Actually real world physics can be used.
Assuming the detector is oriented towards the planet, there will be a slightly different force attracting each end due to the gradient of the gravitational field . This will be very small but can be measurable. This force will be -2*GMml/ R^3 where M and m are the masses of the body and the negative gravioli detector and l is the length of the detector.
This can be used to calculate the distance R and hence the gravitational field.
Einsteins equivalence principle holds for a single frame of reference - which technically exists at a single point. However, if we treat the detector as an extended object it is indeed possible to calculate the field.