Instantaneous gravity in equation of motion for ephemerides calculation The equation of motion used for the calculation of orbits of solar system objects (Eq(27) in https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf ) is formulated in terms of instantaneous variables, that is the acceleration of an object is assumed to depend on the instantaneous positions, velocities and accelerations of all other objects in the solar system (this has been confirmed to me by the authors of this publication). Would this not mean that information travels infinitely fast and thus contradict Relativity?
Would this not mean that information travels infinitely fast and thus contradict Relativity?

Look more closely at equation 27 in the referenced document. I'll simplify this as
$$\boldsymbol{\mathrm a} = \left(\sum_{B \ne A}\frac{GM_B\,(\boldsymbol{\mathrm r}_B - \boldsymbol{\mathrm r}_A)}{r_{AB}^{\,3}} \Bigl(1 + \text{other terms}\Bigr)\right) + \text{another term} + \text{yet another term}$$
Assuming Newtonian gravity, the &quot;other terms&quot;, &quot;another term&quot;, and &quot;yet another term&quot; all vanish, simplifying the equation to
$$\boldsymbol{\mathrm a} = \left(\sum_{B \ne A}\frac{GM_B\,(\boldsymbol{\mathrm r}_B - \boldsymbol{\mathrm r}_A)}{r_{AB}^{\,3}} \Bigl(1 + 0\Bigr)\right) + \boldsymbol{\mathrm 0} + \boldsymbol{\mathrm 0}$$
or just
$$\boldsymbol{\mathrm a} = \sum_{B \ne A}\frac{GM_B\,(\boldsymbol{\mathrm r}_B - \boldsymbol{\mathrm r}_A)}{r_{AB}^{\,3}}$$
All of those extra terms in equation 27 in the referenced document are due to a linearization of general relativity assuming that distances are very large compared to the Sun's Schwarzschild radius and that velocities are very small compared to the speed of light.