58 research outputs found
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
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