Part A The nearest neighboring star to the Sun is about 4 light-years away. If a
ID: 1400460 • Letter: P
Question
Part A
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 550 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.
D=
Explanation / Answer
sintheta =1.22l/d
l = wavelength
d = diameter
sintheta = R/sqrt(R^2+ L^2)
R = distance from planet
L = distance from sun
d = 1.22*l*sqrt(R^2+L^2) / R
d = 0.0424 = 4cm