Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond

Details Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond

2009-04-23

arxiv.org/abs/0904.3704v3

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

24 pages, 2 figures, Report for GAIA astrometric mission

Scientific paper

Numerical integration of the differential equations of light propagation in the Schwarzschild metric shows that in some extreme situations relevant for practical observations (e.g. for Gaia) the well-known standard post-Newtonian formula for the boundary problem has an error up to 16 \muas. The aim of this note is to identify the reason for this error and to derive an extended formula accurate at the level of 1 \muas as needed e.g. for Gaia. The analytical parametrized post-post-Newtonian solution for light propagation derived by \citet{report1} gives the solution for the boundary problem with all analytical terms of order $\OO4$ taken into account. Giving an analytical upper estimates of each term we investigate which post-post-Newtonian terms may play a role for an observer in the solar system at the level of 1 \muas. We conclude that only one post-post-Newtonian term remains important for this numerical accuracy and derive a simplified analytical solution for the boundary problem for light propagation containing all the terms that are indeed relevant at the level of 1 \muas. The derived analytical solution has been verified using the results of a high-accuracy numerical integration of differential equations of light propagation and found to be correct at the level well below 1 \muas for arbitrary observer situated within the solar system.

Affiliated with

Also associated with

No associations

Rating

Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytical solution for light propagation in Schwarzschild field having an accuracy of 1 micro-arcsecond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-409406