It is shown that relativity predicts a variable G. The proof starts by considering a dimensionless particle in an empty universe. Then two particles, three particles, and an infinite set of particles are studied. This allows to calculate space-time structure for any realistic energy distribution. The proof uses the interchange of limits theorem, and ad hoc sequences of energy distributions. With only one particle, the result is a singularity everywhere if the universe is empty outside of the particle. Those singularities disappear completely with three particles. Then this calculation is done for any realistic energy distribution. An equation of G is given naturally in the process. This equation is a correct approximation in most of the realistic energy distributions. The fundamental principles building Einstein equation are still valid. But it is shown that the G anthropocentric solar system constant must be replaced by a variable value, which is weaker in strong matter density environments, and greater in low matter density environments. It means that the surrounding effect arises, it was introduced by previous works. And this effect was shown to solve the gravitational mysteries of today in astrophysics and in cosmology. Under a unifying relevant assumption, a solution is also given to the Yang-Mills Millennium problem.