Harmonics Theory - Page 11

rtomes · #**301** (**permalink**) 07-September-2007, 04:40 AM

Quote:

Originally Posted by Nereid

Here is one question which (apparently) has not been answered:
What is the formula relating HT cycles to orbital elements of the eight solar system planets?

The only planetary period that I believe is an actual harmonic is Jupiter's. Quite clearly orbital interactions disallow other planets from being in harmonic relationship to Jupiter except special cases like Trojan asteroids. There are more complicated orbital interactions which I referred to before that do show harmonics.

Nereid · #**302** (**permalink**) 07-September-2007, 04:54 AM

Quote:

Originally Posted by rtomes

[snip]

Quote:

Originally Posted by Nereid

If so, what does it quote, for the accuracy?

It quotes that the orbit is known to 0.1" arc accuracy.

Quote:

How does that reference compare with what you have written in this post?

It does not state a formal error in the period, but the facts given support the accuracy being to around 1 part in 10^7 in the motion. That is, the error is in the last digit or a small amount in the second to last digit as I stated earlier.

[snip]

(my bold)

Where does it state that?

What is Table 7, in that reference?

For the record, here is what rtomes stated, in post #80 of this thread (my bold):

Quote:

The following graph is based on satellite periods of all known natural satellites in the solar system

post #87:

Quote:

The data for this was the mean daily motion for all satellites in the solar system known at the time I did the analysis which was June 2005.

Quote:

Originally Posted by rtomes #98 (extract)

Quote:

Earlier in this post you called them "mean daily motion" - how was the "mean" determined?

These are the average per orbit. They are the published figures in any set of planetary of satellite orbital parameters. It is one of the fundamental parameters used for all orbital calculations.^{*footnote added}

Quote:

Which "NASA web site" did you get the "motion data" from?

I think this one, but to the accuracy we require any one will do. http://ssd.jpl.nasa.gov/

post #106

Quote:

Here is a piece from the table I referred to. You can see that the mean daily motion is accurate to many figures, much more than I needed.

[snip]

I used 118 objects.

post #123:

Quote:

How do you know the motions are accurate to the number of figures stated?

I think that they may have small errors in the last digit given, but I do not require anything like that accuracy. These days orbital motions are determined to unbelievable accuracy, near to 11 digits for distances and times for the planets orbits. For satellites in the outer solar system it is a little less.

post #159:

Quote:

As regards the accuracy I am quite confident that the data is far more accurate than is needed for the job. I know how they measure the motions and over what period and it checks with the average motion accuracy that will result. [...] In general the things that have stated error bars have only a single digit uncertainty unless the first digit of the +/- is a "1" such as +/-0.012 and so I think the same applies to the motions.

And so on, until we get to the inputs rtomes claims to have actually used, in posts #232 to 235.

Here's a curious thing about these inputs: the stated epoch, to which the "mean daily motion" refers, ranges from 1950 to 2003; how was that factored in?

........

For something that should be as concrete as the motions of planetary satellites, rtomes' statements have not been consistent, and only after a great many requests were the inputs actually provided. Simple questions about the inputs, which seem to be quite straight-forward and easy to address, reveal what seems to be a curious ambivalence towards the importance of consistency ... even statements concerning the accuracy of the figures taken from the JPL website now seem not so correct^.

Does this matter? For this particular part of rtomes ATM presentations, probably not.

But if such apparently straight-forward and simple inputs are presented with so many inconsistencies, and as no ATM/HT claim (within BAUT's scope) presented here has been published, let alone in a relevant peer-reviewed journal, what credibility can those claims have?

*Note that this is erroneous, as even the JPL site cited by rtomes as his source makes very clear ...
^For interest, check out Nereid - 7 figures, the first digit being a 9 - yet ref 4 gives accuracy to only ~1 part per 100,000.

Nereid · #**303** (**permalink**) 07-September-2007, 05:07 AM

An 2005 arXiv preprint:

Quote:

Many astronomers have speculated that the solar system contains undiscovered massive planets or a distant stellar companion. The acceleration of the solar system barycenter can constrain the mass and position of the putative companion. In this paper we use the most recent timing data on accurate astronomical clocks (millisecond pulsars, pulsars in binary systems and pulsating white dwarfs) to constrain this acceleration. No evidence for non-zero acceleration has been found; the typical sensitivity achieved by our method is a/c=a few times 10^{-19} s^{-1}, comparable to the acceleration due to a Jupiter-mass planet at 200 AU. The acceleration method is limited by the uncertainties in the distances and by the timing precision for pulsars in binary systems, and by the intrinsic distribution of the period derivatives for millisecond pulsars. Timing data provide stronger constraints than residuals in the motions of comets or planets if the distance to the companion exceeds a few hundred AU. The acceleration method is also more sensitive to the presence of a distant companion (> 300-400 AU) than existing optical and infrared surveys. We outline the differences between the effects of the peculiar acceleration of the solar system and the background of gravitational waves on high-precision timing.

