Astronomers have discovered a planetary system orbiting a star, which is at a distance of 5.4 x 10^19 m from the earth. One planet is believed to be located at a distance of 2.0 x 10^10 m from the star. Using visible light with a vacuum wavelength of 556 nm, what is the minimum necessary aperture diameter that a telescope must have so that it can resolve the planet and the star?
The resolving power of a telescope is its ability to show distinctly the images of two distant objects lying close by. It is measured by the angle (alpha) subtended at the objective of the telescope by those two distant objects whose images are just seen as separate through the telescope. Resolving power alpha is given by the following expression ...
Solution includes the definition of resolving power and proceeds to calculate the aperture diameter of the telescope.