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Chapter 35: Q. 47 (page 1019)

Alpha Centauri, the nearest star to our solar system is 4.3light years away. assume that alpha centauri has a planet with an advanced civilization. professor Dhg, at the planet's Astronomical Institute, wants to build a telescope with which he can find out whether any planets are orbiting our sun.

(a). What is the minimum diameter for an objectives lens that will just barely resolve Jupiter and the sun? The radius of Jupiter's orbit is 780millionkm.Assume 位=600nm.

(b). Building a telescope of the necessary size does not appear to be a major problem. What practical difficulties might prevent professor Dhg's experiment from succeeding?

Short Answer

Expert verified

a. The minimum diameter is1.9297脳10-5

b. The practical difficulties might prevent professor Dhg's experiment from succeeding are described below.

Step by step solution

01

Part(a) Step 1: Given information 

We have given that:

The radius of Jupiter's orbitS=780millionkm

distance of nearest star to solar systemr=4.3ly

and the wavelength is位=600nm

We need to find the diameter for an objective lens that will just barely resolve Jupiter and the sun.

02

Part(a) Step 2: Simplification

Firstly we need to solve the minimum angle,

S=r.胃

胃=Sr

胃=780millionkm4.3ly=9.4x1012km/ly

胃=1.9297x10-5.

03

part (b) Step 1: Given Information

We need to find what practical difficulties might prevent professor's experiment from succeeding.

04

part (b) step 2: Calculation

The angular resolution is,

胃=1.22x位d

1.9297x10-5=1.22x(600x10-9d

d=1.22x(600x10-91.9297x10-5

d=3.8cm.

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