In reference to the answer to question 1 above.] Why don the internal electron forces of a star increase at the same rate as gravitational forces?
In short, the degenerate electron pressure in the star depends upon the density of the gas in a specific way that has no direct dependence upon how gravity and density are related. If you’d like a mathematical relationship, its: the pressure is proportional to the density raised to the 5/3 power. This power is determined by the properties of quantum mechanics (and has nothing to do with gravity). On the other hand, the gravitational force at the surface (for example) of the star is proportional to the mass of the star and inversely proportional to the square of its radius (because of Newton’s universal law of gravity!) If I try to express this surface gravity in terms of the density of the star (it’s average density), I find M/r^2 is proportional to density times r. So, you see, “density times r” is not anything like “density raised to the 5/3 power.
In short, the degenerate electron pressure in the star depends upon the density of the gas in a specific way that has no direct dependence upon how gravity and density are related. If you’d like a mathematical relationship, its: the pressure is proportional to the density raised to the 5/3 power. This power is determined by the properties of quantum mechanics (and has nothing to do with gravity). On the other hand, the gravitational force at the surface (for example) of the star is proportional to the mass of the star and inversely proportional to the square of its radius (because of Newton’s universal law of gravity!) If I try to express this surface gravity in terms of the density of the star (it’s average density), I find M/r^2 is proportional to density times r.
