   Chapter 27, Problem 65PE

Chapter
Section
Textbook Problem

(a) The planet Pluto and its Moon Charon are separated by 19,600 km. Neglecting atmospheric effects, should the 5.08-m-diameter Mount Palomar telescope be able to resolve these bodies when they are 4.50 × 10 9 km from Earth? Assume an average wavelength of 550 nm.(b) In actuality, it is just barely possible to discern that Pluto and Charon are separate bodies using an Earth-based telescope. What are the reasons for this?

To determine

(a)

Should the 5.08-m-diameter Mount Palomar telescope be able to resolve these bodies when they are 4.50×109km from Earth if the planet Pluto and its Moon Charon are separated by 19,600 km? Neglecting atmospheric effects and Assuming an average wavelength of 550 nm

Explanation

Given info:

λ=550nm=5.5×107mD=5.08mΔy=19600km=1.96×104kmx=4.50×109km

Formula used:

Angle,

θ=1.22λD , λ is the wavelength and D is the diameter of the aperture, lens, mirror etc.

Calculation:

We have,

θmin=1.22×5.5×1075

To determine

(b)

What are the reasons for it is just barely possible to discern that Pluto and Charon are separate bodies using an Earth-based telescope?

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