Time delay in the quadrupole field of a body at rest in 2PN approximation

The time delay of a light signal in the quadrupole field of a body at rest is determined in the second post-Newtonian (2PN) approximation in harmonic coordinates. For grazing light rays at Sun, Jupiter, and Saturn the 2PN quadrupole effect in time delay amounts up to 0.004, 0.14, and 0.04 pico-second, respectively. These values are compared with the time delay in the first post-Newtonian (1PN and 1.5PN) approximation, where it turns out that only the first eight mass-multipoles and the spin-dipole of these massive bodies are required for a given goal accuracy of 0.001 pico-second in time-delay measurements in the solar system. In addition, the spin-hexapole of Jupiter is required on that scale of accuracy.