Question

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

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 $9.3777486\times {10}^{10}km$.

Step-by-step solution

Part(a) step 1: Given Information

We have given that:

Diameter of mirror $D=2.4m$and

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

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

Part (a) step 2: Calculation

By using the formula ,

$A_r=1.22\left(\frac{\lambda }{D}\right)$

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

We get value for angular resolution $A_r$,

$A_r=1.22\left(\frac{\lambda }{D}\right)$

Substituting the values in equation,

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

$A_r=3.30x{10}^{-7}.$

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:

$\chi =30000x(3.30x{10}^{-7})ly$

$$\begin{gathered} \chi =9.9x{10}^{-3}ly \\ \chi =(9.9x{10}^{-3})x(9.4605295x{10}^{12}) \\ \chi =9.3777486x{10}^{10}km. \end{gathered}$$

Here,$X$is the distance.