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How do we know that the Sun is not at the centre of the Milky Way galaxy?

Answer
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Hint: When you look up at the sky, do you see an even distribution of star clusters? If that is not the case, think of why this happens. Is it because the stars are not centred about the Earth or the Sun or is it just because of interstellar dust obstructing light from distant stars reaching us or a combination of both? Use your deduction to explain the question given to us.

Complete answer:
The Milky Way galaxy is the spiral shaped galaxy that contains our Solar System along with large groups of stars, gas and dust bound by gravity. It is called a barred spiral galaxy since it has a central bar-shaped structure composed of stars, and has spiral arms that extend from the ends of the bar.
The position of the Sun in the Milky Way can be pinned down by measuring the distance to all the stars that we can see. Astronomer William Herschel attempted to do this following which he concluded that the earth was in the centre of a cloud of stars, but he was unaware of the presence of interstellar dust which obscures light incoming from distant stars. We appeared to be at the centre because we just could not see any further in all directions, just like how we’d think that a forest stretches equally away in all directions if we were tied to a tree in the foggy forest.
Following this, another scientist Harlow Shapley, measured the distance to a large spherical group of stars called the globular clusters and noticed that they were spherically distributed about the constellation Sagittarius. Additionally, using the Cepheid variable stars, he estimated the size of the Milky Way and the Sun’s position within it. He conclusively found that the centre of the universe lay somewhere near the Sagittarius constellation and that the Sun was in fact nearly $3/5^{th}$ of the way from the centre.
We now know that the centre of the Milky Way has a supermassive blackhole near the Sagittarius constellation, the gravity of which causes all star clusters to revolve around it, and that the Sun lies in the inner edge of one of the spiral arms, 25,000 light-years away from the centre, at the periphery of the Milky Way. We also see that when we look up at the sky, the distribution of globular clusters is uneven. This clearly means that they have a different symmetric orbit about which they are distributed, which we know to be the supermassive black hole at the centre of the galaxy.

Note:
According to the International Astronomical Union, the position of the supermassive black hole Sagittarius A* is adopted as the true zero coordinate point for the system of galactic latitude and longitude. Thus, the position of any celestial body in the galaxy can be quoted in terms of galactic coordinates.