sci.environment

On Tue, 18 Sep 2007 18:42:28 +0000, Jonathan Kirwan wrote:

> On Tue, 18 Sep 2007 12:01:40 -0400, Whata Fool wrote:
>
>>
>>> Who said I'm a mathematician? Just looking at how much energy
>>>the earth can intercept. It can intercept pi*r^2 from the sun, but has
>>>a surface area of 4*pi*r^2.
>>
>> But while the solar energy in real time (essentially
>>parallel rays because the sun is 1100 times the diameter of the Earth)
>>may be split half and half with the lighted and dark side, the center
>>area of the lighted side gets direct sun mostly, but the other half of
>>the lighted area does not get the full solar insolation.
>>
>
> All this has already been worked out, WhataFool, by people who now all
> this quite well. You can do this as integration by parts and get exactly
> the same answer as Robert gave you, the relationship is simply the area of
> the circle vs the area of the sphere.
>
> The 'rays' are parallel not because the sun has a diameter of a million
> miles, as you say, but instead because the sun is nearly 100 million miles
> away from the Earth and it's diameter of a million miles at that distance
> isn't terribly important -- I think it presents about 1/2 degree from the
> earth: 2*tan^-1((1/2)/93), expressed in degrees. You are thinking
> incorrectly, here. The variation in angle from one limb of the sun
> towards the Earth vs the angle from an opposite limb of the sun towards
> the Earth is about 1/2 degree of variation -- which is why the 'rays' are
> essentially parallel. They cannot vary by that much, because the sun's
> diameter presents only a tiny patch of the sky, from Earth.
>
> You go on to also write terribly incorrectly. You suggest that the center
> region of the lit side of the Earth gets full insolation while the rest of
> the area (towards the limbs) "does not get the full insolation." This is
> not the way to view it. The distance from the sun at the equator and the
> distance from the sun at the pole is so close to not being different that
> the insolation (per unit area intersecting the solar radiation) is nearly
> identical. The difference cannot be be larger than
> (92*10^6/92.004*10^6)^2 or "down four 9's." By this, I mean the difference
> is about 87 parts per million. That's not much difference in insolation.
> The issue that makes the huge difference is that the same land area nearer
> the lighted limbs of the Earth present a smaller "intersection" vs the
> solar insolation. So while an acre in the center of the lit surface
> intersects an acre of light, so to speak, an acre elsewhere presents
> COS(zenith angle) of an acre to the incoming light. That's what accounts
> for the difference you imagine. So when the sun appears at 45 degrees
> from vertical to your location, you are receiving sqrt(2)/2 or about 70.7%
> of the insolation per unit land area nearby you, from your perspective.
>
> The solar insolation constant itself remains unchanged. It's just a
> matter of how the Earth's surface presents its spherical surface area at
> an angle into that insolation.

Are you implying that the Earth's albedo is independent of angle of
incidence?