Producing stable orbits in 4d using exponential decay laws

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Producing stable orbits in 4d using exponential decay laws

Postby 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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Re: Producing stable orbits in 4d using exponential decay la

Postby anderscolingustafson » Thu Dec 11, 2014 5:09 am

I tried using (r^-3) and r^-3 and found that they produce different results in the simulation indicating that there is a problem with the simulation interpreting the parentheses. This indicates that the simulation may have a problem showing what really happens when r^-3 is multiplied by e^-r so I could be wrong about multiplying r^-3 by e^-r producing stable orbits in 4d.
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Re: Producing stable orbits in 4d using exponential decay la

Postby anderscolingustafson » Fri Dec 12, 2014 4:32 am

I found that when I fixed the problem with the simulation so that (r^-3) and r^-3 produced the same result (e^-r)*(r^-3) did not produce stable orbits although sin(r)*(r^-3) did.
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Re: Producing stable orbits in 4d using exponential decay la

Postby ICN5D » Fri Dec 12, 2014 4:55 am

It seems that gravity in 4D would dissipate naturally, as is the case with even-dimensional wave propagation.
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