Ask HN: What's the limits of planetary imaging?
Is there a limit for some reason of the optical pictures that we could get of planets in other systems?
What's the best theoretical direct image picture possible of a planet in another system?
What's the best theoretical direct image picture possible of a planet in another system?
There are different limits depending on your choice of technology. One is the angular resolution. https://en.wikipedia.org/wiki/Angular_resolution . The wider the telescope diameter, the better the resolution.
Here's the best that Hubble could see of Pluto - http://www.nasa.gov/mission_pages/hubble/science/pluto-20100... . A planet the size of Earth could be resolved to the same detail if it were 5.5x the distance as Pluto, or about 200-250 AU, which is about 30-35 light hours away.
The nearest star system is light years away, so Hubble won't work.
It's possible to make a larger telescope. The key realization is that "D" in the equation doesn't mean the entire telescope must be that far apart, only that the two most distant points are D. This is called https://en.wikipedia.org/wiki/Interferometry . The Cambridge Optical Aperture Synthesis Telescope, for example, "was the first long-baseline interferometer to obtain high-resolution images of the surfaces of stars other than our sun." https://en.wikipedia.org/wiki/Cambridge_Optical_Aperture_Syn...
Yellow light has a λ=580 nm wavelength. If your target resolution is 1000km (the Earth is 6,371 km across, so a 6x6 image) at Proxima Centauri some 4.24 light years away, then:
θ = 1000/4E13 = 1/4E10
D = 1.22 λ/θ = 1.22*580*40 m = 28 km across
This is the limit due to diffraction. The atmosphere makes it worse, so you probably want this in space. I believe it's also a difficult engineering problem, as the wavelengths needs to be in phase - it's not simply a matter of having telescopes on both sides of the planet and combining the results.
There are other methods, like gravitational lensing. I don't know enough to say anything about it.