An astronomer is observing a binary star that is $15$ pc away. The two stars have an orbital separation of $5\mathrm{.}5$ AU $.$ If the astronomer is observing the binary star at a wavelength of $720$ nm $,$ what is the minimum aperture of the telescope that is needed in order to resolve the two stars? $($Note: pc $($short for parsec$)$ and AU $($short for astronomical unit$)$ are length units used in astronomy. $1pc=206265AU,$ and $1AU=1\mathrm{.}469{10}^{8}km)$

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