Second-order Compton-Getting effect on arbitrary intensity distribution

Theoretical studies of energetic particles in space are often referred to a special frame of reference. To compare theory with experiment, one has to transform the particle distribution from the special frame to the observer's frame, or vice versa. Various methods have been derived to obtain the directional distribution in the comoving frame from the directional fluxes measured on a spacecraft. These methods have become progressively complicated as increasingly detailed directional particle data become available. A set of 2nd order correct formulae for the transformation of an arbitrary differential intensity distribution, expressed as a series of spherical harmonics, between any two frames in constant relative motion is presented. These formulae greatly simplify the complicated procedures currently in use for the determination of the differential intensity distribution in a comoving frame.