Changes between Version 7 and Version 8 of u/GasPhiBE

Timestamp:

10/04/12 12:59:17 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/GasPhiBE

@@ -18 +18 @@
 By this method, I found the mass in the light ambient medium to be:
 {{{#!latex
-M = {0.0007 * {4 \over 3} \pi ({15.4^3 -1 })} = 10.7 * Mscale = 4.77 * 10^36 g = 2,248 Solar Masses ~ \red 14 Mbe
+M = {0.0007 * {4 \over 3} \pi ({15.4^3 -1 })} = 10.7 * Mscale = 4.77 * 10^36 g = 2,248 Solar Masses
 
 }}}
 
-That is, Mamb~14Mbe.
+That is, '''Mamb~14Mbe'''.
 
-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!
+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!
 
 2. What is the theoretical potential of the sphere outside of the Rbe? 
@@ -42 +42 @@
 }}}
 
+
+
 =>
 
@@ -50 +52 @@
 
 From this we can that when rho is small in ambient, phi is dominated by the first term. That is phi can be approximated as due to the BE sphere as a point gravity source. For non-negligible rho, however, we can expect the r^2^ term to dominate at large r. This would make phi more and more negative.
+
+We can arrive at this same equation by taking a slightly different conceptual route. We can consider phi in ambient medium to be due to the superposition of a uniform sphere on top of a point mass object. In pictures, this is like:
+
+
+
+