## Kotov’s Method of Commensurability

Valery Kotov and colleagues  have made much study of 160 minute oscillations in a wide variety of astronomical phenomena, but especially the Sun. In some cases he uses a commensurability measure to determine the best fit values for oscillations. The main purpose of this article is to explain Kotov’s method of commensurability and the way that I use it to produce graphs that are a type of spectrum derived from a set of discrete measurements, usually of time periods or distances.

For this purpose, I am going to use the distances of the 9 traditional planets from the Sun in AU (astronomical units). Unlike the Titus Bode method where the fit is to a more or less  geometric series, this looks for something more like an arithmetic series. It does this by having a test value that is varied in tiny steps and for each value a measure of commensurability is determined. The test value is divided into each of the data values and the absolute difference from the nearest integer is found. In the case where the data value is less than the test value, the division is done the other way around so that the result is greater than one, then the difference from an integer is found. The sum of these “errors” is determined. In my method I then use the reciprocal of the sum. That then makes the graph look like a typical spectrum with peaks at the possibly interesting test values.

So with our example of the 9 traditional planet mean distances from the Sun the result is a graph that looks like this: The two strongest peaks are at very close to 5 and 10 AUs. This is hardly surprising because the 4 outer planets are at rather close to 10, 20, 30 and 40 aAU from the Sun. With Jupiter at close to 5 AU we can easily understand these peaks. But we do see the arithmetic series 10, 20, 30 and 40 AU. For the inner planets there are also two peaks at around 0.35 and 0.7 AU. Again they make an approximate series at 0.35 AU intervals, but the regularity is less in this case. There is also a peak at about 120 AU. If there is meaning in this process then we might expect to find some additional matter concentration floating about at this distance from the Sun.

Here are the tables of fits to the best test values. The interesting thing is that although the 5 and 10 AU spacings obviously fit the 5 outer planets, they also fit 3 of the 4 inner planets. Only Mars is not near an integer fraction of 5 and 10 AU. I have also shown the 515 AU distance which commutes the best of all with the planets, having a sum of differences from integer of only 0.797.

Kotov has shown with many examples that there is a pervading 160 minute oscillation throughout the solar system, galaxy and even further afield. He has found this period in binary stars, planetary distances, and galactic cores as well as various solar phenomena. I have found further examples, and agree with him that this is a universal wave phenomenon. I refer generally to 3, 6, 80 and 160 minutes waves.

The solar system also shows a shorter wave of around 0.12 AU. If these waves are real then there should be consequences beyond the data that was feed in and indeed there is.

The asteroids density with distance show peaks at spacings of 0.12 AU. There are additional objects between and beyond the outer planets and these also favour multiples of 5 AU. So we can reasonably conclude that this method has shown us something real that is happening in the solar system (and beyond). I close with the opening graph but having added exact ratios between values showing that the waves have harmonic relationships to each other.  