Re: Democratic candidates address the issue of global warming while Republicans snooze...

On Sun, 6 Jan 2008 23:36:56 -1000, "Alvin E. Toda" <aet@xxxxxxxx>
wrote:

On Sun, 6 Jan 2008, Rumpelstiltskin wrote:

On Sat, 5 Jan 2008 12:02:33 -1000, "Alvin E. Toda" <aet@xxxxxxxx>
wrote:

On Sat, 5 Jan 2008, Rumpelstiltskin wrote:

On Sat, 05 Jan 2008 07:55:00 -0800, Islander
<nospam@xxxxxxxxxxx> wrote:

Rumpelstiltskin wrote:
On Fri, 04 Jan 2008 18:24:22 -0800, Islander
<nospam@xxxxxxxxxxx> wrote:

<snip>


OK, I think that the two of you are talking about
different things. My response to Jean had to do
only with the change in the tilt of the earth's
axis, not the difference in the distance of the
earth from the sun.

The change in the tilt is a maximum of only 3
degrees and that occurs over a period of about 41K
years. The specific cycles that Jean referred to
happen over shorter cycles, but are still pretty
long.

The change of distance between the earth and the
sun is only about 4 million miles (95M at aphelion
and 91M at perihelion. But, don't forget that the
intensity of the sun's rays varies as a cube law
(space is 3D). So, the difference in intensity
between perihelion and aphelion as a percentage is
(95M**3 - 91M**3)/95M**3 = 13%


Hmm. That's actually only as the square, isn't
it? not the cube. It's true that the volume of a
sphere increases by the cube of the diameter, but
when we receive light rays, we're not receiving
them from the volume, but only from what portion of
the spherical shell containing the light emitted
from the sun at a given instant in the past falls
on us or our measuring device. The surface area of
such a shell increases by the square of the
diameter, not the cube. (Disregarding any
absorption by interstellar gas, of course.)

http://tinyurl.com/25dc9q

That correlates (and has to correlate) with the
fact that the apparent size of the sun in the sky
diminishes by the square of the distance we are
from it. The brightness per apparent unit area
doesn't change (disregarding absorption), but the
net luminosity received diminishes in proportion to
the diminishing apparent size, which is the square
of the distance.

The brightness of a distant star identical to
the sun is the same (disregarding absorption) as
the brightness we receive from an "average" piece
of the sun exactly the same area as the apparent
size of the distant star (if we could make out the
diameter of the star, which we usually can't).

<snip>



You are right! But, you are also younger. That was
a dumb mistake, but at least I'm still young enough
to admit it!

That reduces the difference to 8.2%



Actually, your post sounded pretty good at first.
I read it just before going out, and wasn't really
thinking about it in the front of my mind, but then
the thought popped up that if luminosity diminished
by the cube rather than by the square from the
source, then we wouldn't be able to see stars at
all! I'm not sure if that was what made me realize
something had to be wrong, or if it was the fact
that the proportion of the sky occupied by the sun
diminishes only by the square of the distance, so
if the luminosity diminished by the cube, that
would violate conservation of energy.

There are greater worries about planetary orbits.
It's an oldie but once astronomers were not sure
that Saturn and Jupiter were in stable orbits. Since
the many body problem is non-linear (varies as the
square), it is an unsolvable problem.


I think it's generally agreed that solar systems are
fundamentally unstable, though since there's no
non-algorithmic solution to the three-body problem,
so-far or ever, that can only be "opinion". Our
system has apparently been around for four or
five billion years in relative stability, but the fact
that protocomets and asteroids are occasionally
flung out of their stable positions in their belts by
close gravitational contact or collision suggests
how quickly a cascade of events might change
things.





I'm not yet completely willing to give up and say
that the three-body (mult-body) is unsolvable, but
some people, such as Steven Wolfram, I think have
speculated that the only way to solve the problem is
algorithmically, and that's why time exists - the
steps of time (presumably quantized) are the
working-out of the algorithm. (I hope that's not
just something I made up, but it might be.) That idea
fits in nicely with the idea that time doesn't
actually move at all, but that each slice of time is
just the next step in the algorithm, and that's also
why each slice has a "memory" of the previous step in
the algorithm, but no forward-looking equivalent of
"memory" because the next step has not "yet"been,
and cannot "yet" be, computed, until the algorithm
proceeds to the next step based on the status at the
previous step.

