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Can you solve my gravity-maths problem in Mathematica?
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).