Post-Newtonian and Post-post-Newtonian effects in the theory of light propagation for high-precision astrometry
Final Report Abstract
The ESA astrometry missions Hipparcos (nominal mission: 1989-1993) and Gaia (nominal mission: 2013-2018) have established a new era in astrometric science. In particular, the Hipparcos final catalogue provides accuracies of stellar positions up to 1 milli-arcsecond, while the Gaia mission has arrived at precisions up to a few micro-arcseconds in angular observations of stellar objects. The impressive progress has encouraged the astrometric science to proceed further in near future. Several astrometry missions have been proposed to ESA (e.g. Gaia-NIR, Theia, NEAT) aiming at the micro-arcsecond, sub-micro-arcsecond and nano-arcsecond level of precision. Such unprecedented accuracies necessitate corresponding advancements in the theory of light propagation in the Solar system, that means the determination of trajectories of light signals, emitted by some celestial object and which propagate through the curved space-time of the Solar system towards the observer. For high-precision astrometry on the sub-micro-arcsecond level of accuracy it is of fundamental importance to determine and to investigate the first terms of the post-Newtonian (PN) expansion of the light trajectory. Thus far, the 1PN and 1.5PN terms have only been determined either for light propagation in the field of N point-like bodies in motion or for N extended bodies at rest. Within the project, the 1PN and 1.5PN terms of the trajectory of a light signal, which propagates in the gravitational field of N extended bodies moving along arbitrary world lines, have been determined. In the approach, the gravitational field of the Solar system is described in terms of the full set of intrinsic mass-multipoles and spin-multipoles of each individual massive body, hence allowing for arbitrary shape, inner structure, oscillations and rotational motions of these bodies. The intrinsic multipoles are defined in the local reference system of each individual massive body, in line with the requirements of the theory of relativistic reference systems and in accordance with the resolutions of the International Astronomical Union. Furthermore, expressions for timedelay and light-deflection have been given. Regarding the 1PN and 1.5PN terms, it has been found that only the first ten mass-multipoles and the first two spin-multipoles need to be taken into account for astrometry on the nano-arcsecond level. Astrometry on sub-micro-arcsecond level requires also to consider some 2PN terms. Thus far, however, the 2PN terms were only known for light propagation in the field of one monopole at rest. In this project, the initial and boundary value problem of light propagation in the field of one arbitrarily moving monopole has been solved and the 2PN light trajectories are expressed in terms of the retarded position of the moving body, which simplifies the expressions and makes the retardation of gravitational action evident. In reality, the bodies are not spherically symmetric but are of arbitrary shape. In order to go beyond the monopole approximation, the 2PN metric for one body at rest having arbitrary shape and inner structure has been determined. Finally, it has been found that in 3PN approximation only the monopole term needs to be taken into account for astrometry on the nano-arcsecond level, while the 4PN monopole term is irrelevant for astrometry missions observing in the exterior of some solar-aspect angle of a few degree between the Sun and the instrument spin axis of the space-based observer. The results of the project represent a basis for subsequent investigations, aiming at the sub-micro-arcsecond and nano-arcsecond level of astrometric measurements.
Publications
- Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry, Physical Review D 92 (2015) 063015
S. Zschocke
(See online at https://doi.org/10.1103/PhysRevD.92.063015) - Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry, Physical Review D 93 (2016) 103010.
S. Zschocke
(See online at https://doi.org/10.1103/PhysRevD.93.103010) - Light propagation in the field of one arbitrarily moving pointlike body in the 2PN approximation, Physical Review D 94 (2016) 124007
S. Zschocke
(See online at https://doi.org/10.1103/PhysRevD.94.124007) - Light propagation in the Solar System for astrometry on sub-microarcsecond level, Conference Proceeding: IAU Symposium 330: Astrometry and Astrophysics in the Gaia sky, 24 - 28 April 2017, Nice/France
S. Zschocke
(See online at https://doi.org/10.1017/S1743921317005245) - Light propagation in 2PN approximation in the field of one moving monopole I. Initial value problem, Classical and Quantum Gravity 35 (2018) 055013
S. Zschocke
(See online at https://doi.org/10.1088/1361-6382/aa9976) - Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem, Classical and Quantum Gravity 36 (2019) 015007
S. Zschocke
(See online at https://doi.org/10.1088/1361-6382/aaeb4c) - On the post-linear metric of a solar system body, Conference Proceeding: Journees 2019: Astrometry, Earth Rotation, Reference Systems in the Gaia era, 7 - 9 October 2019, Paris Observatory, Paris/France
S. Zschocke
- Post-linear metric of a compact source of matter, Physical Review D 100 (2019) 084005
S. Zschocke
(See online at https://doi.org/10.1103/PhysRevD.100.084005)
