Changes between Version 14 and Version 15 of HydroStaticStar
- Timestamp:
- 02/26/18 11:19:28 (7 years ago)
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HydroStaticStar
v14 v15 9 9 we can translate the image above into the condition: 10 10 11 {{{ 12 #!latex 13 \frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\ 14 }}} 11 12 $\frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\$ 15 13 16 14 where dP/dh is the change in pressure with respect to height, ρ(r) and g(r) are respectively density and gravitational potential. … … 54 52 To calculate a pressure profile we need to interpret: 55 53 56 {{{ 57 #!latex 58 \frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\ 59 }}} 54 $\frac{dP}{dh} + \rho(r) \cdot g(r) = 0\\$ 60 55 61 56 62 57 in a discrete way, this gives: 63 58 64 {{{ 65 #!latex 66 P(h) = P(h+\Delta h) + g(h)\cdot\rho(h)\cdot\Delta h 67 }}} 59 60 $P(h) = P(h+\Delta h) + g(h)\cdot\rho(h)\cdot\Delta h$ 68 61 69 62 The 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 :