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

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'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.

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.

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.
.

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