The Matter in Newtonian Static Gravitational Field

In contemporary physics, there is an observed discrepancy in the mass calculations used to determine the strength of celestial gravitational fields. Therefore, physics is searching for dark matter candidate particles, such as weakly interacting massive particles (WIMPs) and axions, while attempting to modify Newtonian dynamics and the law of universal gravitation. Inspired by the classical theories of electric and magnetic field mass-energy calculations, the present work proposes a new theoretical attempt to explore the dark matter in the universe and challenge theories that modify Newtonian dynamics and the law of universal gravitation. Like the formulas for calculating the mass-energy density of electric and magnetic fields, Newtonian static gravitational fields also have a mass-energy density. The matter in the gravitational field will also generate a new gravitational field and thus derive the formula for calculating the mass-energy of matter in the gravitational field. In this way, the gravitational mass-energy of celestial bodies should consider the ordinary visible matter and invisible matter of the gravitational field. The strength of a gravitational field is a vector, and the mass-energy density of a gravitational field is proportional to the square of its strength. The greater the strength of the gravitational field, the greater the mass-energy density of the gravitational field at that location. Assuming that ordinary matter is distributed uniformly within a sphere, it deduces that the mass-energy of the celestial body is not only related to that of ordinary matter but also to its structure. The higher the celestial structure factor of that body, the greater the mass-energy density of matter in the gravitational field inside and outside the body.