Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure

The tangent vector of the light trajectory at future infinity and the angle of total light deflection in the gravitational field of an isolated axisymmetric body at rest with full set of mass-multipoles and spin-multipoles is determined in harmonic coordinates in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. It is found that the evaluation of the tangent vector and of the angle of total light deflection caused by mass-multipoles and spin-multipoles leads directly and in a compelling way to Chebyshev polynomials of first and second kind, respectively. This fact allows to determine the upper limits of the total light deflection, which are strictly valid in the 1PN and 1.5PN approximation. They represent a criterion to identify those multipoles which contribute significantly to the total light deflection for a given astrometric accuracy. These upper limits are used to determine the total light deflection in the gravitational field of the Sun and giant planets of the solar system. It is found that the first few mass-multipoles with l \le 10 and the first few spin-multipoles with l \le 3 are sufficient for an accuracy on the nano-arcsecond level in astrometric angular measurements.Comment: 56 pages, 1 figure, 3 table

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.Comment: 34 pages, 1 figur