  Light scalar fields can form gravitationally bound compact objects called
boson stars. The profile of boson stars in the Newtonian limit is described by
the Gross-Pitaevskii-Poisson equations. We present a semi-analytic solution to
these equations and construct the profile of boson stars formed by a
non-interacting scalar field. Our solution is stable with respect to numerical
errors and has accuracy better than $10^{-6}$ over the entire range.
