Did you see the movie "Sunshine"?
It might have been exaggerated for artistic effect, but gold-plated spacesuits didn't last long in direct sunlight. Which is kind of odd because the reflective plates of the ship's sunshield were also gold-plated and they weren't melting away.
Another thing is the filter of the observation lounge. Now that is how I envisage the canopy working.
The spaceship would have panels with a pure vacuum separating them from the ship. So as long as the panels had an effective cooling system, the ship itself wouldn't heat up even it was on the surface of the sun. The suits were much smaller so it was easy to heat up the mass until it radiated blackbody heat back into the wearer, so even if there was a vacuum layer built into it, it would still heat up eventually. ED ships apparently have pretty good insulation, however they produce their own heat from the nuclear furnace in the power plant, and if they are dealing with heat from without and from within, the cooling system can be overloaded.
If the canopy blocked out enough light to look at the sun like in "sunshine", it would also block out the light from any dim stars. However, we can still see the distant sky box stars, while looking straight at the sun, so that can't be quite the answer. Perhaps the canopy isn't really glass and is actually a two way video monitor? Like the chameleon material that bends light around it to make the objects invisible. Only in this case it would make the canopy "glass material" seem invisible, and it would filter out the harmful radiation.
However, if it IS on the far side it would not suffer from light reflected by the Earth when the observatory were in the dark. My previous post does take that into account (When it is in shadow...)
Telescopes are directional. They take in only the light from a relatively tiny column of sky, and simple baffles can block out all other light except ambient light from the atmosphere. Since there is no atmosphere on the moon,
there is no ambient light. Hence it doesn't matter if the moon is on the dark or the light side, or facing the the earth. It will function like a space telescope in either case. It would only be impacted by he earth or the sun if it looked directly at either object. If the telescope is on the sunny side of the moon though it will be hotter which will create electronic heat noise in the image.
Concord, when it was flying, had several layers of gold in the laminate of the main canopy (the bit that slid into place as she altered to flight configuration), to protect the pilots from the sun.
We can still the see the skybox and the milky way while fairly close to the star, so it would have to very selective in the way it rejected energy. The clear sections would have to let in 99.999% of the light, and the darkened sections would have to reject 99.999% of the light from the nearby star. That would be quite a trick of technology, even for the 34th century. Microscopic darkening panels would have to "slide in place" at the all the right places at all the right times to ensure a continuous image without frying the pilot.
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Isn't it just easiest to think we have photo-chromic glasses on?
Or a photo-chromic canopy? That's how I've always pictured it.
It still wouldn't explain why we cany see anything at all besides the sun. Because to look directly at the sun we would need to block out all but .0001% of the light, and that would render all dimmer objects, including planets and even some binary stars,
invisible.
