Tests of modified gravity theories in the Solar System

We review the case for testing preferred acceleration scale theories of gravity (sometimes falling under the guise of modified Newtonian dynamics) in the Solar System using the forthcoming LISA Pathfinder (LPF) mission. Using a combination of analytical and numerical results, we suggest that different types of theory should be detectable using the predicted anomalous tidal stresses effects around the saddle points of the Newtonian gravitational field. The saddle point bubbles' expected extent of similar to 400 km are to be contrasted with potential miss parameters of <= 10 km, making such a test in easy reach of LPF. We also consider routes to constraining our theories from data, based on scenarios of both null and positive results.