Re: [tuning] Digest Number 1057

Hi Paul,

> No -- it's mode-locked into a 3:2 ratio. What Monz meant was that the orbit
> is very elliptical, and so its speed varies quite a bit.

Yes, it is _very_ eccentric (0.248) compared with the others (except for Mercury
which also has an eccentric orbit, eccentricity 0.206, Earth's is only
0.07 by comparison).

Yes, I understand what Monz meant now.

Fact that it is mode locked with Neptune just means that if the orbital periods
vary, the two planets have to vary their orbits in synchrony. It is perfectly
possible that this happens. Indeed, I'd have thought its likely there is such
an effect, as all the orbital periods vary a bit under the influence of all the
other planets, it's just a question of how large the variation is.

As with Jupiter's satellites, the (mean) 3/2 will be very slightly tempered,
- the effect is that any well defined point in the orbits, such as Pluto's aphelion,
say, will slowly drift round the sun.

There is some kind of theorem about this - maybe I can look it up
when next in the maths / science library here.

All the eccentricities of the planets slowly vary with time too.

> >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.

> This is irrelevant because precise astronomical measurements allow us to
> very accurately forecast (and retrodict) Pluto's motion for thousands of
> years.

Can be very accurately forecast if you know the numbers. There are
some clever computer programs that get astonishing accuracy that
I remember about.

Though eventually, on large time scales, they are chaotic
in the sense that it is impossible to predict Pluto's exact location in
its orbit, even though the general position of the orbit can be
predicted.

There is something about that, and more about resonances of orbits
in the solar system here:
http://members.nbci.com/Templarser/solarsys.html

However, astronomers get a much more accurate value for a planet's
orbit once it completes a full cycle.

Also when a spacecraft visits a planet, you get much more accurate data
about it's current position.

Sorry, don't know the details about that though.

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

> Yes, the golden ratio and other noble numbers are very important in orbital
> dynamics because they are the ratios that minimize the potentially
> destabilizing effects of resonances.

Interesting idea.

Would make sense for the asteroid belt, where asteroids are cleared out of
(some) of the resonances - the Kirkwood gaps,

Now that's another set of ratios in astronomy, this time, an absence of
orbits at various resonances:
http://ssd.jpl.nasa.gov/a_histo.html

I wonder if that could be used for music too.

The gaps aren't completely empty, some asteroids actually orbit
in a gap and stay in resonance with Jupiter for a substantial
length of time - see
http://members.nbci.com/Templarser/solarsys.html
again,

Robert

Robert wrote,

>However, astronomers get a much more accurate value for a planet's
>orbit once it completes a full cycle.

No, I don't know why you're assuming that. Nothing special happens when the
cycle is completed.

>> Yes, the golden ratio and other noble numbers are very important in
orbital
>> dynamics because they are the ratios that minimize the potentially
>> destabilizing effects of resonances.

>Interesting idea.

>Would make sense for the asteroid belt, where asteroids are cleared out of
>(some) of the resonances - the Kirkwood gaps,

Exactly, and also the material in the rings of Saturn.

Thanks for the links, they're very informative.