Logarithmic Spirals (APOD 17 May 2008)

Sputnick · Post by **Sputnick** » Sun May 18, 2008 12:51 am

May 17 2008 - http://antwrp.gsfc.nasa.gov/apod/astropix.html

Logarithms are somehow like math, eh? (I'm a high schooler only.)

"...the coincidental fact that the number of inches in a statute mile is approximately equal to the number of astronomical units in one light year." (from an article on 'The Electrical Universe.

We were talking a while back about standard measure versus metric .. perhaps there is a why to the wherefore.

rigelan · Post by **rigelan** » Sun May 18, 2008 1:46 am

Yup, I'm entirely sure the correlation is coincidental. . . All measurements are manmade anyway.

Pete · Post by **Pete** » Sun May 18, 2008 2:05 am

Yep, math! The name "logarithmic spiral" comes from the relation between the radius r and angle θ (polar coordinates) of a point on the spiral. If c and w are constants, then

r = c * e^(w * θ),

or

θ = (1/w) * ln (r / c) ...there's the logarithm.

Yet another place where the spiral crops up is in the easy "textbook" problem in classical mechanics of a bead constrained to slide on a frictionless wire rotating at a constant angular velocity ω. The bead's radial equation of motion integrates to r = c * e^ (ω * t), i.e. it diverges exponentially from the origin, tracing out a logarithmic spiral as the wire rotates. (Sorry, exams were just written...)

Sputnick, what grade are you in? Do you plan to take higher-level physics and/or math courses?

Sputnick · Post by **Sputnick** » Sun May 18, 2008 11:11 am

Hi Rigelan,

I believe coincidences are almost always declarations of the unseen power which rules not only the universe (universes) but also puts into our minds that which will declare that power to us .. that power also allowing for "time and chance to happen to all men" but also governing. or at least pointing towards a direction, for the smallest movement of the smallest particle. Can particles have will to rebel against direction?

Hi Pete,

It must be nice to have the kind of mind which can calculate those kinds of equations. I'm not in school . . I'm nearly a senior citizen, and while I know that's no handicap I'm a purpose driven person and the only grand purpose for me to take courses would be to increase my income. But hey .. I suppose a math course would improve my mental capabilities .. what would you suggest for a guy with very basic algebra (a + b = c). My math stopped at the grade 9 level and that was 45 years ago .. probably a grade three level today. I am grateful for people with higher education who have the time and spirit to share their knowledge .. thanks for sharing yours.

zbvhs · Post by **zbvhs** » Sun May 18, 2008 1:50 pm

That spiral form for hurricanes arises from a phenomenon known as vorticity. Is it possible that an analogous gravitational vorticity exists that would give spiral galaxies their shape?

Sputnick · Post by **Sputnick** » Sun May 18, 2008 4:38 pm

http://en.wikipedia.org/wiki/Vorticity

"One way to visualize vorticity is this: consider a fluid flowing. Imagine that some tiny part of the fluid is instantaneously rendered solid, and the rest of the flow removed. If that tiny new solid particle would be rotating, rather than just translating, then there is vorticity in the flow."

An apod forum contributor expressed the opinion that fluid dynamics do not compare with the movement of energy/matter in space. However, I believe instinctively hat it compares very well. For instance .. if the borders of plasma currents flowing at different speeds in space encounter each other what law is there to say matter cannot be created by that interation. We know matter does form from energy. The first created bit of matter would almost certainly rotate due to the movement of the current .. so .. the first created particle of a spiral galaxy could very well direct the shape for the entire galaxy.

TimeTravel123456789 · Post by **TimeTravel123456789** » Sun May 18, 2008 5:28 pm

I enjoy the pattern provided by the Bernoulli equation logarithm.

It helps see a pattern in spiral galaxy and hurricane. Further one gains an understanding that ellipticals and barred spirals could have similar vortical structure like a Bernoulli equation logarithm.

I do want to say that not all spirals match the Bernoulli logarithm. Certainly not all hurricanes match the pattern. The pattern comparison is rough and vague in some cases.

We know from hurricane development that warm air rises and spins with regard to the Earth's spin in part. So we can guess at a similar pattern for spirals. Heated plumes or jets are rising in spinning areas and the pattern formed is vortical. Thank you for the pointer on that. I was just saying that ellipticals are compressed spirals possibly.

By the way it is hurricane season again. I was personally seeing images of Burma that showed people seeking relief supplies and at first I did not know the gravity of the event. Hurricanes spiral arms are critical to hurricane response; miss the eye and you still get hit by a spiral arm.

Another interesting thing is Dr. Zadeh's writing on some galaxy centers being black holes. THese hurricanes have eyes with high pressures; galaxies have black holes with high pressures as well.

Happy Memorial Day in the US.

