How far off are we from being able to image an exoplanet?
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My math is below.
Note: I'm not an astronomer.
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The angular resolution limit for a telescope is roughly the wavelength of the light it's sensitive to over the diameter.
If we want to sense things 10m across, with light at the shorter end of the visible spectrum (400 nm), we'd need a telescope with a diameter of about 1/4th of an AU (i.e. the distance from the earth to the sun), around 40 million kilometers.
More practically we could use a telescope array with this diameter, which could conveniently be in lot of orbits about 1 AU out. But the area is still a problem: assuming this 100m^2 object is as bright as it would be on earth under midday sun, it's going to be reflecting around 100 kw of energy. One of these photons has an energy of around 3 eV, so we're getting 2e23 of them a second. Unfortunately these spread out over a sphere with a surface area of 1e31 km^2 by the time they reach earth, meaning we see one every second if we have a telescope array with an area of 50 million square km.
Ok, so let's go kind of sci-fi and say we can build a 30 km diameter space telescope. It would be impressive (and unprecedented) but since it's floating in space and could be made of thin material you might be able to imagine it with today's technology and a lot of coordination. That gets us around 1000 square km! Now we just do it 50,000 more times.
Great, now we have 1 Hz of photons coming from each 100 m^2 patch of Alien Manhattan! I'm sure in the process of building 50k mega-projects we'll figure out a way to filter out the noise, and with a few years of integration we'll have a nice snapshot!