Alpha Centauri, the nearest star to our solar system, is 4.3 light years away. Assume that Alpha Centauri has a planet with an advanced civilization. Professor Dhg, at the planet’s Astronomical Institute, wants to build a telescope with which he can find out whether any planets are orbiting our sun.
a. What is the minimum diameter for an objective lens that will just barely resolve Jupiter and the sun? The radius of Jupiter’s orbit is 780 million km. Assume λ = 600 nm.
b. Building a telescope of the necessary size does not appear to be a major problem. What practical difficulties might prevent Professor Dhg’s experiment from succeeding?