The nearest neighboring star to the Sun is about 4 light-years away. If a planet

Question

The nearest neighboring star to the Sun is about 4 light-years away. If a planet happened to be orbiting this star at an orbital radius equal to that of the Earth-Sun distance, what minimum diameter would an Earth-based telescope's aperture have to be in order to obtain an image that resolved this star-planet system? Assume the light emitted by the star and planet has a wavelength of 550nm . The Earth-Sun distance is 149.6 The nearest neighboring star to the Sun is about 4 light-years away. If a planet happened to be orbiting this star at an orbital radius equal to that of the Earth-Sun distance, what minimum diameter would an Earth-based telescope's aperture have to be in order to obtain an image that resolved this star-planet system? Assume the light emitted by the star and planet has a wavelength of 550nm . The Earth-Sun distance is 149.6

Explanation / Answer

rayleight criterion

sin theta = 1.22 lambda/D

and y/L = tan theta

small angle so sin theta = tan theta

y/L = 1.22 lambda/D

149.6E9/(4*9.461E15) = 1.22*550.0E-9/D

D=0.1697 m

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