Coming through college and all my physics classes associated with my engineering degree, it always bugged me that a formal distinction between heterogeneous and homogeneous accelerations was never made.  Instead, gravity was always treated as a special case.  

When a solid body is accelerated by an applied force, whether a point force or distributed pressure, every point on the body experiences the same acceleration by virtue of internal stresses and strains which transfer the force to every point.

Alternatively, when every point of a solid body is given identical acceleration, as in the application of a gravitational field, the solid body experiences similar uniform acceleration but without any of the previous internal stresses or strains. 

Those internal stresses are the only things that can be measured or felt.  (Please someone tell me I am wrong!)

Gravity becomes one typical case of homogeneous acceleration, but  not the only one.  

This works unless you define space in such a way that a body in freefall is a body at rest.

Now, what can we determine from what?

First lets design an instrument consisting of a body with a known possion's ratio and install on the body three orthogonal strain gages.  Now we need to tare the instrument.

Homogeneous accelerations will not affect the instrument, only heterogeneous ones will do that.  We need to remove every force from the body long enough to tare the gages.  We need to remove the reactionary force from the floor keeping it from falling as well as air resistance.  Dropping the device down a long tube in a vacuum will remove all heterogeneous forces and establish the body's natural strain.

We can now measure gravity by measuring the strains developed from the reactionary forces when the device is motionless relative to the source of the gravity.

The device will not detect acceleration from sources for which it is not motionless relative to.  For example, gravity from the Sun, which it is in freefall relative to.

So the question is... how do we detect homogeneous acceleration from sources for which we are in freefall relative to?  If you could do that, you could establish absolute accelerations, which would extrapolate to absolute positions in space.  Something physics is fairly certain doesn't exist.