It's not at all clear what you mean by "detect space-time". Ich assumed you meant "detect the curvature of space-time" which is probably the best interpretation. As he said, Gauss attempted to determine if space is Euclidean by measuring the angles in a triangle formed by 3 mountain peaks using the best surveying equipment. He found any deviation from 180 degrees to be less than the error of measurement.
One difficulty with that is defining how you are going to measure things. Imagine using, say, Pluto, Uranus, and Neptune, at times when they are farthest apart in their orbits, as vertices of a triangle and thin steel bars as straight edges! Since, in relativity, there are no perfectly rigid materials, those bars would "sag" inward toward the sun- you would find the angles to be less than 180 degrees- elliptic geometry- and dependent upon the rigidity of the materials.
It would make much more sense to use laser beams as straight lines. Since it has been experimentally verified that light beams bend as they pass a star (the sun), your lines would appear curved and you would find the sum of the angles to be greater than 180 degrees- hyperbolic geometry- and that the curvature changed from moment to moment as the masses in the system moved.