Solar structure without computers

Physics

Scientific paper

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Scientific paper

We derive succinctly the equations of solar structure. We first present models of objects in hydrostatic equilibrium that fail as models of the sun in order to illustrate important physical requirements. Then by arguing physically that the pressure gradient can be matched to the simple function dP/dr=-kre-(r/a)2, we derive a complete analytic representation of the solar interior in terms of a one-parameter family of models. Two different conditions are then used to select the appropriate value of the parameter specifying the best model within the family: (1) the solar luminosity is equated to the thermonuclear power generated near the center and/or (2) the solar luminosity is equated to the radiative diffusion of energy from a central region. The two methods of selecting the parameter agree to within a few percent. The central conditions of the sun are well calculated by these analytic formulas, all without aid of a computer. This is an original treatment, yielding much the best description of the solar center to be found by methods of differential and integral calculus, rendering it an excellent laboratory for applied calculus.

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