of spacetime is taken into consideration, the acceleration determined for free fall is found to be equal to zero. So free fall is equivalent to an inertial frame of reference. $\endgroup$ – Chet Miller Apr 5 '16 at 13:07

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