dynamical ephemeris of the solar system (at the Newtonian approximation) by eliminating the motion of the Sun via the algebraic relation expressing that the total dipole mass moment of the solar system vanishes for all time (in a suitably mass-centered frame; [@jpl]).

In Sec. II we consecutively discuss the cases of the mass-energy integral, linear momentum integral and briefly comment on the angular momentum integral. Sec. III contains a summary of our results. Throughout the paper we follow the terminology and notation used in Refs. [@dam1; @dam2; @dam3; @dam4].

FIRST INTEGRALS OF THE DYNAMICAL LAWS
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Comments on the change of time-simultaneity integration domains
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As mentioned in the preceding section, transformation of integrals from the global to several local time simultaneity surfaces is a common point to all particular cases of conservation laws. We shall thus start our discussion with a brief technical comment concerning such transformations.

Considering a specific body $A$, we study some integral $${\cal I}_A(t) = \int_A d^3x\, f(t,{\bf x})\; ,\label{one}$$ performed on the global time $t={\rm const}.$ surface, where $f(x^\mu)$ is some given function defined on the [*compact*]{} support of body $A$. We seek a transformation of the right hand side of ${\cal I}_A$ such 