James T. Struck

orin stepanek · Post by **orin stepanek** » Sun May 18, 2008 5:42 pm

I believe the eye of a hurricane is a low pressure area.
http://www.wunderground.com/blog/Weathe ... amp=200803
The center of the galaxy has a black hole. similar to a low pressure area in that it draws things toward it. This attraction seems to be what holds a galaxy together. ( my opinion )

Orin

Sputnick · Post by **Sputnick** » Sun May 18, 2008 5:53 pm

orin stepanek wrote: The center of the galaxy has a black hole. similar to a low pressure area in that it draws things toward it. This attraction seems to be what holds a galaxy together. ( my opinion )
Orin

According to other opinions on the forum the gravitational influence of the black hole is very small (relatively) and does not affect the arms .. which persuades me further that the spiral is formed from pressure or influences outside itself, and that those influences will create a high pressure in the black hole .. the result being the jets seemingly 'squeezed' out of the hole.

astrolabe · Post by **astrolabe** » Sun May 18, 2008 8:33 pm

Hello Sputnick,

I may be going off topic here but the general school of thought is that the so far elusive DM is concentrated as a halo which holds the galaxies together. And yes the gravitational pull of a black hole is much less at the edge of a galaxy, so much so that material can be influenced or lost to another perhaps stronger neighbor but I think the jets result from a black hole that has reached beyond it's critical point of matter containment.

There must be a mathmatical calc for the maximum physical density of matter on account of the fact that the jets signal to me that the answer can't be an infinite density. If the density of a black hole is in fact infinite then the jets, IMO, shouldn't exist but they do. What are they if not an indicator of a finite state?

Ergo, (I've always wanted to say that!) the black hole has become a vehicle for matter which it must eject as it accretes new matter, i.e. stop the influx- stop the jet. I wonder what would happen if this powerful mechanism wasn't in place? At 10 billion tons (give or take a coupla pounds) per teaspoon it seems the black hole hits the wall and either ejects matter (protons,electrons etc.) or it...........

henk21cm · Post by **henk21cm** » Sun May 18, 2008 9:11 pm

orin stepanek wrote: The center of the galaxy has a black hole. similar to a low pressure area in that it draws things toward it.

Yes, similar to an area of low pressure. Look e.g. at the hourly images from Eumetsat or GOES whether satelites. The reason why the bands of clouds curl inwards is that the earth is spherical. Take a trip at 50 degrees North and go 20 degrees to the east. That is a considerably shorter distance than at the equator. As a result the bands of coulds at lower lattitude, traveling with the same speed as at higher altitude, stall with respect to those at higer latitude. At the southern hemisphere the same effect occurs, although the bands of clouds curl inwards in the direction opposite to that on the northern hemisphere.

When you look at the rotation curve of galaxies, the disc is not massive like a frisbee and so the the velocities of stars do not increase linearly from center to the edge. Assuming the stars orbit in nearly circular orbits around the center of the galaxy, a similar pattern as in low pressure areas occurs. If the galaxy has a radius R, within the first 10% of the radius the orbital velocity increases linearly with distance from the center. From about 0.1R the orbital velocity is nearly constant. In the same way as the clouds at lower latitude, the stars further away from the center have to travel a lot more lightyears for one orbit than stars closer to the center. So the stars further away from the center can't follow those closer to the center and as a result the stars close to center curl inwards.

Sputnick · Post by **Sputnick** » Sun May 18, 2008 10:00 pm

Hi Astro - I'm always so far from the general school of thought that I can't take shelter from the storm in their cafeteria. Same as with halos - if Dark Matter exists I think it is flowing in currents and heaving ever so slowly in waves and pooling in pools. Same with Dark Energy. I cannot see a possibility for 'nothingness' .. the more 'nothingness' tries to establish itself the more 'something' comes from within 'nothing'. That's why I can't see Dark Matter as being halo. What lies between the halos?

astrolabe · Post by **astrolabe** » Mon May 19, 2008 12:10 am

Hello Sputnick,

You may not be as far from the school as you'd like to think. Here's one for you, speaking from the "realm of possibility" (which is the exact opposite of the venerable "Cone of Silence"): it's entirely probable that we are saying the same thing but using our own imagery to convey the idea.

For instance,you may find the APOD for 3/30/08 to your likening of dark matter being possessed of currents. After all does anything in this universe stand still? There is belief that visible matter clumps where DM filaments intersect.

The point of my previous post was to present the perspective (a little alliteration for you folks at home) of a small but extreme gravity well with regard to your "squeezed" black-hole jet. As in sailing, is wind pushing on the sail or is it the negative pressure behind the sail pulling? I personally have an easier time understanding the effects of gravity over outside pressures, DM notwithstanding.

Dont't forget, I for one believe dark matter collects into gravity-rich objects whose electrons, in going to a less energetic state, give off photons, and then we can see 'em!

