Comments on: Infanticide http://www.voicesoa.net/infanticide/ An Orions' Arm E-zine Sun, 25 Jul 2010 05:36:52 +0000 http://wordpress.org/?v=2.9.1 hourly 1 By: Adam http://www.voicesoa.net/infanticide/comment-page-1/#comment-38536 Adam Tue, 01 Sep 2009 21:52:50 +0000 http://www.voicesoa.net/infanticide/#comment-38536 Newton's approximation for spherically symmetric bodies allows us to treat the gravity of that body as if it were coming from a point at the center. However, removing the shells of matter above a given point significantly reduces the gravitational potential, since mass is proportional to volume which grows as r^3 in 3-space. Indeed, for n-dimensional spheres, most of the volume lies near the surface. Since mass is proportional to volume, and gravity is proportional to mass, this is accurate from this perspective: without the layers above, the gravity would not be as large. Newton’s approximation for spherically symmetric bodies allows us to treat the gravity of that body as if it were coming from a point at the center.

However, removing the shells of matter above a given point significantly reduces the gravitational potential, since mass is proportional to volume which grows as r^3 in 3-space.

Indeed, for n-dimensional spheres, most of the volume lies near the surface. Since mass is proportional to volume, and gravity is proportional to mass, this is accurate from this perspective: without the layers above, the gravity would not be as large.

]]> By: selden http://www.voicesoa.net/infanticide/comment-page-1/#comment-32393 selden Fri, 13 Jun 2008 20:46:44 +0000 http://www.voicesoa.net/infanticide/#comment-32393 A minor quibble: at the beginning: "constrained by the gravity of thousands of kilometers of dense hydrogen above it." isn't right. In a spherical body, like a gas giant, gravitational forces are due to the layers below. The gravitational pull from layers above cancels out. Of course, there's plenty of pressure due to the layers above. s. A minor quibble: at the beginning:
“constrained by the gravity of thousands of kilometers of dense hydrogen above it.” isn’t right. In a spherical body, like a gas giant, gravitational forces are due to the layers below. The gravitational pull from layers above cancels out. Of course, there’s plenty of pressure due to the layers above.

s.

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