Question

Tau Ceti is a star that is located 11.753 ly away. There is a planet orbiting this star with an orbital radius of 0.538 AU (AU stands for astronimcal unit - the average distance between Earth & the Sun). Fill in the table below by determining the minimum diameter the objective of a telescope would need to be in order to resolve the planet from the star at the stated wavelengths. 1 ly = 9.461 × 10¹⁵ m & 1 AU = 1.496 × 10¹¹ m.

Ask Your Teacher 11. + -110 points Optical Instruments: Observing exoplanets My Notes Tau Ceti is a star that is located 11.753 ly away. There is a planet orbiting this star with an orbital radius of 0.538 AU (AU stands for astronimcal unit- the average distance between Earth & the Sun). Fill in the table below by determining the minimum diameter the objective of a telescope would need to be in order to resolve the planet from the star at the stated wavelengths. 1 ly 9.461 × 1015 m & 1 AU 1.496 x 1011 m. 200 400 600 800 1000 (nm) minimum diameter of objective Submit Answer

Answer 1

D = 1.22 $\lambda$ / $\theta$

where $\theta$ = d/L where

L is the distance from star to planet and d is the orbital radius (all in m )

Therefore,

D =  1.22 $\lambda$ L / d

For $\lambda$ = 200 nm

D = 1.22 * 200e-9 * 11.753 * 9.461e15 / 0.538*1.496e11

D = 0.337 m

For $\lambda$ = 400 nm

D = 1.22 * 400e-9 * 11.753 * 9.461e15 / 0.538*1.496e11

D = 0.674 m

For   $\lambda$ = 600 nm,D = 1.011 m

For   $\lambda$ = 800 nm,D = 1.348 m

for   $\lambda$ =1000nm,D=1.6855m