Quote:

Originally Posted by rtomes (post #183)

If the stellar grid that is observed is stable, then the acceleration would be of this order of magnitude, I expect probably between 10^-6 and 10^-5 cm/s^2.

rtomes, in post #198 (my bold):

Quote:

Originally Posted by Nereid

Specifically, if high quality, repeated observations show* that the solar system barycentre's acceleration is <~10-9 cm/s2, what implications are there for the ATM idea you have presented in this thread?

I am claiming that using some older and not so good data I found that the stars do show periodicity of distance and that the periods in light years match Dewey's common cycles in years. This does need to be repeated with the much more accurate and extensive data on stellar distances. However I expect that this will confirm the previous results and show that the nearby stars are not located randomly but the distances between pairs of stars will favour common cycles and multiples of these.

If such an arrangement exists, then we can reasonably state that it is not something special at this moment in time, but is an ongoing thing. There are two possible ways that this can be so, and one of them would need to be true. I would regard it as a failure if neither could be demonstrated.

1. That the stars remain in a lattice like grid and there are accelerations of the order that I indicated. This is the most likely situation.

2. That the stars do not remain in a grid, but that their motions continue to preserve the histogram of distances that shows the same common cycle periods. This situation is similar to the cymatics experiment and would be a surprising result, although perhaps not as surprising as 1.

Although I think that 1 is the case, 2 is just as interesting because it actually provides a means to explain how galaxy periodicity could exist without totally disproving the big bang. I would rather disprove the big bang though. The case 2 is easier to achieve only local periodicity rather than global, but I think there are ways to achieve global periodicity too given the huge spaces between clusters.

I guess the weight of HT now rests on "case 2" ...

Nereid · #**304** (**permalink**) 07-September-2007, 05:19 AM

Quote:

Originally Posted by rtomes

In the solar system there are two main scales of distance with regard to the planets. The Titus-Bode law does not really work, because the planets are more like two sets of arithmetic series than a single geometric seriesm, although Jupiter is an exception. This shows the outer planets above and the inner ones below. Each diagram is to scale. The outer planets form a neater wave than the inner planets which are a bit haphazard.

This diagram is produced by the Kotov method of analysis of the 9 planets (Pluto hadn't been demoted when I did this

) and so shows the tendency to commutation of any distance with the 9 planetary distances. I have previously posted this graph without the red triangles and numbers, and at that time I gave the individual planet commensurations with the 5 biggest peaks.

The red triangles are at exact ratios apart of the red numbers in between them. You can see that the labeled peaks are fitted well by this series of ratios. The ratios continue beyond the planetary distance scales. They show further commutations at 2, 4 and 12 times the outer planet wave, ending at near 120 AU. They show a further wave at 1/3 of the inner planet smallest wave. These waves are not obvious in the data, but are produced by the Kotov method without any coaxing. They make predictions about additional wave structures in the solar system.

We can expect matter to be found at near 120 AU from the Sun. We can expect minor planets to be found on these same waves. The objects beyond Pluto show a strong cluster 5 AU further out, right on one of these waves. The asteroids themselves show a distinct tendency to occur at intervals of the shorter 0.12 AU wave. This is rather odd, because the asteroid locations are already considered to be explained by Jupiter resonances, and to a large extent they are. It so happens that the Jupiter resonances say where asteroids should not be and the Harmonics theory says where they should be and the two agree over the range that most asteroids are found. Beyond that range they disagree and we have few asteroids. Complimentary predictions.

Although the lower graph was entirely produced by Kotov's method, in addition to the main ratios in red can be seen some additional
regular peaks following the ratio 2 peaks to the left of the ratio 7. There are two more at ratio two here, unlabeled. Actually there are a lot more similar relationships present in the graph. In all the details it is just like many of the sections of the harmonics theory predicted structure with many ratios of 2, a few of 3 and the other odd prime.

Quote:

Originally Posted by rtomes

Quote:

Originally Posted by Nereid

Here is one question which (apparently) has not been answered:
What is the formula relating HT cycles to orbital elements of the eight solar system planets?

