2pn

2PN, or second post-Newtonian order, is a level of approximation in general relativity used to describe the motion of gravitating bodies in weak-field, slow-motion regimes. In the post-Newtonian expansion, physical quantities are expressed as a series in v/c, where v is a characteristic velocity and c is the speed of light. The 2PN term comprises corrections of order (v/c)^4 beyond Newtonian gravity and is largely conservative, affecting orbital dynamics without accounting for gravitational radiation.

In the two-body problem, the 2PN corrections modify the equations of motion, energy, and angular momentum. Different formulations exist (for example in harmonic or ADM coordinates), and results are usually written in terms of the total mass M, reduced mass μ, and symmetric mass ratio η. The 2PN terms refine predictions such as periastron precession and the relation between orbital period and energy.

Applications include modeling inspiraling compact binaries and generating gravitational-wave templates used by detectors like LIGO and Virgo. While 2PN improves accuracy over Newtonian and 1PN results, higher PN orders (3PN, 3.5PN) and numerical relativity are typically employed to describe the late inspiral and merger.

Limitations: the post-Newtonian expansion assumes v ≪ c and weak gravity; near merger the series converges poorly and full numerical relativity is required. 2PN remains an important building block in the broader efforts to describe relativistic two-body dynamics.