The Milky Way and Mathematics?

From what we learned in this conceptual objective, distance and size of stars, I was able to find this article, “The Milky Way’s Most Distant Stars May Be Stolen Goods“, and see how modern day scientists are using what we learned in class to observe space.

In the article, it states that astronomers have observed several stars being shifted from one galaxy to another and it can be a little difficult to imagine that they were able to track the movements. Already, our solar system is an enormous place (it takes us 9 years to get to Pluto!) and the Milky Way galaxy is even bigger! It’s amazing how we’re able to detect and study stars like the Sagittarius dwarf, located 70,000 light years away. Another star that we’ve identified, Betelgeuse is located 642.5 light years away. With those varying distances, how was it that astronomers were able to measure those distances? Are those distances correct? Even with the best technology, the best telescopes, we cannot physically measure the distance of those stars from Earth. Like previously mentioned, it already takes us 9 years to get to Pluto and to reach stars that are light years away, it’s essentially impossible to do.

The answer to those questions is that astronomers rely on the mathematical components of science. They use a concept called parallax to determine the distances of stars.

parallaxecp

 

Parallax is an effect where the position of an object (stars) changes when view from different positions (on Earth). As you can see from the diagram, the relation of the Earth, nearby star and Sun forms a triangle. The small angle just below the distant star and are formed by the longest sides of the triangle is called the parallax angle. Knowing the parallax angle will allow us to determine the distance of stars. The smaller the parallax angle, it would mean that star would have to appear near the top of the diagram, forming a narrower triangle. This would mean the star would be farther away from Earth and that is the relation discovered through the mathematic mechanics of astronomy. The smaller the parallax angle, the farther the star is from Earth. Knowing this, it allows scientists to observe the “streams of stars” leaking into the Milk Way and determine that they can “reach as far as one million light-years from the Milky Way’s center”. Similarly, this is how scientist were able to discover the distances of Sagittarius dwarf (70,000 lightyears) and Betelgeuse (642.5 light years).

The unit that astronomers use to measure the length or distance of stars are called parsecs. The unit that they use to measure the parallax angle is arcseconds. 1 parsec = 1 arcsecond. 1 arcsecond is = 1/3600 of a degree.

So with mathematics, we were able to discover a method astronomers may use to determine the distance of nearby and faraway stars, now how do they determine the size of stars? Well, it’s more math. One way is if we know the luminosity and temperature of a star, we can combine Stefan-Boltzmann and Wien’s Law to generate an equation where we can solver for the radius of a Star.

lect13_eq5eqn_starradius

According to an example in the book, if we know that Betelgeuse has a surface temperature of 3650 K and luminosity of 120,000 L, after plugging it into the equation we are able to figure out its radius to be 590 billion meters. This is four times the distance between the Earth and Sun and is why we call Betelgeuse a supergiant.

As you can see, there are times where science doesn’t just rely on the latest technology to discover new things in space. They may have to use math, which is why it’s important to understand and recall laws like Stefan-Boltzmann and Wien, or Kepler and Newton. With these laws, astronomers manipulate them and are able to determine star sizes. By understanding the relationship between parallax angles (measured in arcseconds) and distances of stars (measured in parsecs), scientists are able to accurately measure stars without having to actually physically measure them themselves, because it’s impossible.

 

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