Astronomers have discovered a planetary system orbiting a star, which is at a distance of 3.3 x 1017 m from the earth. One planet is believed to be located at a distance of 1.3 x 1012 m from the star. Using visible light with a vacuum wavelength of 553 nm, what is the minimum necessary aperture diameter that a telescope must have s0 that it can resolve the planet and the star? Number Units

2) Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HB (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first-order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm.