  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.
