Astronomers have discovered a planetary system orbiting the star Upsilon Andromedae, which is at a distance 4.2 1017 m from the earth. One planet is believed to be located at a distance of 1.2 1011 m from the star. Using visible light with a vacuum wavelength of 550 nm, what is the minimum necessary aperture diameter that a telescope must have so that it can resolve the planet and the star?
______m
I keep coming up with 2.3 m, why is this not correct
______m
I keep coming up with 2.3 m, why is this not correct
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Define an angle q subtended by the telescope to be the planet's orbital radius, a, divided by the distance from the earth to the star, r:
q = a/r
Now set this equal tothe diffraction limited angle defined by some telescope paerture diameter D at wavelength wl:
q = a/r = 1.22 wl/D ---> solve for D
D = 1.22*wl*r/a = 1.22*550x10^-9 * 1.2x10^11 /(4.2x10^17) = 2.35 m
q = a/r
Now set this equal tothe diffraction limited angle defined by some telescope paerture diameter D at wavelength wl:
q = a/r = 1.22 wl/D ---> solve for D
D = 1.22*wl*r/a = 1.22*550x10^-9 * 1.2x10^11 /(4.2x10^17) = 2.35 m