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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
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 Fall '09
 dion
 Astronomy

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