Gravitation as Source of Energy
The source of star energy is considered nowadays to be basically related to the fusion process. The explanation has its shortcomings, but it is hoped that sooner or later, “as the science progresses”, these will be overcome. What we really can say is that the conditions for realization of a steady cycle based upon the fusion process, cannot occur but only in the inner core of a star. In other words, not the whole volume of the star is the source of energy it spreads around, but only its inner core.
This fact offers a redeeming chance to the Newtonian theory of gravitation. It is well known that an evaluation of the age of our Sun, based on this theory, done by Lord Kelvin, gave some 20 million years. This figure was too small by comparison with the age of rocks on Earth, which was evaluated to be 2-4 billion years. So the classical evaluation was rejected.
Now, if we consider that the energy of a star comes indeed from an inner core, which undergoes the tremendous gravitational squeezing due to external matter of the star, the things might come in handy even for the classical theory of gravitation. However, when we try to apply this philosophy, the real problem pops up: we don’t know the density of matter inside the star. The only possibility of evaluation of that density is given by Poisson equation, but for the Newtonian force this equation reveals a zero density. The Newtonian force is a vacuum force!
What can be done? First realize that, being a vacuum force, the Newtonian force is only an approximation: that approximation valid in the limit of great distances between celestial bodies. Then find what is the most probable “exact” force whose approximation is the Newtonian force, and the corresponding “exact” potential. Based on this calculate the density and the extension of the region inside the star that gives the required energy spread around by the star, as well as the age of that star, exactly like in the classical case.