  In the core accretion paradigm of planet formation, gas giants only form a
massive atmosphere after their progenitors exceeded a threshold mass: the
critical core mass. Most (exo)planets, being smaller and rock/ice-dominated,
never crossed this line. Nevertheless, they were massive enough to attract
substantial amounts of gas from the disc, while their atmospheres remained in
pressure-equilibrium with the disc. Our goal is to characterise the
hydrodynamical properties of the atmospheres of such embedded planets and their
implication for their (long-term) evolution. In this paper -- the first in
series -- we start to investigate the properties of an isothermal and inviscid
flow past a small, embedded planet by conducting local, 2D hydrodynamical
simulations. Using the PLUTO code we confirm that the flow is steady and bound.
This steady outcome is most apparent for the log-polar grid (with the grid
spacing proportional to the distance from the planet). For low-mass planets,
Cartesian grids are somewhat less efficient as they have difficulty to follow
the circular, large speeds in the deep atmosphere. Relating the amount of
rotation to the gas fraction of the atmosphere, we find that more massive
atmospheres rotate faster -- a finding consistent with Kelvin's circulation
theorem. Rotation therefore limits the amount of gas that planets can acquire
from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc,
the planet's atmosphere will reach Keplerian rotation before self-gravity
starts to become important.
