Re: The infamous internally mirrored sphere!

On 26 aug, 14:10, af...@xxxxxxxxxxxxxxxxxxx (John Park) wrote:
Damien Valentine (valen...@xxxxxxxxx) writes:
Mr. Park, it seems that the rocky inner sphere won't be evenly lit,
but dimmer by some fraction at the equator. Would it be even darker
on the opposite pole from the light source?

Depends on how "lossy" the mirror is--whether or not the losses due to
diffuse reflection and subsequent absorption outweigh the decreasing
diameter in the lower half of the sphere.

What if the light source
isn't on the rocky sphere, but on the inside of the mirrored shell?
Does that change matters at all?

Off the top of my head: not much. (In fact that's what I was assuming.)


I assume that it changes a lot.

Consider the rays from light source on inside of the mirrored shell.
Some rays are emitted at large angles to the shell and mostly hit the
rocky sphere and are absorbed. However, some are nearly along the
surface of the mirrored shell, and never get close to the rocky sphere
before they are reflected at low angle. Those rays never meet much air
- because in 1 g, the air is concentrated in the first few km next to
the rocky sphere, and most of the few thousands of km gap is vacuum.
Thus, the interior of the shell away from the sphere and its
atmosphere is full of light propagating near-parallel to the shell.
And then there will be the rays which just skim the upper atmosphere
and which therefore lose some but not all/or much of their intensity
to scattering at every passage. For example, given 12 000 000 km
diametre of rocky shell (1000 X Earth) and 5000 km gap, the horizon is
250 000 km away and a near-tangent of atmosphere is about 500 000 km
from reflection to reflection, or from upper atmosphere passage to
upper atmosphere passage. 20 000 000 km half circumference would
include about 40 atmospheric passages.

If the light source were on the rocky sphere, there would be little or
no rays skimming the inside of sphere. Since all rays are generated on
the rocky sphere, they all must reach the rocky sphere after
reflection.


You're right, Mr. Throop. I'm not sure how air at the very highest
altitudes would be kept from sinking lower. If anyone has some ideas
on this, I'd appreciate them.

On the other hand, if the whole space is filled with air, given that your
optical path lengths are several light-seconds long, you're going to get
extreme reddening at the very least, and probably massive absorption.
(Think of a sunset, but with a thousand times more atmosphere between you
and the sun.)

And if you have anything like normal weather, a few gigametres of cloudy
atmosphere will produce stygian darkness with no trouble at all. I think
your idea has a chance *only* if the atmospere is confined to the bottom
few percent of the gap between the rock and the mirror. (So birds and
other fliers would probably be safe.)

By the way, if the atmosphere *is* only few km deep, heat transfer from the
rocky surface would have to be by radiation, so your mirror should probably
be absorbant or transparent outside the visible region.

--John Park

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Relevant Pages

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