The gravitational time delay in the field of a slowly moving body with arbitrary multipoles

•The Time-Transfer-Function (TTF) is used to calculate the gravitational time delay.•The time delay for a body with arbitrary multipoles at rest is calculated in a very simply manner.•The gravitational time delay induced by a slowly moving body with arbitrary multipoles is derived for the first time.

We calculate the time delay of light in the gravitational field of a slowly moving body with arbitrary multipoles (mass and spin multipole moments) by the Time-Transfer-Function (TTF) formalism. The parameters we use, first introduced by Kopeikin for a gravitational source at rest, make the integration of the TTF very elegant and simple. Results completely coincide with expressions from the literature. The results for a moving body (with constant velocity) with complete multipole-structure are new, according to our knowledge.