ay45c5-page13 - correct for all cases but it will allow us...

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Unformatted text preview: correct for all cases, but it will allow us to learn some interesting things about some real stars, and will let us defer the whole subject of \radiative transfer" (involving T; L; ; K , and E ) to later courses, Astronomy 145 and 150. 5.2.3 Equations of stellar structure Equation of Hydrostatic Equilibrium Consider an element of gas in equilibrium in the star density ρ r + dr r g The pressure P (r) is larger than the pressure P (r + dr) by just the weight per unit area of the material between r and r + dr in the local gravitational acceleration g. If the element is of area dA, we have ! mass of =  dA dr element # ! " weight of = g dA dr = GM (r) (r) dA dr element r2 ! weight of element = G(r)M (r) dr : per unit area r2 So, dP = P (r + dr) P (r) = G(r)M (r) : dr dr r2 The minus sign is because pressure increases as r gets smaller (downward direction). Mass Equation 125 ...
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