1pN

1PN stands for the first post-Newtonian order in the post-Newtonian expansion of general relativity. This approximation is used in weak gravitational fields and for motions slow compared with the speed of light, to add relativistic corrections to Newtonian gravity. The corrections are of order v^2/c^2 or GM/(rc^2), and they account for phenomena such as time dilation, gravitational redshift, and small relativistic modifications to orbital dynamics.

In standard weak-field coordinates, the spacetime metric is expanded around Minkowski space. To 1PN order it involves the Newtonian potential U, which satisfies the Poisson equation ∇^2U = -4πGρ, along with additional potentials that encode mass currents and spatial curvature. The equations of motion for bodies acquire 1PN corrections, producing a1PN terms in the acceleration. These corrections yield observable relativistic effects while remaining solvable with Newtonian intuition.

One notable consequence of 1PN gravity is the perihelion precession of planetary orbits. For a bound orbit with semi-major axis a and eccentricity e, the periapsis advances by Δφ ≈ 6π GM/(a(1−e^2)c^2) per orbit, a result that matches the observed precession of Mercury. Other 1PN predictions include gravitational time dilation, light deflection by mass, and the Shapiro time delay, all described by the same metric expansion.

1PN accuracy underpins much of solar system tests and modeling of binary systems where radiation-reaction effects appear at higher orders. It is the leading correction beyond Newtonian gravity; higher post-Newtonian terms (2PN, 2.5PN, etc.) refine the description and incorporate gravitational radiation effects. In the parametrized post-Newtonian framework, general relativity corresponds to gamma = beta = 1 at 1PN order.