The Andromeda galaxy

Classical Mechanics Level 2

The Andromeda galaxy is a giant spiral cluster of stars whose mass is that of $300$ billion Suns. You can see it with the naked eye as a faint elongated cloud in the night sky. Inasmuch as it subtends an angle of $4.1^{\circ}$ and is known to be larger than our own galaxy [ $163 \times 10^3$ light-years (units of ly) in diameter for Andromeda as compared to $100 \times 10^3$ light-years for our galaxy], how far away is it in light-years?

4.6 \times 10^6 \text{ ly}

1.7 \times 10^6 \text{ ly}

5.9 \times 10^5 \text{ ly}

2.3 \times 10^6 \text{ ly}

1 solution

Chew-Seong Cheong
Aug 4, 2014

Let the Andromeda galaxy be $D$ $ly$ away. Then, $\tan{\left( \frac{4.1^\circ}{2}\right)}=\cfrac{\frac{163\times 10^3}{2}}{D}$ $\Rightarrow D=\cfrac{8.15\times 10^4}{\tan{2.05^\circ}}=\boxed {2.3\times 10^6}\space ly$

The Andromeda galaxy

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