Yahoo Tuning Groups Ultimate Backup tuning Planetary resonances revisited

Hi Paul,

This thread is from before I started reading and posting to TL.

However, I wonder if the topic of the resonances of Jupiter's moons was brought up.

Io, Europa and Ganymede are in a 4 to 2 to 1 resonance (The outermost of Jupiter's
four moons, Callisto, doesn't join in with this).

It's not completely exact - in fact it's been shown that a totally exact resonance is
impossible.

Intriguingly, web search in google turns up possiblity that they may have had
earlier resonances of 3/4 2/3 1/2

http://www.planetary.brown.edu/planetary/geo287/seminar2_23.html

What happens is that the whole system slowly loses energy, so all the orbits are
speeding up as this happens. (I think I've got this the right way round,...?)

The satellites keep lining up in lines of three, but each time a little earlier in their
orbits.

So, slightly tempered octaves.

By asking where all that energy can be going to, some researchers predicted that
Io would be extremely volcanic just before the Voyager spacecraft arrived there
- a rather spectacular scoup!

http://www.ucl.ac.uk/geolsci/edu/students/planet/student/work/io.htm

I imagine the Pluto to Neptune fifth must be very slightly tempered too.

There's an almost 5/8 resonance in orbital periods of Venus and Earth.

There's also an almost resonance between the rotation period of Venus and the orbital
period
of Earth, which is rather remarkable, as Earth's gravitational influence on Venus would
be very slight.

It's a 5/8 resonance too, and independent of the orbital period resonance.

http://sunra.colorado.edu/david/ch5.html

Robert

🔗Mary <lucid@home.com>

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Robert Walker" <robert_walker@r...> wrote:

http://www.egroups.com/message/tuning/17671

> Hi Paul,
>
> This thread is from before I started reading and posting to TL.

Hi Robert,

Someone named "Troubledoor" starting posting pseudo-cosmic stuff
here around mid-August 2000, and since I had just spent the
summer studying the Sumerians (including their astronomy), I
jumped right in and wrote a "piece" (really just a static chord)
which was an aural mapping of the orbital-period ratios of
the planets in our Solar System.

There are two MIDI versions of the piece, found here:
http://www.egroups.com/files/tuning/monz/solarsystem/

> ...
> I imagine the Pluto to Neptune fifth must be very slightly
> tempered too.

It is. But Pluto's orbit is far more erratic than those of
the other planets, and so the amount of "tempering" is harder
to pin down.

>
> There's an almost 5/8 resonance in orbital periods of Venus
> and Earth.

I don't know why astronomers insist on calling this 5/8; it's
really much, much closer to 8/13.

Anyway, all the data is in several posts I sent to this list.
The most relevant are as follows:

This is where it all began:
http://www.egroups.com/message/tuning/11867

This is the first post describing my "piece":
http://www.egroups.com/message/tuning/11923

This post has links to scientific software to help elaborate
on the piece, should anyone wish to collaborate with me on this:
http://www.egroups.com/message/tuning/11943

Here's the revised version of the piece with more accurate data:
http://www.egroups.com/message/tuning/11995

If you search the Tuning List archives for "solar", you'll
get a list of *all* the posts referring to this thread (by others
as well as by me); the most relevant ones are between August 25
and around August 29 of 2000.

One of these days I'll finally put together a webpage about
all this...

>
> There's also an almost resonance between the rotation period
> of Venus and the orbital period of Earth, which is rather
> remarkable, as Earth's gravitational influence on Venus would
> be very slight.
>
> It's a 5/8 resonance too, and independent of the orbital
> period resonance.
>
> http://sunra.colorado.edu/david/ch5.html

I would have recommended David Grinspoon's excellent book
_Venus Revealed_, but you've obviously found it already, and
anyone who follows the links from this one will too.

http://www.egroups.com/message/tuning/17671

> [Robert again]
> ... the Earth's tug on the Moon...

I just wanted to point out that it's really more accurate to
think of the Earth and Moon as a double-planet system than as
a planet-with-satellite. The Moon does not really revolve
around the Earth, but rather, they both revolve around a
common center of gravity. That's one reason why the Moon
always presents the same face to the Earth.

The situation may be similar with Pluto/Charon; otherwise the
Earth/Moon is the only double-planet example in our Solar System;
Mars, Jupiter, Saturn, Uranus, and Neptune are all clearly
planets-with-satellites. The best essay I've seen about this
was one by Isaac Asimov, "Just Mooning Around", which was
written before the discovery of Charon.

If you're interested in helping me to refine my piece, and
give it some dynamic qualities (the pitches changing over time
to reflect actual time-sensitive orbital ratios), let me know.
The math is way beyond my capabilities.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Mary wrote,

>Could you repeat tht link or summarize what was found? The link you
>gave is no longer active.

