  The barometric equation predicts the molecular concentration $n(z)$
exponentially decaying with altitude $z$. Because the mean free path
$l=1/n\sigma$ increases exponentially, at high altitudes $z$, the equation is
no longer within the domain of applicability of the standard kinetic theory.
\cite{grimsditch} Here, we predict the dependence $n(z)\propto z^{-2}$ for the
case $l\gg L$ in uniform gravity and $n(z)\propto [\ln(1+z/R_0)]^{-2}$ when
$z\gg R_0$ for a planet of radius $R_0$. It corresponds to a non-stationary
planetary atmosphere with hydrogen accretion. The accretion is accompanied by a
release of gravitational potential energy that could be the elusive source
driving the formation of stellar coronas. Other consequences include slowly
decaying tails of planetary atmospheres and periodical hydrogen explosions of
white dwarfs.
