The 4 Equations of Stellar Structure:

    The 4 equations of stellar structure are the basic equations of hydrostatic stellar structure. They must be solved simultaneously on the computer.

    But these are just the basic equations for the very basic stellar structure of main sequence stars. They do NOT account for:

      stellar rotation, 3-dimensional convection (they approximate 1-dimensional convection, but this approxiamtion is a weak point), stellar magnetic fields, asteroseismology (of which a special case is helioseismology), starspots (of which a special case are sunspots), stellar activity (of which a special case is solar activity), the centrifugal force, the Coriolis force, close binary system effects, leftover star formation effects, stellar evolution, post-main-sequence evolution, etc.

    In fact, writing a computer code for solving the 4 equations of stellar structure with simplified physics ingredients is a graduate student course project. It's relatively easy. Doing state of the art stellar structure calculations is, of course, very hard.

    The 4 equations of stellar structure are differential equations that embody physical law. To expand on the last sentence, see the insert below (local link / general link: physical_law_solution.html).

    https://commons.wikimedia.org/wiki/File:Inclinedthrow2.gif Caption: To illustrate the solutions of differential equations, see the animations showing the projectile motion trajectories for an inclined launch with NO drag (black), Stokes law drag (blue), and Newton drag (green). Launch angle = 70° and in natural units little g = 1, launch speed v = 1.25, and terminal velocity for both drag types vmax=0.65.

    The trajectories are solved for from differential equations: analytically and simply in the case of NO drag, analytically, but NOT so simply, in the case of Stokes law drag, and by numerical solution in the case of Newton drag which has NO exact analytic solution it seems (Wikipedia: Projectile Motion: Trajectory of a projectile with Newton drag).

    Credit/Permission: © User:Greek3, 2020 / Creative Commons CC BY-SA 4.0.
    Image link: Wikimedia Commons: File:Inclinedthrow2.gif.
    Local file: local link: stellar_structure_4_equations.html.
    File: Star file: stellar_structure_4_equations.html.