Changes between Version 30 and Version 31 of u/GasPhiBE
- Timestamp:
- 01/15/16 15:06:04 (9 years ago)
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u/GasPhiBE
v30 v31 5 5 To answer this question, first some preliminaries: 6 6 7 1) How massive is the critical BE sphere in my simulations compared to the ambient medium?7 Q1) How massive is the critical BE sphere in my simulations compared to the ambient medium? 8 8 9 * A) The BE sphere is 150 solar masses. The mass of the ambient medium then is given by the equation:9 A1) The BE sphere is 150 solar masses. The mass of the ambient medium then is given by the equation: 10 10 11 11 [[latex(${4\over3} \pi \rho ({r^3-Rbe^3})$)]] … … 21 21 Since in the matched case, the density becomes 0.07, Mamb=100*Mamb_light~'''1,400 Mbe'''. Or, in astronomical units, Mamb_matched=224,800 Solar Mass! 22 22 23 2.What is a theoretical approximation to the potential of the sphere outside of Rbe?23 Q2) What is a theoretical approximation to the potential of the sphere outside of Rbe? 24 24 25 * A) We can look at this problem in 2 ways that give the same answer. First we can add the potential of the BE sphere as though it were a point charge with M=Mbe to the potential of the ambient, approximated as a uniform sphere of r=l/2, where l is box length:25 A2) We can look at this problem in 2 ways that give the same answer. First we can add the potential of the BE sphere as though it were a point charge with M=Mbe to the potential of the ambient, approximated as a uniform sphere of r=l/2, where l is box length: 26 26 27 27 [[latex($\phi = -{G*Mbe \over r } - {G*Mr \over r} \space (for ~\space r > Rbe)$)]] … … 46 46 47 47 Point: 48 48 49 [[latex($m = Mbe - {4 \over 3} * \pi * Rbe^3 * \rho $)]] 49 50
