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Watching this video describing the "next generation" space telescope, it seems like the biggest mirror will be ~6 meters in diameter.

Theoretically, if a telescope was built in space instead of shipping it pre-built, and the mirror was, not a few meters, but a few kilometers, (and whatever other important aspects of a space telescope that a novice like myself has no idea about, multiply them by a few orders of magnitude) would it provide benefits proportional to the size difference?

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Yes, absolutely! The performance of any telescope depends on its diameter. A larger instrument not only collects more light, but also provides better resolution than a smaller instrument. The resolution limit is calculated from:

$R_{arcsec}\ = {1.22\ \lambda \over D_{mm}}$

whereas limiting magnitude is calculated from

$L_{mag}\ =\ 2.5\ +\ 5\ log\ D_{mm}$

I suppose there are eventual limits to $R_{arcsec}$, but I have never heard of any. As for limiting magnitude, as it’s a logarithmic formula, it grows very slowly as $D_{mm}$ increases, but a larger telescope is still a gain.

The whole thing is to balance $R_{arcsec}$, $L_{mag}$, and $$$, of course!

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