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Can you solve my gravity-maths problem in Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg62828] Can you solve my gravity-maths problem in Mathematica?
• From: "Paul" <paulbird at whsurf.net>
• Date: Tue, 6 Dec 2005 00:04:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello, I have been working on a simple model of quantum gravity. Like
atoms have a minimum electron shell distance caused by the quantisation
of the electromagnetic force my approximation for the average distance
between particles held together by a graviational force, using my
model, becomes :

"Find r at the maximum value of:

f(r)   =  exp( m*r )  *  integrate(  exp(-2*m*r)/r^2 , r )

(r>0) "

Where we use constants such that c=h=G=1. In this system for example
electron mass is something like 10^(-23) I believe. (The graviational
bond enegy in this model becomes m^5 in my units.)

So I need to find f'(r)=0.

Can anyone find a good way to solve this for r, maybe as a series in
terms of m? Also, I would be interested in seeing a graph of f(r).

• Follow-Ups:
  • Re: Can you solve my gravity-maths problem in Mathematica?
    • From: "Carl K. Woll" <carlw@wolfram.com>