  Owed to their compactness, neutron stars involve strong gravity and extreme
density physics. Nevertheless, at present, there are a variety of problems
where progress (at least conceptually) can be made in the context of weak
gravity. Motivated by this we examine how accurately one can model neutron
stars using the post-Newtonian approximation to general relativity. In general,
we find there is a significant degree of freedom in how the post-Newtonian
equations of stellar structure can be formulated. We discuss this flexibility
in the formulation and provide examples to demonstrate the impact on stellar
models. We also consider the (closely related) problem of building neutron
stars using isotropic coordinates. In this context, we provide a new strategy
for solving the equations (based on a scaling argument) which significantly
simplifies the problem.
