Starship Asterisk*

Hello
Recently I tried charting planetary orbits by aligning circles, centered exactly on the star, to the distances of the aphelions and perihelions.
Here's an example:



What you see, in gray, are the actual planetary orbits. The dotted line circles are the aphelion and perihelion distances. The solid centered circles in black are the square root distances between the aphelions and perihelions. If the outer dotted circle is reduced by .81 and then by .81 again, it reduces to .6561. The minor axis of the planetary orbit is therefore the square root of the distance between the aphelion and the perihelion. It would appear that it always is. For the inner planet here, the aphelion to perihelion drop is .5904 with the orbit minor axis at the square root of that, .7684.

The diagram has been downloaded from the Open Exoplanet Catalogue

http://www.openexoplanetcatalogue.com/systems.html

If you scroll down you'll see the list of extrasolar planets, click one,scroll down and you'll see the diagram.

For the HD 73526 system, there are only three aphelion/perihelion circles. There should be four but the aphelion distance of HD 73526 b is also the perihelion distance of HD 73526 c. Why that is, is unknown as is why the orbit minor axis is at the exponential halfway point between the aphelion and perihelion distances.

For an orbital cartograher, this is a delight to see and it's not the only one.

The orbit minor axis of HD 7449 c aligns to the aphelion distance of HD 7449 b. Once again, that's the square root of the distance between the aphelion and perihelion. .5455 x.5455 = .297.



The drop from aphelion to perihelion of HD 13808 c is .387 which is the relative proportion between the mean average distances of Earth and Mercury to the Sun.



Between the perihelion of HD 13808 c and the aphelion of HD 13808 b is a gap - indicated here by the yellow ring. The inner edge of the ring is .8538 of the distance to the outer edge of the ring and this is the same proportional relationship as the aphelion and perihelion of the orbit of Ceres.



This is consistent with the actual numbers: Ceres perihelion 380,951,528km divided by the aphelion 446,428,973km = .8533.

In a survey of one hundred extra-solar orbits it was found that the orbits tend to come in groups. The following have the same proportions as Ceres in terms of heliocentricity and eccentricity.





The inner ring is .8538 of the outer with the orbit at the square root of .8538, .924. About .005 of the inner orbit has been allowed for star wobble and/or data inaccuracy hence the slightly offset center points. From the sample of one hundred extra-solar orbits, seven were found to be of Ceres dimensions.

.8538 x .8538 = .729. In an orbit where the perihelion is at .729 to the aphelion, the square root of that, and therefore orbit minor axis, will be at .8538 of the aphelion. Such is the case with HD 143361 b. There were five other orbits at these proportions found in the 100 orbit sample.



If the square root circle is tracked to the perihelion, it becomes apparent that it will not reach far enough to form a transfer orbit. The gap that results is the eccentricity.



The greater the difference between the perihelion and the aphelion, the more the orbit is eccentric. .8538 x .8538 x .8538 = .622. That's the difference between the aphelion and perihelion of HAT-21-b. As a result, the eccentricity increases. Only one orbit of this type was found in the 100 sample.



For Gliese 649 b, the perihelion/aphelion difference is .531441. (.622 x .8538 = .531441) with the orbit minor axis at .729 of the aphelion. Three orbits of this type were found.



The orbit of Venus is at .729 that of Earth so the square root circle will be .8538 of that. It's an exact match for HD 143361 b except that the aphelion and perihelion circles of the orbit of HD 143361 b are the actual orbits of the Earth and Venus.

The perihelion of Mercury is at .43 of the distance to the perihelion of Venus from the sun.

The square root of .43 is .6561 which is the aphelion circle of the Mercury orbit. The Mercury orbit aphelion is then the logarithmic halfway point between the perihelion of Mercury and the perihelion of Venus.



The difference between the aphelion of Mercury and the perihelion of Mercury is also .6561 with the Mercury orbit at the square root of .6561, .81.

The distances can be charted with .81 increment circles. The square root of .81 is .9.



It might seem that .8538 ratio and .9 are different but they are intertwined. It works like this:

.8538 ratio increments are 1 (x.8538 =) .8538, .729, .622, .531441, .453, .387, .33, .2824 etc

.9 ratio increments are 1 (x.9=) .9, .81, .729, .6561, .5904, .531441, .478, .430, .387, .348, .313, .2824 etc

The square root of .9 is .9487. .9 x .9487 = .8538. If the relative difference between perihelion and aphelion distances is .729, there is no halfway point occurring on .9 ratio so that distance splits to .8538 which is the logarithmic halfway point of .729 and 1. That distance then splits by the square root of .8538 which is .924 and then by the square root of that,.9613. If the relative distance between perihelion and aphelion is .6561, the square root of the distance between the two is .81 which is a .9 ratio increment. .81 then splits to .9 which then splits to .9487, then to .974 and so on.

