Re: Can you solve my gravity-maths problem in Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg62853] Re: [mg62828] Can you solve my gravity-maths problem in Mathematica?
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Tue, 6 Dec 2005 23:10:28 -0500 (EST)
• References: <200512060504.AAA02783@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Paul wrote:
> 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) "
>

You really need to distinguish between r the integration variable, and r
the argument to f. Also, if the r^2 in the denominator is the
integration variable, then the integral over r>0 does not converge. So,
change the name of the integration variable, and spell out the limits of

Carl Woll
Wolfram Research

> 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).

```

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