Not sure I’ve got a good source for you, but if you use the
Rayleigh criterion
you get that you can just about make out earth-sized objects using visible light at 4 ly. You could use much higher energy photons (better resolution from lower wavelength), but this gives you other problems. Anything beyond visible light won’t make it through the atmosphere (1 km is a BIG thing to put into space), and x and gamma rays are really hard to build optics for.
Not sure I’ve got a good source for you, but if you use the Rayleigh criterion you get that you can just about make out earth-sized objects using visible light at 4 ly. You could use much higher energy photons (better resolution from lower wavelength), but this gives you other problems. Anything beyond visible light won’t make it through the atmosphere (1 km is a BIG thing to put into space), and x and gamma rays are really hard to build optics for.
Yeah, if you want to build a space telescope 1km in diameter, you’d better build it out of local materials.