Changes between Version 2 and Version 3 of u/SurfacePressureApprox

Timestamp:

10/18/13 17:04:20 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/SurfacePressureApprox

@@ -66 +66 @@
 
 [[latex($M_{init} = \frac{4}{3}\pi R_0^3 \rho_0$)]]  
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+I used mathematica to numerically solve the equation of motion for a uniform sphere as given in Carroll and Ostlie, and checked the solution was correct against a result they published in that book. For the 1/50 case, the function R(t) looks like,
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+rho(t) looks like
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+Here you see that the R(t) drops to zero at the freefall time. You see the density diverging at this point, given the unphysical condition r=0. The collapse accelerates in time, becomming faster and faster by the end. The density increases everywhere uniformly, and is only a function of time. 
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+For all the plots I made, the simulation time was less than the freefall time of the ambient. Additionally, R(t) never fell inside of the BE sphere.
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+Here are the results,