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 650 nm . The Earth-Sun distance is 149.6×106km, and 1ly=9.461×1015m. Express your answer to one significant figure and include the appropriate units.

Explanation / Answer

Angular Resloution of telescope is gvien by Rayleigh criterion as

theta = 122 L/D

where L is wavelength

D is Diameter

also as angle = arc/radus

S = 149.6 e 11

theta = 149.6 e 11/(4* 9.46 e 15)

theta = 3.95 e -6 rad

so,

D = 1.22 * 650 e-9/3.95 e 06

D = 20 cm

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