New theorems on the flux of the gravitational field strength vector are presented, free from the limitations inherent in Gauss's theorem. Gauss's theorem is not sufficient for a complete description of gravity. It is shown that the relationship between the gravitational field flux and the mass of sources is not the only method for representing the gravitational field flux. Unlike Gauss's theorem, the new theorems do not include the mass of sources. The first theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the body's orbit. The second theorem establishes a relationship between the flux of the gravitational field strength vector and the parameters of the universe. The third theorem concerns the total gravitational force that actually acts on the body and is caused by the gravitational interaction of the test body with all bodies in the universe. From these theorems, two new laws of gravitation and a new law of universal gravitation are derived, which for the first time describes gravity taking into account the action of all bodies in the universe. Unlike Newton's law of gravity, the new law of universal gravitation does not include the mass of sources and the gravitational constant G. The new theorems relate to the gravitational field, which obeys the inverse-square law, and to the gravitational field of the universe, where the inverse-square law does not apply. The new theorems and new laws of gravity provide a complete description of the gravitational interactions of all N-body bodies in the universe. The new theorems demonstrate the existence of a workaround instead of searching for a direct solution to the gravitational N-body problem (for N ≥ 3).