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

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:

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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).

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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. 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.

It's a metaphor really, but as in electron systems, it the spins that usually cause magnetic properties rather than orbitals. Pairing of the spins of the outer electrons cause strong covalent bonds with other atoms. The internal pairing in the lower orbitals are so strong that usually the electrons from the completed inner shells do not enter into any properties of the substance-- chemical or physical.
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