Changes between Version 19 and Version 20 of u/SurfacePressureApprox
 Timestamp:
 10/18/13 17:36:35 (11 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

u/SurfacePressureApprox
v19 v20 66 66 [[latex($M_{init} = \frac{4}{3}\pi (R_0^3R_{BE}^3) \rho_0$)]] 67 67 68 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. 69 68 70 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, 69 71 … … 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. 78 80 79 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.81 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. 80 82 81 83 Here are the results,