to measured gravity of the object, or to the inertia. In general relativity, the self-energy affects both the gravitional field and inertia, and does so equally. Other modern theories, such as string theory, quintessence, and various forms of quantum gravity, almost all predict a violation of the Strong Equivalence Principle at some level. Additionally, many puzzling experimental results, such as galaxy rotation curves that imply the existence of dark matter or supernova observations that imply the existence of dark energy, could also potentially be explained by alternative theories of gravity (see, for example, MOND). Therefore, experimentalists believe it is important to make the most precise measurements of gravity possible, looking for any possible anomalies or confirming Einstein's predictions. Precise ranging to the Moon can test the SEP since the Earth and the Moon have a different fraction of their mass in the energy component. Precision measurements are needed since this component is very small – if mE is the self energy of the Earth — the energy needed to spread the atoms of the Earth out to infinity against the attraction of gravity — then the mass of the Earth is by about mE/c = of the Earth’s total mass. The self energy of the Moon is smaller yet, about of its mass. (The contribution for any object of laboratory size is negligible, about , so only measurements of planet-sized or bigger objects would allow this effect to be neasured.) If the Moon revolved around only the Earth, there would be no way to tell what fraction of the Moon's or the Earth's gravity was caused by each form of mass, since only the total can be measured. However, the orbit of the Moon is also strongly affected by the gravity of the Sun – in essence, Earth and Moon are in free fall around the Sun. If the energy portion of mass behaves differently from the conventional portion, then the Earth and the Moon will fall differently toward the Sun, and the orbit of the Moon around the Earth will be affected. For example, suppose the energy part of the mass does affect gravity, but does not affect inertia. Then: From our perspective on Earth, this would appear as a displacement, or polarization, of the lunar orbit away from the Sun with an amplitude of 13 meters. If the violation went the other way, with the self energy possessing