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un:equations-of-stellar-structure [2025/10/27 00:27] – asadun:equations-of-stellar-structure [2025/10/27 00:33] (current) – [Primary and secondary] asad
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 This equation determines the degree of ionization and thus sets \(\kappa(\rho,T)\) and \(\mu(\rho,T)\) for the opacity and equation of state. This equation determines the degree of ionization and thus sets \(\kappa(\rho,T)\) and \(\mu(\rho,T)\) for the opacity and equation of state.
  
-===== - Primary and secondary equations explained =====+===== Primary and secondary =====
  
 The **first five equations** — for hydrostatic balance, mass conservation, luminosity, and the two temperature gradients — are **primary** because: The **first five equations** — for hydrostatic balance, mass conservation, luminosity, and the two temperature gradients — are **primary** because:
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   * They are **differential equations** that describe the **structural variation** of a star with radius \(r\).     * They are **differential equations** that describe the **structural variation** of a star with radius \(r\).  
   * They express the **fundamental conservation laws** of physics:     * They express the **fundamental conservation laws** of physics:  
-    – (1) mechanical equilibrium,   +    * (1) mechanical equilibrium,   
-    – (2) conservation of mass,   +    * (2) conservation of mass,   
-    – (3) conservation of energy, and   +    * (3) conservation of energy, and   
-    – (4–5) energy transport by radiation or convection.  +    * (4–5) energy transport by radiation or convection.  
   * Their solutions give the radial profiles of \(P(r)\), \(\rho(r)\), \(T(r)\), \(M(r)\), and \(L(r)\).   * Their solutions give the radial profiles of \(P(r)\), \(\rho(r)\), \(T(r)\), \(M(r)\), and \(L(r)\).
  
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 Together, the primary and secondary equations form a **closed system** of seven equations with seven unknown functions. Together, the primary and secondary equations form a **closed system** of seven equations with seven unknown functions.
  
-===== - Interdependence and boundary conditions =====+===== Interdependence and boundary conditions =====
  
 These seven equations describe how \(P(r),\,\rho(r),\,T(r),\,L(r)\), and \(M(r)\) vary with radius in a spherically symmetric, non-rotating star.   These seven equations describe how \(P(r),\,\rho(r),\,T(r),\,L(r)\), and \(M(r)\) vary with radius in a spherically symmetric, non-rotating star.  
un/equations-of-stellar-structure.1761546434.txt.gz · Last modified: by asad
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