Changes between Version 14 and Version 15 of HydroStaticStar


Ignore:
Timestamp:
02/26/18 11:19:28 (7 years ago)
Author:
Erica Kaminski
Comment:

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  • HydroStaticStar

    v14 v15  
    99we can translate the image above into the condition:
    1010
    11 {{{
    12 #!latex
    13 \frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\
    14 }}}
     11
     12$\frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\$
    1513
    1614where dP/dh is the change in pressure with respect to height, ρ(r) and g(r) are respectively density and  gravitational potential.
     
    5452To calculate a pressure profile we need to interpret:
    5553
    56 {{{
    57 #!latex
    58 \frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\
    59 }}}
     54$\frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\$
    6055
    6156
    6257in a discrete way, this gives:
    6358
    64 {{{
    65 #!latex
    66 P(h) = P(h+\Delta h) + g(h)\cdot\rho(h)\cdot\Delta h
    67 }}}
     59
     60$P(h) = P(h+\Delta h) + g(h)\cdot\rho(h)\cdot\Delta h$
    6861
    6962The condition above determines the pressure profile starting from the top of the column until its base. This implies we specify the pressure at the highest distance from the point mass, ideally infinity. This value can be adjusted in problem.data :