The only planetary period that I believe is an actual harmonic is Jupiter's. Quite clearly orbital interactions disallow other planets from being in harmonic relationship to Jupiter except special cases like Trojan asteroids. There are more complicated orbital interactions which I referred to before that do show harmonics.

What is the relationship between the pretty picture, with standing waves, in post #156 and Jupiter's period ("an actual harmonic")?

What is the relationship between the formula in the Kotov material you reproduce on your website, and this "actual harmonic"?

Given the constraints on unmodelled mass in the solar system (per the arXiv preprint in my previous post), what is the status of this HT prediction: "We can expect matter to be found at near 120 AU from the Sun."

rtomes · #**305** (**permalink**) 07-September-2007, 05:20 AM

Quote:

Originally Posted by Nereid

(my bold)

It seems my question was not sufficiently clear; let me try again, with specific reference to galaxy redshifts.

Would you please walk through the steps involved in making an estimate of a galaxy's redshift, indicating in which steps the major sources of uncertainty (in the galaxy redshift) arise.

For those key steps - in terms of the source of uncertainty in an estimate of a galaxy's redshift - please indicate how that uncertainty is estimated.

For a set of 'galaxy redshift' inputs, each derived redshift having an estimated uncertainty, please describe the steps involved in estimating any periods in the set, and indicate in which steps the major sources of uncertainty (in the estimated period) arise.

For those key steps - in terms of the source of uncertainty in an estimate of a redshift period(s) of the set - please indicate how that uncertainty is estimated.

You get a telescope and point it at the object, and it has a slit and a prism or other device for separating the spectrum into colours. You put a device that can measure the intensity into the spectrum after focusing it, and take readings all the way along. These days I think that CCD devices are used to pick up the whole spectum at once. If it is a CCD device then the number of pixels is obviously critical to the resolution. You need to have calibrated the spectrometer with some ordinary spectrum on Earth first. To determine the redshift you need to do a correlation of some similar reference spectra that has lines expected to be found (e.g. Hydrogen, Helium, metals etc) by sliding the two until agreement is reached (this will be done mathematically today I imagine - that is most easily achieved by converting the spectrum to a log basis). The amount of slide is the redshift as measured - the difference between the wavelengths as a fraction of the wavelengths. You then adjust for the part of the vector of Earth's motion that is toward or away from the object to get a solar system based redshift.

The biggest problems in getting a redshift are I imagine the light gathering power and the resolution of the device for measuring the light (CCD?). It may need a long exposure if it is a distant object. If it is a dim object you cannot use a wide dispersion or there will be too little light captured. If you measure the wavelength of the light to an accuracy of 1A then you can calculate the spectrum to about a z of +/-.0002 from a single line. If you use many lines and there are no systematic errors (everything has been well calibrated) then this might be improved a bit by averaging many lines. Of course spectral lines are not infinitely small, as for a galaxy there might be 500 km/s dispersion which is about 10 A in the spectral lines. This is less of a problem for a star obviously. So you aim to get the centre of the peaks or dips depending whether it is emission or absorption. That will be the point of maximum correlation.

The best way to measure the uncertainty is by taking multiple measurements of a few different objects with different equipment. Then you can get a s.d. of the errors. This is more certain that estimating from the components effects. You will not expect to get more accurate than the resolution of the measurements permits.

To calculate the periodicity of redshifts you need a dataset with some limit of inaccuracy. If you have accuracy of about 10 km/s or z+/-.00003 then you will be able to detect a 72 km/s periodicity but not a 36 km/s one. It doesn't matter if you have a mixture of accuracies, but the worst case ones will largely determine the limit.

The best procedure for determining any periods present is as follows (this is possibly not what is used, but is the best, much better than using histograms). Let there be n galaxy redshifts with z(i) for i=1 to n. Then for each test periodicity in z of p (in z units), e.g. for 72 km/s p=.00024, perform the following logic. The result will give a phase and an amplitude (or covariance if you want). By varying p you can optimize the solution to the highest amplitude.

s = sum over i of sin(2*pi*z(i)/p)
c = sum over i of cos(2*pi*z(i)/p)

the amplitude of the cycle with period p is then a=(s^2+c^2)^0.5 and the phase is given by s and c taken as a vector.

Provided there is a unique peak in the graph of p in a vicinity (I mentioned multiple in some cases of Tifft's) then the maximum amplitude will be the estimate, and the uncertainty can be found by the range of redshifts and the period of the cycle and the amount of data. If you have 100 cycles then you can get accurate to about 1/400 in the period or better. With many objects this will improve if the cycle is strong.

