Pluto and its moon Hydra are separated by $64800$ km $.$ An undergraduate researcher wants to determine if the $5\mathrm{.}08$ m diameter Mount Palomar telescope can resolve these bodies when they are $7\mathrm{.}40{10}^{9}km$ from Earth $($neglecting atmospheric effects$).$ Assume an average wavelength of $575$ nm $.$

To determine the answer, calculate the ratio of the telescope's angular resolution ${}_T$ to the angular separation ${}_{PH}$ of the celestial bodies.

$\frac{{}_T}{{}_{PH}}=$