Estimating the strength of Lorentzian distribution in noncommutative geometry by solar system tests

In this paper, we study four classical tests of Schwarzschild spacetime with Lorentzian distribution in noncommutative geometry. We performed detailed calculations of the first-order corrections induced by the noncommutative parameter on planetary orbital precession, light deflection, radar wave delay, and gravitational redshift. The study showed that the impact of the noncommutative parameter on the time-like geodesics is significantly greater than its effect on the null geodesics. By using a series of precise experimental observations, the allowable range for the noncommutative parameter is ultimately constrained within [Formula: see text], which is given by Mercury’s orbital precession. This result aligns with the view that [Formula: see text] is of the order of the Planck length. Moreover, this constrained parameter range exceeds the Planck scale by a significant margin.