Question

Problem: 3. Our neighbor galaxy, Andromeda, has a luminosity (intrinsic brightness)
3 times as bright as the Luminosity of our Milky Way galaxy, LAndromeda = 3LMW, and
is at a distance of dAndromeda = 0.7 Mpc. The flux we observe from the Andromeda
galaxy (apparent brightness) is 10,000 times brighter than the flux observed from a distant
quasar, fAndromeda = 104fquasar. This quasar has a luminosity that is 1000 times the
luminosity of our Milky Way galaxy, Lquasar = 103LMW. What is the distance d to the
quasar? (4 points)

A. 1.28 × 10−1Mpc
B. 3.85Mpc
C. 1.28 × 103Mpc
D. 2.36 × 106Mpc
E. 3.85 × 1012Mpc

Answer 1

Question:

Problem: 3. Our neighbor galaxy, Andromeda, has a luminosity (intrinsic brightness) 3 times as bright as the Luminosity of our Milky Way galaxy, $LAndromeda = 3LMW$, and is at a distance of $dAndromeda = 0.7$ Mpc. The flux we observe from the Andromeda galaxy (apparent brightness) is 10,000 times brighter than the flux observed from a distant quasar, $fAndromeda = 104fquasar$. This quasar has a luminosity that is 1000 times the luminosity of our Milky Way galaxy, $Lquasar = 103LMW$. What is the distance $d$ to the quasar? (4 points)

A. $1.28 \times 10^{-1} Mpc$

B. $3.85 Mpc$

C. $1.28 \times 103 Mpc$

D. $2.36 \times 106 Mpc$

E. $3.85 \times 1012 Mpc$

Solution:

We can use the formula:

$$f \propto \frac{L}{d^2} \quad \text{or} \quad f = C \times \frac{L}{d^2}$$

where $C$ is a constant.

So we can write:

$$\frac{f(Andromeda)}{f(Quasar)} = \frac{L(Andromeda)}{L(Quasar)} \times \frac{d^2(Quasar)}{d^2(Andromeda)}$$ $$\frac{d^2(Quasar)}{d^2(Andromeda)} = \frac{f(Andromeda)}{f(Quasar)} \times \frac{L(Quasar)}{L(Andromeda)}$$ $$\frac{d(Quasar)}{d(Andromeda)} = \sqrt{\frac{f(Andromeda)}{f(Quasar)} \times \frac{L(Quasar)}{L(Andromeda)}}$$ $$\begin{array}{l} \frac {d (\text {Quasar})}{d (\text {Andromeda})} = \sqrt {1 0 ^ {4} \times \frac {1 0 ^ {3} L _ {M W}}{3 L _ {M W}}} \\ d (\text {Quasar}) = \sqrt {\frac {1 0 ^ {7}}{3} \times 0 . 7 M p c} = \sqrt {1 8 5 6 \times 0 . 7 M p c} = 1. 2 8 \times 1 0 ^ {3} M p c \\ \end{array}$$

Answer: $1.28 \times 10^{3} \mathrm{Mpc}$ (C)

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