by anderscolingustafson » Tue Dec 09, 2014 5:32 am
I know simply using the inverse cube law produces unstable orbits, which is a problem for 4d solar systems and life as in 4d the simplest way for gravity to drop with distance is with the inverse cube law. I have found however that exponential decay laws produce stable orbits when I run simulations using them and when I multiply the inverse cube law by exponential decay laws it produces stable orbits. While r^(-3) does not produce stable orbits (r^(-3))*(e^(-r)) does produce stable orbits. If the graviton decayed at a rate e^(-t) where t is the time then the drop off rate for gravity with distance would be (e^(-r))*(r^(-3)) in four spatial dimensions as the drop off rate from the number of dimensions would be multiplied by the drop off rate from the decay of gravitons. It's actually very easy to produce stable orbits using (e^(-r))*(r^(-3)) and the stability produced by the equation e^(-r) wins out over the instability produced by the equation r^(-3). So it would seem that the way to produce stable orbits in 4d would be for the graviton to decay over time.
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