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’s 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 $3.30 \times 10^{- 7}$ .

b. The distance as a multiple of the distance of Jupiter from the sun is $9.3777486 \times 10^{10} k m$ .

Step by step solution

Part(a) step 1: Given Information

We have given that:

Diameter of mirror $D = 2.4 m$ and

the wavelength of red light $λ = 650 n m \to 6.5 x 10^{- 7} m$ .

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

Part (a) step 2: Calculation

By using the formula ,

$A_{r} = 1.22 (\frac{λ}{D})$

Here, $λ$ is wavelength of red light and $D$ is the diameter of the mirror.

We get value for angular resolution $A_{r}$ ,

$A_{r} = 1.22 (\frac{λ}{D})$

Substituting the values in equation,

localid="1650216005430" $A_{r} = 1.22 (\frac{6.5 x 10^{- 7} m}{2.4 m})$

$A_{r} = 3.30 x 10^{- 7} .$

Part (b) step 1: Given Information

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

Part(b) step 2: simplification

Now Distance x is:

$χ = 30000 x (3.30 x 10^{- 7}) l y$

$χ = 9.9 x 10^{- 3} l y χ = (9.9 x 10^{- 3}) x (9.4605295 x 10^{12}) χ = 9.3777486 x 10^{10} k m .$

Here, $X$ is the distance.

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Short Answer

Step by step solution

Part(a) step 1: Given Information

Part (a) step 2: Calculation

Part (b) step 1: Given Information

Part(b) step 2: simplification

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