## (r^-3)/(cos(r)+rsin(r))

What did you draw?
AlternateGravity
Posts: 70
Joined: Thu May 15, 2014 5:45 pm

### (r^-3)/(cos(r)+rsin(r))

I found that it is not only possible to get stable orbits using this law for gravity but also to get solar systems of multiple planets.

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This solar system has seven planets and after hours of running the simulation only one planet was kicked out of the solar system as it originally had eight planets.

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This planet had a moon that was in a metastable orbit and the planet orbited its star three times before its moon escaped.
Attachments
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Gravitons would be my favorite particle as their existence could prove extra dimensions.

AlternateGravity
Posts: 70
Joined: Thu May 15, 2014 5:45 pm

### Re: (r^-3)/(cos(r)+rsin(r))

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This helps show where the force of gravity is positive and negative and where the force is negative helping to show the period of the gravitational force. Much closer than the end of the first period of gravity there are no stable orbits as the gravitational force can be approximated by r^-3.
Gravitons would be my favorite particle as their existence could prove extra dimensions.

testtubegames
Posts: 1008
Joined: Mon Nov 19, 2012 7:54 pm

### Re: (r^-3)/(cos(r)+rsin(r))

Oh wow, that's quite a force law. At first, I thought maybe it was one of those functions that surprisingly behaves nicely... but nope:
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(from wolfram alpha)

I just had fun placing objects and seeing what happens in that force law - but I can imagine making those (mostly) stable systems took quite a bit of work? Was there a trick to building them? And how in the heck did you come up with that force law?

AlternateGravity
Posts: 70
Joined: Thu May 15, 2014 5:45 pm

### Re: (r^-3)/(cos(r)+rsin(r))

The way I built those systems was by flinging planets at distances and velocities I thought were most likely to be stable a bunch of times until I would finally get ones that would orbit the star. Most would either be repelled by the star at some distances causing them to fly off into space or reach the escape velocity of the star and so escape into space.

The way I came up with this law is that in the Riemanian Universe the equation for an electric field is -(q/(4pir^2))(cos((ω_m)r)+rsin((ω_m)r))*(e_r)

http://www.gregegan.net/ORTHOGONAL/04/EMExtra.html#CS

so I would suspect that in a 4 spatial dimension Riemanian Universe the equation for an electric field would be -(q/(2(pi^2)(r^3)))(cos((ω_m)r)+rsin((ω_m)r))*(e_r) and so I would also expect that if there was another force that was based on a type of charge that its equation would have the same form as that of electromagnetism. Actually I did seem to make a mistake as I divided when I should have multiplied but my idea is that a Riemanian Universe with four spatial dimensions could have stable orbits provided those orbits were held together by a force other than gravity.
Gravitons would be my favorite particle as their existence could prove extra dimensions.