Abstract
The theoretical basis for modelling astrometric measurements is the analysis of the light-ray equation, or the equation of null geodesics. Only for a few gravitational systems such as black-hole space-times, exact solutions for null geodesics are known. For more complex situations, e.g., for the propagation of light-rays in the gravitational field of solar system bodies, one might resort to approximation schemes such as the post-Newtonian (PN) or the post-Minkowskian approximation. At the first PN (1PN) level one approximates the exact null-geodesic trajectory x γ(t) in some suitably chosen coordinate system (ct, x) by neglecting c −3 terms, in the 2PN approximation one neglects c −5 terms. In the first post-Minkowskian approximation (1PM) one neglects G 2 terms, in the 2PM approximation G 3 terms etc.
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Notes
- 1.
The following section is based upon private notes by Zschocke (2017).
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Soffel, M.H., Han, WB. (2019). Light-Rays. In: Applied General Relativity. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-030-19673-8_11
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