Pluto and its moon Charon are separated by 19600 km. Neglecting atmospheric effe

Question

Pluto and its moon Charon are separated by 19600 km. Neglecting atmospheric effects, should the 5.08 m diameter Mount Palomar telescope be able to resolve these bodies when they are 5.40 x 10^9 km from Earth?

Assume the average wavelength of 545 nm. To determine the answer, calculate the ratio of the telescope's angular resolution to the angular separation of the objects.

Hints: Use the Rayleigh criterion and trigonometry to calculate the two angular quantities. Also, don't forget to convert to SI units.

Explanation / Answer

Telescope's angular resolution,(theta) = 1.22*lambda(wavelength)/D(diameter){as theta is small}

Here, angular resolution(From Rayleigh criterion) = 1.22*545*10^-9/5.08 rad =130*10^-9 rad

And, the seperation between the objects can be determined by trigonometry, tan(theta1) => (theta1){as it is small} = 19600/(5.4*10^9) rad = 3629*10^-9 rad

So, the ratio is = 130/3629 = 0.0358(Ans.)

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