AbstractI review the elementary theory of gravitational waves on a Minkowski background and the quadrupole approximation. The modified conservation laws for energy and momentum keeping track of the gravitational‐wave flux are presented. The theory is applied to two‐body systems in bound and scattering states subject to newtonian gravity generalized to include a force allowing for orbital precession. The evolution of the orbits is studied in the adiabatic approximation. From these results I derive the conditions for capture of two bodies to form a bound state by the emission of gravitational radiation.