Problem with a computer approximation of the orbits is
that it is difficult if not impossible to simulate all
the possible conditions of an orbit to see if it is
stable. Orbits are a little different from weather. It
is possible to make predictions of orbits. But the
stability of an orbit with many bodies is another
question completely.


Yes. Stephen Wolfram in "A New Kind of Science"
was the one from whom I got the idea that "time"
might be the steps of an algorithm, and any solution
other than the actual working out of the orbits in the
real world would, not only in practice but specifically
"in principle", take more time than the actual physical
working out. That's assuming, of course, that we
really never can have a calculus-like solution to the
three-body problem "in principle".

Here's what looks like the book online, though
I'm not suggesting you read it online. You might
glance at something that piques your interest, though
this book is quite a project to tackle. I didn't finish
it and I didn't come anywhere near mastering it, just
out of laziness when I saw what a project it would
be to really get an adequate understanding of it.
http://www.wolframscience.com/nksonline/toc.html

Here's a briefer and pretty good discussion in
Wikipedia. Note the term "computational
irreducibility" which is perhaps the most important
single concept in the book.
http://en.wikipedia.org/wiki/A_New_Kind_of_Science



But purturbations about the current stationary
orbits under all circumstances might be done to see
if there are any instabilities. IIRC it took quite a
while (until the 20th century) before the
mathematics were deemed to converge (I guess series
expansions of an integral expression?). But I think
that it's obvious that if they have not left the
solar system for billions of years due to some
instability, that their orbits are stable. The earth
is much further in and closer to the sun, that it's
orbit is probably much more stable that either
Jupiter or Saturn.


Perturbations are another way of talking about
steps in the algorithm, except that as far as I
know it hasn't been compacted into a process
such as calculus but remains in the state of the
pre-calculus "delta process". If it can be

I'm not familiar with the methodology, but I would NOT
try to look at this problem as an approximation to
solving the problem, or an algorithm to compute
something. The conceptual problem is to take the close
solution and see if the series expansion of the
integral (may involve the Hamiltonian of the three
possible interactions?) converges and the properties of
the solution indicate stable orbital patterns for
Jupiter and Saturn.

You lost me on "Hamiltonian", I'll have to look
that up.

OK, after checking old-faithful Wikipedia it seems
that if I just think of it as analogous to Feynman's
"sum over histories", that will be close enough for
present purposes.



The worse thing that can happen for planetary orbits
would be to have mathematical non-linearities in the
governing equations that can lead to chaotic orbits.
Thankfully that's been shown not to happen. I hope we
are not tempting global warming naysayers with this
discussion.


Yeah, not "non-linear" but the linearity can get
so extraordinary, as with close gravitational
interactions of asteroids such as I mentioned above,
that if the orbits can't get non-linearly "chaotic",
they can get so out-of whack that they might as
well, for practical purposes, be thus. What if
there were a major interaction between two of the
biggest asteroids that sent one of them careening
out of the asteroid belt, which hit Mars and threw
Mars' orbit off enough that it could come under
the influence of Earth's gravity enough that its
path would eventually lead to the possibility of
collision with the earth?

A Mars-sized component of the early solar
system actually did collide with the earth early in
the history of the solar system, according to
current ideas about the formation of the earth-
moon system. The moon seems to be made up
of light rocks such as are found on the outside
of differentiated bodies, whereas the Earth has
an excess of heavier rock such as would be
found in the cores of the early earth and the
body with which it collided.

We recently had the amazing collision of the
fragments of comet Schumaker-Levy-9 with
Jupiter, and now there's a fair chance that an
asteroid will collide with Mars in the not-too-
distant future. Back in the time of Tycho Brahe,
a bright spot was seen to appear on the edge
of the moon, after which the moon seemed to
"ring like a bell" (visually, of course, not
sonically) according to contemporary observers.
The crater created by that impact is thought to
be now known (It's not the crater named
"Tycho").

Here's a blurb on the possible coming Mars
impact:
http://neo.jpl.nasa.gov/news/news153.html




.

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