The link is still active, you just need to paste the address back together
since it will be broken here:

http://physics.about.com/science/physics/gi/dynamic/offsite.htm?site=http://
c.moreover.com/click/here.pl%3Fx14099424

In case you still can't get to it, here is what it says (sans pictures):

SPACE SCIENCE

Researcher Validates Discovery of Planets' Gravitational "Dance"

Gliese 876 at Exoplants.Org
Berkeley - Jan. 9, 2001
A team of planet hunters today announced a discovery that will help
researchers better understand planet migration and how planets'
gravitational pulls influence each other. The discovery was announced at the
American Astronomical Society meeting in San Diego.
The planet sleuths from the University of California at Berkeley, NASA and
other institutions discovered the planetary pair locked in what appears to
be "resonant" orbits, moving in synch around the star with orbital periods
of 60 and 30 days. Because of the 2-to-1 ratio, the inner planet goes around
the star twice for each orbit of the outer one. They gravitationally tug on
each other to maintain this synchronicity.

"The resonance between the two orbiting planets is among the most exciting
planet detection discoveries to date," said Dr. Jack Lissauer, a NASA Ames
Research Center scientist based in the heart of California's Silicon Valley.
A "resonance" is similar to the harmonic vibration produced by plucking two
notes on a stringed instrument. This gravitational pas de deux between the
two planets is common among moons and asteroids, but not planets. The axes
of the two newly detected planets' elliptical orbits also appear to be
nearly perfectly aligned.

Lissauer and State University of New York at Stony Brook graduate student
Eugenio Rivera used a numerical model to demonstrate the stability of the
nearly twin orbits around the star known as Gliese 876, a dim red dwarf 15
light years from Earth in the constellation Aquarius. "Questions about
planetary migration and gravitational influence are still very much
unsolved," Lissauer said.

"This discovery is significant for several reasons," said Lissauer. "This is
the first extra-solar planetary system to show a strong resonance. It also
is the smallest star known to have any orbiting planets, much less two," he
said.

The two gravitationally linked planets have masses of at least 0.5 and 1.8
times the mass of Jupiter, he said. The inner planetary companion was not
recognized at first because the orbital resonance allowed the pair of
planets to masquerade as a single planet with an elongated orbit.

The two orbiting planets are located relatively close to each other, within
0.08 Astronomical Units (the distance between the Earth and the sun) of each
other, less than one-third the distance from the Earth to its nearest
neighbor, Venus. In our solar system, the only known resonances between a
pair of planets is Pluto, which orbits the sun twice for every three times
Neptune circles the sun.

Besides Lissauer, the planet-hunting team that discovered the system
includes Drs. Geoff Marcy and Debra Fischer of the University of California
at Berkeley; Dr. Paul Butler of the Carnegie Institution of Washington; and
Dr. Steve Vogt of the University of California at Santa Cruz.

Though significant and unusual, the discovery will require more modeling
before researchers can determine what the resonance they discovered actually
means.

The team based both sets of its conclusions on 6 years of precise Doppler
measurements and observations made at the Keck I telescope atop Mauna Kea in
Hawaii and the Lick Observatory telescope in California. The research is
part of a multi-year project to look for planets among 1,100 stars within
300 light years of Earth. The project is supported by NASA, the National
Science Foundation and Sun Microsystems.

More information about these discoveries is available at
http://www.exoplanets.org.

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

Hi Monz,

> There are two MIDI versions of the piece, found here:
> http://www.egroups.com/files/tuning/monz/solarsystem/

Really interesting chord to listen to!

> It is. But Pluto's orbit is far more erratic than those of
> the other planets, and so the amount of "tempering" is harder
> to pin down.

Does the orbital period fluctuate greatly over time then?

I know that the orbital periods of all the planets are changing
slightly all the time.

Also, that Pluto's orbit is also not so well known as the others
as it hasn't completed a full cycle yet, and also, no spacecraft
has visited it.

> I don't know why astronomers insist on calling this 5/8; it's
> really much, much closer to 8/13.

Yes, so it is (224.7*13/8=365.1275).

Suggests the golden ratio doesn't it, as Mary
mentioned in her post.

However, the ratio of rotation period of Venus to earth's orbit
is very close to 5/8 I believe.

On note 9 of the site I mentioned before:
http://sunra.colorado.edu/david/ch5.html

author says that it takes 2300 years for Venus to turn round
once relative to Earth based observers!

This really seems almost too much for coincidence for
such a low number ratio, don't you think.

(I see from the site that the author is a planetologist by profession,
so should have got his numbers right!)

> This is where it all began:
> http://www.egroups.com/message/tuning/11867

> This is the first post describing my "piece":
> http://www.egroups.com/message/tuning/11923

> This post has links to scientific software to help elaborate
> on the piece, should anyone wish to collaborate with me on this:
> http://www.egroups.com/message/tuning/11943

> Here's the revised version of the piece with more accurate data:
> http://www.egroups.com/message/tuning/11995

> I would have recommended David Grinspoon's excellent book
_Venus Revealed_, but you've obviously found it already, and
anyone who follows the links from this one will too.

