Picosecond-level corrections to the Shapiro time delay in a Schwarzschild spacetime

We present an exact analytical equation for the Shapiro time delay (STD) due to a spherical non-rotating body. As a result, accurate values of the STD in comparison with first and second-order expressions for Schwarzschild spacetime (1Sch and 2Sch) and first-order post-Newtonian formalism (1PN) are achieved. Accordingly, the lowest STD discrepancies between our exact equation and these approximations lie within the picosecond and sub-picosecond level for light beams affected by the Sun's gravity. Our results might be useful for time delay measurements in the solar system or extragalactic binary pulsar systems, where a high accuracy level is required.