A challenge astronomers face is that any telescope on the ground must look through many kilometers of air to peer into space. The air is not of uniform refractive index and is also turbulent, which limits the angular resolution of any telescope to approximately 1 arc second (1/3600 of a degree).
(a) What is the maximum diameter of a ground-based telescope where the resolution limit by diffraction (Rayleigh limit) is equal to that of atmospheric turbulence? Assume a wavelength of 450 nm (blue light) for the calculation.
(b) Find the angular separation of Pluto and its moon Charon, which are separated by approximately 2.3 x 10⁴ km. Assume Pluto and the Earth are at their closest. Would this telescope be able to resolve Pluto from Charon?