Comment by adrian_b

If you measure acceleration in a single point, without other information you cannot know whether it is caused by gravitational attraction or by movement that is not rectilinear and uniform.

However, if you measure acceleration in many points, you typically can discriminate the 2 cases, because the spatial variation of the 2 kinds of acceleration fields is normally very different.

If you also move relatively to the local system of reference while measuring acceleration, you have additional distinguishing information from Coriolis forces.

So with enough measurements, gravitational forces and inertial forces can always be separated.