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Chapter 35: Q. 46 (page 1019)

The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.

a. What鈥檚 the distance (in km) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.

b. For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?

Short Answer

Expert verified

a. The distance between two stars that are marginally resolved is 3.30脳10-7.

b. The distance as a multiple of the distance of Jupiter from the sun is 9.3777486脳1010km.

Step by step solution

01

Part(a) step 1: Given Information

We have given that:

Diameter of mirror D=2.4mand

the wavelength of red light位=650nm鈫�6.5x10-7m.

We need to find distance. between two stars that are marginally resolved.

02

Part (a) step 2: Calculation

By using the formula ,

Ar=1.22位D

Here, 位is wavelength of red light and Dis the diameter of the mirror.

We get value for angular resolution Ar,

Ar=1.22位D

Substituting the values in equation,

localid="1650216005430" Ar=1.226.5x10-7m2.4m

Ar=3.30x10-7.

03

Part (b) step 1: Given Information

we need to find the distance as a multiple of the distance of Jupiter from the sun.

04

Part(b) step 2: simplification 

Now Distance x is:

蠂=30000x(3.30x10-7)ly

蠂=9.9x10-3ly蠂=(9.9x10-3)x(9.4605295x1012)蠂=9.3777486x1010km.

Here,Xis the distance.

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