  Modified gravity theories can produce strong signals in the vicinity of the
saddles of the total gravitational potential. In a sub-class of these models
this translates into diverging time-delays for echoes crossing the saddles.
Such models arise from the possibility that gravity might be infrared divergent
or confined, and if suitably designed they are very difficult to rule out. We
show that Lunar Laser Ranging during an eclipse could probe the time-delay
effect within meters of the saddle, thereby proving or excluding these models.
Very Large Baseline Interferometry, instead, could target delays across the
Jupiter-Sun saddle. Such experiments would shed light on the infrared behaviour
of gravity and examine the puzzling possibility that there might be well-hidden
regions of strong gravity and even singularities inside the solar system.
