  This work presents arbitrary high order well balanced finite volume schemes
for the Euler equations with a prescribed gravitational field. It is assumed
that the desired equilibrium solution is known, and we construct a scheme which
is exactly well balanced for that particular equilibrium. The scheme is based
on high order reconstructions of the fluctuations from equilibrium of density,
momentum and pressure, and on a well balanced integration of the source terms,
while no assumptions are needed on the numerical flux, beside consistency. This
technique allows to construct well balanced methods also for a class of moving
equilibria. Several numerical tests demonstrate the performance of the scheme
on different scenarios, from equilibrium solutions to non steady problems
involving shocks. The numerical tests are carried out with methods up to fifth
order in one dimension, and third order accuracy in 2D.
