Changes between Version 19 and Version 20 of u/SurfacePressureApprox

Timestamp:

10/18/13 17:36:35 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/SurfacePressureApprox

@@ -66 +66 @@
 [[latex($M_{init} = \frac{4}{3}\pi (R_0^3-R_{BE}^3) \rho_0$)]]  
 
+Since the radius of the collapsing sphere decreases more rapidly than the density is increasing, M(t) is a decreasing function. At t=0, M(t) = Minit, and Mshell = 0. As time goes on, M(t) < Minit, thus, Mshell is a (slowly) increasing function.
+
 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 in a box of r = 90, the function R(t) looks like,
 
@@ -77 +79 @@
 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. 
 
-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.
+For all the plots I made, the simulation time was less than the freefall time of the ambient. More importantly perhaps, R(t) never fell inside of the BE sphere.
 
 Here are the results,