Nereid · #**306** (**permalink**) 07-September-2007, 05:30 AM

Quote:

Originally Posted by rtomes

Quote:

Originally Posted by Nereid

(my bold)

It seems my question was not sufficiently clear; let me try again, with specific reference to galaxy redshifts.

Would you please walk through the steps involved in making an estimate of a galaxy's redshift, indicating in which steps the major sources of uncertainty (in the galaxy redshift) arise.

For those key steps - in terms of the source of uncertainty in an estimate of a galaxy's redshift - please indicate how that uncertainty is estimated.

For a set of 'galaxy redshift' inputs, each derived redshift having an estimated uncertainty, please describe the steps involved in estimating any periods in the set, and indicate in which steps the major sources of uncertainty (in the estimated period) arise.

For those key steps - in terms of the source of uncertainty in an estimate of a redshift period(s) of the set - please indicate how that uncertainty is estimated.

You get a telescope and point it at the object, and it has a slit and a prism or other device for separating the spectrum into colours. You put a device that can measure the intensity into the spectrum after focusing it, and take readings all the way along. These days I think that CCD devices are used to pick up the whole spectum at once. If it is a CCD device then the number of pixels is obviously critical to the resolution. You need to have calibrated the spectrometer with some ordinary spectrum on Earth first. To determine the redshift you need to do a correlation of some similar reference spectra that has lines expected to be found (e.g. Hydrogen, Helium, metals etc) by sliding the two until agreement is reached (this will be done mathematically today I imagine - that is most easily achieved by converting the spectrum to a log basis). The amount of slide is the redshift as measured - the difference between the wavelengths as a fraction of the wavelengths. You then adjust for the part of the vector of Earth's motion that is toward or away from the object to get a solar system based redshift.

The biggest problems in getting a redshift are I imagine the light gathering power and the resolution of the device for measuring the light (CCD?). It may need a long exposure if it is a distant object. If it is a dim object you cannot use a wide dispersion or there will be too little light captured. If you measure the wavelength of the light to an accuracy of 1A then you can calculate the spectrum to about a z of +/-.0002 from a single line. If you use many lines and there are no systematic errors (everything has been well calibrated) then this might be improved a bit by averaging many lines. Of course spectral lines are not infinitely small, as for a galaxy there might be 500 km/s dispersion which is about 10 A in the spectral lines. This is less of a problem for a star obviously. So you aim to get the centre of the peaks or dips depending whether it is emission or absorption. That will be the point of maximum correlation.

The best way to measure the uncertainty is by taking multiple measurements of a few different objects with different equipment. Then you can get a s.d. of the errors. This is more certain that estimating from the components effects. You will not expect to get more accurate than the resolution of the measurements permits.

[snip]

How closely does this correspond to what Tifft and Croasdale (or rather the astronomers who actually took the relevant observations) did, to obtain estimates of galaxy redshifts?

How closely does this correspond to what Croasdale reports, in the paper you cited, are the greatest sources of uncertainty?

What does Croasdale's paper say about how he measured, and addressed, uncertainty, at the level of individual galaxy redshifts, and as a set?

rtomes · #**307** (**permalink**) 07-September-2007, 05:31 AM

Quote:

Originally Posted by Nereid

What is the relationship between the pretty picture, with standing waves, in post #156 and Jupiter's period ("an actual harmonic")?

What is the relationship between the formula in the Kotov material you reproduce on your website, and this "actual harmonic"?

Given the constraints on unmodelled mass in the solar system (per the arXiv preprint in my previous post), what is the status of this HT prediction: "We can expect matter to be found at near 120 AU from the Sun."

The pretty picture shows distance harmonics not period ones.
The first graphic was done before I knew about Kotov's method, just fitting by hand calculation as it were.

Sorry, but I do not understand the second question.

It is simply that 120 AU will correspond to a moderately strong harmonic. In discoveries of matter beyond Pluto I would expect it to most often be found near as many of these waves as possible - 5 AU, 10 AU, 20 AU, 30 AU, 40 AU, 60 AU, 120 AU. So for example the objects just beyond Pluto cluster at ~44.5 AU which is 5.0 AU beyond Pluto. If many small objects are found then I expect the greatest numbers to be at multiples of the above distances. Obviously 120 AU is a multiple of them all, so it is a favoured location. I cannot say how much matter, just more than elsewhere in the vicinity. This will be in terms of mean distance from the Sun for the orbits.

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