Energy transfer in collisions of atmospheric O and H$_2$

We report new differential and total cross sections calculated quantum mechanically for O($^3$P) + H$_2(v,j)$ reactive collision using the most recent chemically accurate potential energy surfaces for $^3$A$'$ and $^3$A$''$. Reactive state-to-state calculations were performed at energies important for astrophysical environments and planetary atmospheres for total angular momenta up to $J=100$, and non-reactive cross sections were constructed for higher values of $J$. Corresponding differential cross sections were used to construct the kernel of Boltzmann equation and calculate energy relaxation of hot oxygen atoms in collisions with H$_2$. Escape of molecular hydrogen from planetary atmospheres and the role of angular anisotropy of the scattering are also discussed.