Formal proof of some inequalities used in the analysis of the post-post-Newtonian light propagation theory

Details Formal proof of some inequalities used in the analysis of the post-post-Newtonian light propagation theory Formal proof of some inequalities used in the analysis of the post-post-Newtonian light propagation theory

2009-07-24

arxiv.org/abs/0907.4281v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

18 pages, no figures, report for astrometric GAIA mission

Scientific paper

A rigorous analytical solution of light propagation in Schwarzschild metric in post-post Newtonian approximation has been presented in \cite{report1}. In \cite{report2} it has been asserted that the sum of all those terms which are of order ${{\cal O} (\frac{m^2}{d^2})}$ and ${{\cal O}(\frac{m^2}{d_\sigma^2})}$ is not greater than $15/4 \pi \frac{m^2}{d^2}}$ and $15/4 \pi \frac{m^2}{d_\sigma^2}}$, respectively. All these terms can be neglected on microarcsecond level of accuracy, leading to considerably simplified analytical transformations of light propagation. In this report, we give formal mathematical proofs for the inequalities used in the appendices of \cite{report2}.

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