# Build the Solar System with the golden Section and music intervals

## Panning for gold or a process of distillation?

H.H. Voigt in his book breakdown of astronomy states that Copernicus showed that the earth and the planets circle the Sun, Kepler showed how the planets circle the Sun and Newton showed why the planets circle the Sun. I am just a wannabe Kepler in search of Keplers 4th law of planetary motion.As to why my equations should mean anything I have`nt a clue! I will at some point need to find  a far smarter poor mans Newton to work out why! Untill then I am quite content to play around with my pocket calculater searching for equations that I, at least find beutifull.                                                                                                To begin with it was like panning for gold, just trying to find rough equations that I would soon abandon in favour of better ones applying the simple logic of accuracy on the one hand against elegance on the other. In constructing a model B, it seems this  is more a process of distillation, such that I won`t claim that my anserws are right, more that I have come up with some sort of raw material that needs further destillation to find any kind of truth.

N.A.S.A. has calculated planetary distances for two different time periods.I will be using the 3000 BC to 3000 AD values unless otherwise stated.

Here below are the Mars and Venus values that I will be using in my model B.

Given that 1.875 can also be made up from 1.5 x1.25, then it is also possible to present my music interval equation in three levels as shown below.

Although all of the above equations could be seen as pure coincidence, I find it remarkable that in correcting the music interval power equation to equal Phi squarerd then the resulting changes improve the 2nd equation!

So without any changes the discrepancy was 1.000088909% and after the changes 1.00001185% this is amost a decimal place better.It might be fifty fifty as to it being higher or lower but being more accurate, on a discrepancy so low is something else. The 76th root of the discrepancy would correct the equation.

Here is another coincidence, which I can't find a use for but it is worth mentioning

Well 1.2 the minor 3rd, is by no means an obscure interval and I could use these values in model B or another model. The problem here is that I would have to use the whole thing as a power which would be even more obscure and complicated

This is very much a work in progress and three days ago I discoverd another coincidence which has given me food for thought. I had never used Phi itself as a power before but the square root of Phi to the power Phi power 4 is an exelent value for Jupiter 5.202490525 with a discrepancy of  1.000001987%

Well after much thought I couldn`t find any connection with my Mars and Venus values but I have found something much better!

This is the best equation I have found since I started on this project, whereby Jupiter requires only a 1.000001032%  correction to fit with the original Mars and Venus values.With my manipulated  Mars and Venus values for model B then Jupiter is 5.202479791 and requires only a 1.000000077% correction! a 13th millionth part, too good to be true! Well this has changed everything and so I have decided to delete all the stuff I had originally planned for model B.                                                                                                 Here are equations that define Neptune, they can be factored down but I thought the 1.875 interval looks good.

Using both the original values for Mars and Venus then Nepute has a value of 30.06970832 with a decrepancy of 1.000006013%.Using my manipulated values Neptune would be 30.06968236 which is 1.000005149% away from the original value.Having defined Neptune, the following equation will define Uranus

The Uranus value comes out as 19.18806794 which is 1.00000461% away from the N.A.S.A. value.

Turning to Saturn I am somewhat torn between several alternatives, but for model B I will go for the most accurate option.

Here it is plain to see that any Phi power is achievable, whereby Saturn has a value of 9.541497135 which is 1.000000178% again too good to be true at a 5.6th million part!

Problematic is the relationship between Saturn and the Mars Venus equations, such that Saturn power 13, times Mars power 22, devided by Venus power 22, equals Phi power 95. This has not nearly the same elegance or symetry as the Jupiter Mars and Venus equations.                The Mercury equation that follows seems simple enough but it too doesn`t have a good relationship with Mars and Venus ( I am still trying to get a simple equation out of it)

Using the original Uranus and Neptune values, Mercury comes out to .387099014  which is a 1.00000151% discrepancy but with my modified Uranus and Neptune values the discrepancy is  1.000000227.