An astronomical interferometer is an apparatus that combines a number of telescopes into a much larger equivalent light- gathering instrument. The very fi rst extrasolar planet to be discovered was imaged in 2005 (Fig. P25.63) with the interferometer in the mountains of northern Chile known as the Very Large Telescope (VLT) project, which consists of four separate optical telescopes each 8.3 m in diameter. The interferometer operates with infrared wavelengths (1.4 mm), which are much less affected by atmospheric turbulence than other wavelengths. 

(a) The star system with the extrasolar planet was found to be at a distance of 200 light-years, and the planet orbits the star at a distance of 55 astronomical units (55 times the distance between the Earth and the Sun). What is the angular separation of the planet and star? Give your answer in units of arc seconds.

(b) The interferometer has an angular resolution of 0.0020 arc second. What is its effective aperture? That is, a telescope of what diameter would have such resolution?