Sputnick · Post by **Sputnick** » Mon May 19, 2008 1:43 am

Yupper Astro - we're on the same wavelength sortof. 8)

Here's something I'm sure you've encountered before but I'll post it anyway .. it's a cool website and leads to some tremendous information.

http://www.thunderbolts.info/tpod/2004/ ... -stars.htm

I read a bit of Jeurgens a few years ago, but had lost track of his name and was led back to him by someone here on the forum .. might have been you. My memory short circuits often these days.

astrolabe · Post by **astrolabe** » Mon May 19, 2008 2:10 am

Hello Sputnick,

No, I'm not your Jergens connection but I know what you mean about memory. In a few years I may be asking all these questions and making the same stupid comments all over again. Who knows, maybe I'm already doing it and all of are just nodding your heads and smiling understandingly as you, once again, patiently repost the answer you gave me last week which you saved in your "Poor astrolabe" file.

In the meantime I'll read up on your guy and you can have some fun by typing in "Dark Matter Lensing" on the APOD Search page!

See ya around. By the way, almost made it to the Hollowell Rocks 2yrs. ago, gonna try again next Sept.

Sputnick · Post by **Sputnick** » Mon May 19, 2008 2:20 am

Hollowell Rocks? Please explain.

Nobody that I know is saying, "Poor Astrolabe." But I don't know many people. Hope that makes you feel better. You're a heck of a good guy Astro, I instinctively believe/hope.

Pete · Post by **Pete** » Mon May 19, 2008 3:13 am

Dear Sputnick: Gah!

Now I remember reading something here that revealed that you were an adult. Sometimes my memory short-circuits too. Thanks for brushing off my false assumption so well.

Regarding learning math, the Internet offers lots of good material at the high school level (and far beyond), but a textbook and teacher or tutor would be best. Having never really seen Peterborough, I don't know much about Trent University, but perhaps they offer some kind of standalone math course or lecture series?

Gravitational vorticity... interesting suggestion. I must get my hands on a galactic dynamics book.

neufer · Post by **neufer** » Mon May 19, 2008 1:47 pm

Sputnick wrote:May 17 2008 - http://antwrp.gsfc.nasa.gov/apod/astropix.html

Logarithms are somehow like math, eh? (I'm a high schooler only.)

"...the coincidental fact that the number of inches in a statute mile is approximately equal to the number of astronomical units in one light year." (from an article on 'The Electrical Universe.

We were talking a while back about standard measure versus metric .. perhaps there is a why to the wherefore.

The equiangular 'fractal' spiral has lots of nice features:
http://en.wikipedia.org/wiki/Logarithmic_spiral
http://www.geocities.com/jyce3/spiral.htm
-----------------------------------------------
Sputnick's inch/AU comparison is very nice:

If the Earth were 1 inch from the Sun:

* Pluto is 1 meter from the Sun.

* The Kuiper Belt begins at roughly 1 yard

* 90377 Sedna's orbit ranges between 2 and 25 yards from the Sun
* 8 feet: Termination shock between Solar winds/Interstellar winds/Interstellar medium.

* 8.5 feet: Heliosheath

* 3 yards: Voyager 1

* 30 yards: Beginning of "Inner Oort Cloud"

* 600 yards: Beginning of "Outer Oort Cloud"

* 1 mile: "Outer Oort Cloud" limits (1.0 ly)

* 4.2 miles: Proxima Centauri

* 2.5 million miles: Andromeda Galaxy

Sputnick · Post by **Sputnick** » Mon May 19, 2008 5:38 pm

Pete - my maturity level is far below my physical age so you needn't be embarrased about a natural assumption.

Neufer - wow - there is a lot of 'empty' space out there.

astrolabe · Post by **astrolabe** » Tue May 20, 2008 2:13 am

Hello Sputnick,

The Hollowell Rocks are structures that have been carved out of the coastal cliffs of New Brunswick, Canada by the dramatic tides of the Bay of Fundy. At high tide they appear as islands but at low tide the islands are seen for what they are: tall slender columns of rock.

One can walk the sea floor around them for a short time, maybe an hour or so before the tide comes back in. The 12 meter (you're welcome!) tide can rise as much as a meter or more in 30 minutes or less depending on moonphase so one is strongly advised to be watchful, needless to say even a shallow tidal current is not to be underestimated.

Makes for an unusual photo op.

Sputnick · Post by **Sputnick** » Tue May 20, 2008 3:03 pm

Hi Astro (and all)

Pillars, eh! Like the pillars in space? Being carved by the same processes but with different matter/energy? Yet more evidence for my streams and currents and pools and waves .. and now tides .. yes, tides in space. Oh I wish I were a scientitist of the right persuasion, gifts, talents, equipment, etc to pursue my picture of the cosmos.

Thanks for the east coast geography lesson and safety reminder. I was aware of the tidal flats and surges out east which can trap a person in the muck .. not just out east .. but canoeists on the Hudson Bay coast have also been lost from those effects. I was walking in flip flops on coral in Hawaii when a tidal current in extremely shallow water graplped my flip flop and left me barefoot on the coral .. I suffered severe coral burns and infection from the diseased waters .. I thought I was dying that night. Terrible world we live in now.

Starship Asterisk*

Logarithmic Spirals (APOD 17 May 2008)

Logarithmic Spirals (APOD 17 May 2008)

Spiral Provides Pattern Description- Pointer to GalaxyProces

Re: Logarithmic Spirals