An approximate form of the transport equation is used to investigate stationary and time-dependent neutron slowing down and propagation in the field of gravity. The approximation is based on the expansion of the δ function of the transfer function in a power series of a small parameter s, the ratio of the neutron to atom masses. It is shown that the s and s2 approximations in the stationary neutron slowing down problems are connected with Wigner and Grueling-Goertzel approximations. A simple formula is given for time-dependent neutron slowing down. The influence of the field of gravity on the operation of a reactor and on the propagation of ultra cold neutrons is studied in the point-energy approximation. Also investigated is the neutron space-energy distribution in the field of gravity.