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The focus of recent research is in the relativistic reference frames, and in their experimental realization. The classical, Newtonian theory of astronomical reference frames can be found in classical textbook, e.g.,
Roy, A.E., Orbital Motion, Adam Hilger, 1978
in particular Chapters 2, 3 and Appendixes I, II.
In this Appendix we shall focus on the state of the art in relativistic reference frames, with particular attention to the time coordinates.
The main source for definitions are the IERS conventions, last version 2003, available from www.iers.org
and the IAU resolutions, available from
www.iau.org/static/resolutions/
For a reference describing the work underlying the IAU resolutions, see:
Soffel, M., Klioner, S.A., Petit, G., Kopeikin, S.M., Bretagnon, P., Brumberg, V.A., Capitaine, N., Damour, T., Fukushima, T., Guinot, B., Huang, T.-Y., Lindegren, L., Ma, C., Nordtvedt, K., Ries, J.C., Seidelmann, P.K., Vokrouhlický, D., Will, C.M., Xu, C.: The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron. J., 126, 2687-2706 (2003)
The state of the art has been discussed and updated in a dedicated IAU Symposium, with proceedings published in 2010:
Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, IAU Symposium 261, Klioner, Seidelmann and Soffel eds., Cambridge University Press, 436 pages, 2010.
In the document Relativistic reference frames for radio science experiments with a Mercury orbiter we have summarized the main issues relevant for very high accuracy orbit determination in this case, which of course is the one with the strongest relativistic corrections.
Relativistic reference frames for radio science experiments with a Mercury orbiter, PDF
The IERS conventions (see previous Section) also contain definitions for the realization of the reference frames, both celestial and terrestrial, and on the constants to be used with them.
We plan to add here a discussion on constants, units and especially the scaling problems occurring while implementing orbit determination algorithms.