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?