Question

The search for extrasolar planets is an active area in astronomy. Suppose that a planet is orbiting a star that is 5 × 1016 m (about 5 light-years) away and the radius of the planet's orbit is 1.5 × 108 m (same as Earth's orbit). If the astronomer observes this pair of objects in infrared light (λ = 1000 nm), what diameter aperture D must the telescope have to resolve them? Ignore the fact that the star is much brighter than the planet.