Abstract: We analyze a gasdynamical process in the stellar atmosphere that is driven by a "piston" moving with constant velocity in a weak gravitalional field. Ahead of the piston, the gas is compressed. and this compressed gas uses part of its internal energy and somewhere its kinetic energy to overcome the applied gravity.If we expand the quantities as a series of a small parameter, which is the ratio of a typical escape velocity to the plasma velocity, the basic stale gives a uniform flow, as shown by the case of gasdynamical theory without gravity. The first-order relationships show the influence of the applied gravity on the flow fields. that is, the strength of the shock wave changes slightly, the internat energy of the gas exhausts. For the cases of strong shock wave and near the piston, an analytical solution may be approximately olitained and has the similar features.Because of the importance of the applied gravity in the astrophysical and atmospheric physical processes, these results may shed light on the mechanics of transient process in the stellar and planetary atmosphere.

Key words: generalized inverse, function-valued Pad? approximant, epsilon-algorithm, eta-algorithm, integral equations