Build the Solar System with the golden Section and music intervals

This site is a complete mess but here are my latest ideas!  It was many years ago that in looking for Phi values I quickly found that Jupiter power 7 was a weak approximation to Phi power 24! Now 3 x 7 is of course 21 and 3 x 24 is 72 , which means that the 21st root of Phi power 144 is Jupiter squared! and although this  is weak I am on a roll again, in that higher values of the fibbonaci or lucas sequences  may get better results and indeed they do!

So I am going to start by defining Jupiter as the 1597th root of Phi power 5473 (or the fibbonaci number 10946 devided by two) Saturn will be defined by Jupiter power 12 devided by Saturn power 6 equals Phi power 13. This means like the first part of my blog I have plenty of bites at the same cherry!

All the equations above and below are compatable with the values in model B

I am unsure as to how important these natural number sequences are but here is one with the first four planets (The earth is one!) and it is compatable with model B. I will in future refer to these four equations as my Rocky Planet equations.

So what am I to understand with these chance number sequences? in some ways this is the best pattern I ever found! Could one say that by using the the two inner planets  I have discoverd the first of the outer planets? and perhaps using  Mercury and Venus I could find the next planet Jupiter in a similar manner? Or should I understand that I have found Mercury with the use of Mars and Venus the two planets between which Kepler placed the icosahedron and the dodacahedron? Well this is what I am working on just now!                               

This above, is my latest attempt to build a model B.It is somewhat different to earlier attempts but it starts with defining the Jupiter value by useing two Fibbonaci numbers although Lucas sequence numbers will work as well.The 1597th root of Phi to the power 10946 is close to the Jupiter value squared.On my pocket calulater there are discrepancies creeping in at the ninth and tenth decimal places.To minimize this I have devided the Fibbonaci numbers by 1000 and thus I get a better result.Useing the lower Lucas sequence numbers of 843 and 5778 obtains a better result for the Jupiter value, within a 3.5 millionth part but then it is swings and roundabouts I suppose! Although all the equations will work for higher and lower Fibbonaci and Lucas sequencies the Jupiter power 40 equation only works in this configeration! The Jupiter values seem to arise from the the following, Phi to the power Phi power (Phi power 4 devided by 2).

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 haven`t 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 answers 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.

The picture below is a simple illustration of one astronomical unit, from which all the N.A.S.A. numbers come from and the pentagram, the most obvious  depiction of Phi, the golden section.

It had always annoyed me that my Mars and Venus Phi relationship was based on the music interval 1.875 and not 1.5 and 1.25, because it is these two intervals along with 2 the octave that all other music intervals derive.Splitting my equation into three levels though, clearly shows that I am indeed using 1.5 and 1.25.The badly drawn picture below illustates what I mean and I have squared both factors to show there are 3 levels.

 

It seems almost unfair that in my model B it is the female planet Venus that carries most of the discrepancy but even if I start with the real value of Venus, then Mars comes out at 1.523728738 or 1.000010703% away from the Nasa value and Mercury with .387097415  which is 1.000002622%. So even choosing the least favourable position to start with, Venus allows Mars a discrepancy of a 93000th part and Mercury with a 381000th part error.

Another question is, of course, why am I playing around with music intervals when I have found Phi values without them? The music intervals are only there to spot patterns that otherwise could or would remain undiscoverd. One may also ask why am I looking for Phi powers? Because of their natural beauty! Keper described the golden section as a precious jewel and I wonder if he meant a diamond, which of course can be used as a cutting tool. It could be the case that, in my speculations, Phi is not so much the answer but more the cutting tool to find the answer! My model B may be perhaps a house and the Phi powers more the scaffolding. Or perhaps another  analagy may be the search for a geometric shape that is only possible with the structure of graph paper.

The Reunion of Broken Parts

The Arabic word Algebra, when first translated into Latin, was defind as the reunion of broken parts and I find it nice to think of my Mars and Venus 1.875 equation of two broken parts of Phi squared! The question remains however as to could my Mars and Venus values on their own, each have a Phi value as in the first part of my blog whereby I found the 52nd root of Phi power 35 as an approximation the Venus value? Well to my suprise it turns out that my Venus value (in my old version of model) is the 1649th root of Phi power 1110.This is by no means elegant but I am glad that it breaks down to two rational numbers! Mars it turns out is 5 times 1649 and thus the 8245th root of Phi power 7216. It has taken me a long time but I have finally worked out how I have ended up with the number 1649, it is 52 off the fibbonacci number I597 and of course, in my previous attempt at an approximation to the Venus value I was useing the 52nd root of Phi power 35. I have also come across an equation for a relationship between Jupiter and Saturn ( how did I miss it?) which has again changed everything. I am going to put my latest ideas at the top of this page!

 

A photo of myself at age about 30 from about 1984

I can hardly believe it! but having spent over 20 years playing around with these numbers I have not only got Phi values but also Pi! Now I wasn`t looking for Pi but surely this is too good not to be true?

Below is a picture showing a connection between Phi and musiic intervals, 3.2 devided by 2 is 1.6

As an after thought, there is a special quality to a Phi sequence but not in the world of devision and multiplication but in the exotic world of addition and subtration. Phi power 1 + Phi power 2 equals Phi power 3 and Phi power 2 plus Phi power 3 equals Phi power 4  this is of course true for all Phi powers. Here is a picture to illustrate what I mean.                                                                 

A photo of myself and my wife Regina some 10 maybe 12 years ago!