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## Re: The beginning of space-based light pollution?

 Subject: Re: The beginning of space-based light pollution? Brian Tung Fri, 24 Jun 2005 16:08:52 +0000 UTC sci.astro.amateur
 ```William C. Keel wrote: > Nope, I had quite forgotten about Chandrasekhar's work on this (and > given that review, it doesn't sound worth my time to go through it). > However, it does seem that second-guessing Newton's derivations > is a more common hobby than I would have thought. Getting to his > result about the gravity of a spherical shell cancelling throughout > its interior is a classic - John Faulkner found a calculus-free > way to do it involving the equivalent of image charges. I'm not sure I understand why this is hard: Given any point P inside a spherical shell centered on C, draw the line PC, which intersects the shell at points A and B. Next, extend two tiny and similar cones whose fulcra are at P, and whose bases are centered at A and B. The area of the base at A is approximately to the area of the base at B, as PA^2 is to PB^2. Its mass is therefore in the same ratio. But the attenuation of the force due to distance also goes as PA^2 to PB^2, cancelling out the factor in mass. Thus, the forces exerted on point P by the bases at A and B balance out. We may tesselate the shell completely with such pairs of cones. The balancing out isn't perfect, admittedly, as long as the cones have some positive size. But in the limit, as the cone bases shrink toward zero area, the balance is perfect and the proposition is demonstrated. Is there something I'm missing? Brian Tung <[email protected]/* */> The Astronomy Corner at http://astro.isi.edu/ Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/ The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/ My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt ```
 Current Thread Re: The beginning of space-based light pollution?, (continued) Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Chris L Peterson Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Mike Kreuzer Re: The beginning of space-based light pollution?, RichA Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Mike Kreuzer Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Mike Kreuzer Message not availableMessage not availableRe: The beginning of space-based light pollution?, William C. Keel Re: The beginning of space-based light pollution?, Brian Tung <= Re: The beginning of space-based light pollution?, Chris L Peterson Re: The beginning of space-based light pollution?, lal_truckee Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Ioannis Re: The beginning of space-based light pollution?, tony_flanders Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Brian Tung Re: The beginning of space-based light pollution?, Ioannis Re: The beginning of space-based light pollution?, Paul Schlyter