Both ratios fall on the square root of .9 ratio because .9 x .9487 = .8538 but they have separate square root sequences.

In the 100 orbit survey eight orbits were found to be of the same proportions as Mercury.

Alright. I'll bite. What is the point of all this?

geckzilla,
There are at least a thousand planetary orbits that I have yet to even see. As I view them I realise things that I hadn't thought of. As an example, it looks like the eccentricities enjoy a logarithmic increase that ties in to the orbital ratios somehow. If this process continues, who knows what may be at the end of it. I think it's far too early to come to any conclusions when the bulk of the research has yet to be undertaken.

I get that you're thinking about them and that you are seeing patterns but it looks more like numerology than research.

Planetary orbits in mature stellar systems settle down into stable zones, where resonances are common. And where there are resonances, ratios will be discoverable -- whether they be meaningful or not. See the Wikipedia article on Orbital resonance for lots of info about this well understood phenomenom, especially the section titled Coincidental 'near' ratios of mean motion.

I think that what Guest is "discovering" are more of these coincidental ratios, which only seem like ratios on short time scales. However, to be sure, I'd suggest that Guest quietly do the calculations for the rest of those "thousand planetary orbits that I have yet to even see", compile the results, graph them for ease in presenting the conclusions, and then come back and post a link to the peer-reviewed article. Dribbling out the calculations one at a time like this does no good at all.

Rob

If I take the squares that are generated by the inverse square law increments, I eventually wind up with a square measuring 10 x10 surrounding a square measuring 9 x9. To calibrate to .9 ratio, this is repeated to the center.

Sorry, your squares are upside down.

When reducing from the 10 x 10 square, the 6 x 6 square becomes .6. .6x.6 =.36 so that's a 36th. .6561x.6561 =.43 so that's a 43rd. The 1x1 square is 1% of the 10x10 square and any number between 1-100 will express the diminishing radiance strength as long as the inverse square is taken.

The mean distance of the orbit of Vesta is .8538 that of Ceres. 2.766 x .8538= 2.361AU.



That means the aphelions and perihelions are at .974 increments.



There is an overlap between the aphelion of Vesta and the perihelion of Ceres of .028AU.



The current orbit positions fall on or about the overlap.



Which then becomes a migration path if planetesimals jump the tracks.

Correction: 'That means the aphelions and perihelions are at .974 increments.' - should read "... .924 increments".

You've certainly spent some time pondering these matters and I think that's cool, its also obvious that planetary orbital distances is a subject that you are highly interested in and that's all good too.
More to my point in stating that, the very, very last thing that i would ever want to do would be to discourage you away from that which is of interest to you................But, what rstevenson stated OK

The ratio of .9 and derivatives is also the undelying mathematical structure of the designs known as crop circles.



The center above is matched to a series of circles reducing at .9487. This is typical - the ratio in one form, one context, or another is easily measurable in countless examples of these illustrations.



The outer design perimeter has a clear 1,.9,.9 reduction sequence.



Possibly indicating the polar hexagon of Saturn.



Counter-rotational vortices.

Hello ezip. Are you human or machine?

Lol

ezip wrote:The ratio of .9 and derivatives is also the undelying mathematical structure of the designs known as crop circles.

I'm not surprised you're interested in crop circles... you're surrounded by living finger prints!
What is that crop, by the way?

Rob

I don't think there's any Wonderland down this rabbit hole.

rstevenson wrote:

ezip wrote:The ratio of .9 and derivatives is also the undelying mathematical structure of the designs known as crop circles.

I'm not surprised you're interested in crop circles... you're surrounded by living finger prints!

fingerprints in Oz.jpg

What is that crop, by the way?

Rob

Here i was, looking at the brown area that doesn't look like finger prints, wondering what the hell you were talking about, when i clicked on the picture. Then i realized that i had been looking at just about the only place where there were no finger prints. Neat, Rob!

ezip wrote:Lol

That's the kind of response I've come to expect from a dumb machine.

rstevenson wrote:

ezip wrote:The ratio of .9 and derivatives is also the undelying mathematical structure of the designs known as crop circles.

I'm not surprised you're interested in crop circles... you're surrounded by living finger prints!

fingerprints in Oz.jpg

What is that crop, by the way?

Rob

I would have to guess either Coca or Coffee

BMAONE23 wrote:

rstevenson wrote:What is that crop, by the way?

I would have to guess either Coca or Coffee

Pine trees.

They are exotic pine plantations, within 50km of my location. I don't know where ezip resides.

Edit: maybe Rob just confused my (roughly stated) location with ezip's. I did not immediately notice the co-ords on the fingerprints pic, and had to look it up to figure out it was a pine forest.