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Definition of systems of space-time coordinates within the framework of the General Theory of Relativity

The XXIst General Assembly of the International Astronomical Union,


that it is appropriate to define several systems of space-time coordinates within the framework of the General Theory of Relativity,


that the four space-time coordinates (x_0 = ct, x_1, x_2, x_3) be selected in such a way that in each coordinate system centred at the barycentre of any ensemble of masses, the squared interval ds**2 be expressed with the minimum degree of approximation in the form (with Fortran expressions for squares):

ds**2 = - c**2 . dTau**2

= - (1 - 2U/ c**2). (dx_0)**2

+ (1 + 2U/ c**2). [(dx_1)**2 + (dx_2)**2 + (dx_3)**2],

where c is the velocity of light, Tau is proper time, and U is the sum of the gravitational potentials of the above mentioned ensemble of masses, and of a tidal potential generated by bodies external to the ensemble, the latter potential vanishing at the barycentre.

Notes for Recommendation I

  1. This recommendation explicitly introduces The General Theory of Relativity as the theoretical background for the definition of the celestial space time reference frame.
  2. This recommendation recognizes that space time cannot be described by a single coordinate system because a good choice of coordinate system may significantly facilitate the treatment of the problem at hand, and elucidate the meaning of the relevant physical events. Far from the space origin, the potential of the ensemble of masses to which the coordinate system pertains becomes negligible, while the potential of external bodies manifests itself only by tidal terms which vanish at the space origin.
  3. The ds2 as proposed gives only those terms required at the present level of observational accuracy. Higher order terms may be added as deemed necessary by users. If the IAU should find it generally necessary, more terms will be added. Such terms may be added without changing the rest of the recommendation.
  4. The algebraic sign of the potential in the formula giving ds2 is to be taken as positive.
  5. At the level of approximation given in this recommendation, the tidal potential consists of all terms at least quadratic in the local space coordinates in the expansion of the Newtonian potential generated by external bodies.

Text provided by the former Central Bureau.

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