Within the parameterized post-Newtonian ( PPN ) formalism , there could be an anisotropy of local gravity induced by an external matter distribution , even for a fully conservative metric theory of gravity .
It reflects the breakdown of the local position invariance of gravity and , within the PPN formalism , is characterized by the Whitehead parameter \xi .
We present three different kinds of observation , from the Solar system and radio pulsars , to constrain it .
The most stringent limit comes from recent results on the extremely stable pulse profiles of solitary millisecond pulsars , that gives | \hat { \xi } | < 3.9 \times 10 ^ { -9 } ( 95 % CL ) , where the hat denotes the strong-field generalization of \xi .
This limit is six orders of magnitude more constraining than the current best limit from superconducting gravimeter experiments .
It can be converted into an upper limit of \sim 4 \times 10 ^ { -16 } on the spatial anisotropy of the gravitational constant .