Changes between Version 2 and Version 3 of u/erica/CFringanalysis
- Timestamp:
- 06/29/15 21:07:56 (10 years ago)
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u/erica/CFringanalysis
v2 v3 28 28 '''Uniform Collapse of the ambient''' 29 29 30 Ignoring the pressure of the ambient, the local acceleration of a gas parcel at a distance r away from the origin for a uniform density sphere is given by: 30 Needed to revisit these solutions to develop the model of the ambient infall. This can be followed [https://astrobear.pas.rochester.edu/trac/wiki/u/erica/UniformCollapse here]. 31 31 32 [[latex($\frac{d^2r}{dt^2} = -G\frac{M_r}{r^2}$)]] 32 Of crucial importance to this model is the ram pressure analysis at the bottom of the page. Unfortunately, I noticed today that those calculations aren't correct from the shapes of the curves. I found the bug and will get new plots of that up next. 33 33 34 34 35 Integrating this equation under the boundary conditions, the initial velocity [[latex($\frac{dr}{dt}=0$)]] and the initial radius is the radius of the sphere [[latex($r=r_0$)]], leads to an equation that describes the radius of the outer sphere over time,36 35 ---- 37 36