No, I haven't. It's just general astronomical knowledge -
I'm a quite keen mainly armchair amateur astronomer.

I'll have to look it up.

> I just wanted to point out that it's really more accurate to
think of the Earth and Moon as a double-planet system than as
a planet-with-satellite. The Moon does not really revolve
around the Earth, but rather, they both revolve around a
common center of gravity. That's one reason why the Moon
always presents the same face to the Earth.

Yes, the common centre of gravity is within the Earth, but
only just.

The future evolution of such a system is quite interesting
- astronomers have worked it all out.

Because the day is slowing down faster
than the month, the whole system
is gradually moving towards situation where the
earth is tidally locked to the moon as well, so that
the day is the same length as the month (both longer
than the current month), and the moon is always the
same place in the sky (as the Earth is at present when
seen from the Moon).

If that point were ever reached, then after that, the main remaining
influence on the system would be that the sun would gradually
drag on the earth moon system, effect being that the moon's orbit
speeds up again, and the earth's rotation, both remaining locked together,
and the moon get's closer to the earth, and eventually crashes
into it.

But much will happen before then, don't know the timescale,
but the sun becomes a red giant first, so prob. something
will disturb the system before then, even if the Earth survives
the red giant phase as a planet (which is unlikely I believe)

We are talking about as much time yet to go here as has elapsed
since life begun on the Earth, and much more so for
the moon to hit the earth, if it did reach that point.

However, it is interesting to think that the orbital periods are changing
all the time, even if it is almost imperceptibly slowly on our
every day time-scale.

> The situation may be similar with Pluto/Charon; otherwise the
Earth/Moon is the only double-planet example in our Solar System;
Mars, Jupiter, Saturn, Uranus, and Neptune are all clearly
planets-with-satellites. The best essay I've seen about this
was one by Isaac Asimov, "Just Mooning Around", which was
written before the discovery of Charon.

I think Isaac Asimov is a great science writer - so clear in
his explanations!

I'm also very fond of his Sci Fi writings...

You also get asteroids with "moons" - a recent discovery. I think
the first found might have been Dactyl, the little moon of Ida.

http://www.jpl.nasa.gov/galileo/idamoon.html

> If you're interested in helping me to refine my piece, and
give it some dynamic qualities (the pitches changing over time
to reflect actual time-sensitive orbital ratios), let me know.
The math is way beyond my capabilities.

I could easily add option to FTS to slowly vary the pitch of any sustained note
played according to any formula one likes.

In fact I've already made a start on this via Chann.. | Effects | Vibrato | Frequency
where you can enter any frequency, and a pitch bend amplitude in cents
(which also has option to vary the tremulo effect too, by adding an
extra parameter - see the help).

At the moment, this has a maximum range of two whole tones for
the default pitch bend, but this could easily be overcome by
resounding the note when it has moved too far in pitch to be
changed using pitch bend messages (not too noticeable for some
voices).

So it is just a matter of extending that to any formula, instead of
just sine waves - the programming to do any formula would be only a few lines,
as I have most of it there already, and the user interface wouldn't
take that much work to do.

One could have a table of formulae, one per FTS "voice channel".

Also could have option to change the pitch bend range from the MIDI default of
+- 2 semitones, so that one can continuously bend any notes by as much as
one likes without resounding them (already have option to do this for the
"joystick theremin").

(would be able to continue to play the fractal tune as before using the
large pitch bend range, so could do nice controlled pitch glides in fractal
tunes as well, and maybe it would be nice to be able to define a seed
with pitch bend glides in it - have to see how it goes),

Could be nice to show the planets in a little orrery animation as the
chord progresses.

If one worked out the formulae, then an animation would be easy enough
to do at the same time.

Yes, that would fit in with some of my plans for FTS 1.10.

Don't know when exactly as seems like I have a hundred things
to add to it, but it is now in the FTS "wish list", and I'll see what
I can do about it, maybe including the orrery too if it seems
easy to do - I rather like idea of adding some graphics that
change as the music plays, so may possibly link in with that.

Here are some other ideas, to mull over, not nec. in same
piece:

What also about varying volume according to brightness of the
planet as seen from the earth?

Loudest notes then would be Mercury, Mars, Venus, Jupiter and
Saturn, with these all varying in volume too.

One could also change location, and hear what it sounds
like from any of the other planets, or from a passing comet.

Could sweep in on a comet, and hear the changing relative pitch
of the solar system chord. Then do the orbit so it passes
close to one of the planets on the way, at which point you hear its
moons come into prominence.

Just an idea...

Robert