Planets Orbit their Parent Star(s)
at Predictable Distances

Abstract
The hypothesis herein states that a very large majority of planets, and planetoids in all known star-systems, orbit their parent star(s) at meaningfully predictable distances, measured in astronomical uinits (AU). This paper elucidates an equation used to generate a set of numbers that measure up to within an accuracy of 80% or better, when compared to the empirically observed Semi major axis of (exo)planets from their parent star(s).

Empirical Data
Space agencies, such as NASA and ESA, search distant star systems for exoplanets and have compiled and extensive catalogue of data. Because the orbital distance of planets vary from their parent star(s), space agencies list an averaged measure of a planet’s farthest and nearest orbital distances. This averaged distance is called the Semi-Major Axis (SMA). The catalogue of exoplanets is accessible on line. https://exoplanet.eu/catalog/ https://science.nasa.gov/exoplanets/exoplanet-catalog/
https://simple.wikipedia.org/wiki/Category:Exoplanets

Equation Generated Idealised Data
To reliably predict the SMA of (exo)planets, the hypothesis herein relies on an equation to generate a series of numbers which when taken as astronimical units, predict the distance (exo)planets orbit their parent star. Hence, (exo)planets orbit their prent stars at pedictable distances.

To distinguish the empircally observed SMA from the equation-generated SMAs this paper refers to empirical Semi-Major Axes (ESMA), and Ideal Semi-Major Axes (ISMA), both are expressed in astronomical units (AU).

Thus far, at the writing of the is paper, 98% of all (exo)planets found have been predicted to an accuracy of 20% or better, by the numbers generated by the equation. It is not expected that a planet exists in every equation generated orbit. As will be seen, nor is it the case that there are so many numbers generated that one has to be with 20% of 100% accuracy.

A larger Excel file presents the data for this for the first 117(exo)planets observed, which was around the time this thesis was written, cerca 2006. Since then, several thousand more exoplanets have been found and they await the same analysis.

This introductory example exposition is limited to just 3 star systems: Solar System, 55 Cancri, and Upsilon Andromedea b.

The equation that generates the Ideal Semi Major Axis reads as the “fourth root of N to the power of 3”. Where N is a number from the Fibonacci series (see columns 2 and 3).

Here is how to read the table. Column 1 contains the Fibonacci number series. Column 2 contains the possible Ideal Semi-Major Axes (ISMAs highlighted in blue) that can exist according to the hypothesis.

The empirical Semi-Major Axes (ESMA) for the 3 star systems are found in columns 4, 6 and 8. The reader’s attention is now drawn to the comparative values of the Ideal and empirical SMAs found in columns 4, 6 and 8. These comparative values are presented in columns 5, 7 and 9, as percentages. For example, the empirical SMA for Venus is 0.728 (column 4) and its ideal SMA is 0.7 (column 2). Thus, 0.7/0.728*100 = 96.15% (column 5). So in this example, the Empirical SMA of Venus compared with its Ideal SMA is 96.15% accurate.

Our Solar system is logged in the table and can be similarly checked. We find all ESMAs compare to their ISMAs by 80% or better, with the sole exception of Mercury, which I've highlighted in yellow.

Sometimes the numerator is larger than the denominator and gives a percentage greater than 100. Whatever the cases, one simply checks that the percentage is no more than plus or minus 20% of 100%.

Catalogues are always being updated and links changed, as more planets are added to these star systems.. The best way to search and check data is to simply search the name of the star system, for example: '55 cncri', or 'Ups And B'. There are many exoplanets that the reader may care to be the first to verify.

4th root of N to the power of 3 =
Ideal SMA
(AU)

Solar System
Planets

Solar System
Empirical
SMA
(AU)

%

accuracy

55 Cnc b
Empirical SMA (AU)

%

accuracy

Ups And b
Empirical SMA (AU)

%

accuracy

Click here for the same analysis of the first 117 exoplanets found.
http://hyperphysics.phy-astr.gsu.edu/hbase/solar/soldata3.html#c1
http://www.sciencedaily.com/releases/2006/09/060914155305.htm
http://www.daviddarling.info/encyclopedia/S/Sedna.html
http://exoplanet.eu/catalog/hd_216435_b/