The Nordtvedt Effect: Lunar Laser Ranging Bounds on Gravitational Self-Energy Coupling in the Frame

If gravitational self-energy fell differently from other mass-energy, the Earth and Moon would fall toward the Sun at slightly different rates and their orbit would polarise toward the Sun - the Nordtvedt effect. Lunar laser ranging bounds the Nordtvedt parameter to 4.40e-04 plus or minus its uncertainty (Williams et al.), a two-standard-deviation magnitude limit of 1.34e-03. The Earth-Moon difference in gravitational self-energy fraction is -4.45e-10, so the permitted difference in their solar free fall is 5.96e-13 fractionally, corresponding to a synodic range signature no larger than about 1.76e-02 metres. In the frame, where the bound density depends on total energy density including self-energy, the result limits any anomalous self-energy coupling to the stated level. Computed from published values, not measured.