Using Astrophysics to Answer Star Questions

Nowadays, we are able to say things like “Proxima Centauri is 4.24 light years from the sun and is the closest star to our solar system,” or things like “Stars are mostly made of gas, particularly hydrogen and helium.” But how? It’s not like we’ve ever been to another star, so we haven’t physically measured the distance or composition. Some basic methods of astronomy and astrophysics give us a way to answer these questions.

First, distance.

The easiest way most people know how to measure distance is with some kind of ruler. For further distances, a person can get in a car and drive to their destination, keeping the same speed the entire time and multiplying by how long it took him/her to get there to get the total distance traveled. But neither of those options is plausible for stellar distances, at least not with the current technology we have. Instead, astronomers figured out a way to use geometry to calculate the distance to the stars (yes, some people actually do use geometry again after high school!).

Stars exhibit what scientists call “parallax,” which is just a fancy word for tiny changes in a star’s position in the sky over a long period of time. You can choose a star in the sky and make note of its exact position at the same time every night, and after six months, you’ll notice even though you’re still observing at the same time, the star has moved a bit in relation to the other stars around it. This is due to the fact Earth itself is orbiting around the Sun, so six months after starting your observations, the Earth will be on the opposite side of its orbit and you’ll be viewing the star from a slightly different perspective than previously. The amount the star changes position can be measured as the angular change on the sky between the differing positions — aka parallax.



Basic geometry will give us the distance to stars. Picture:
Basic geometry will give us the distance to stars. Picture Credit: hyperphysics

So, using the geometry of a right triangle drawn between Earth, the sun, and the star, we can calculate the distance to that star! Remember one of the trig identities of a right triangle is tan(θ) = opposite/adjacent, where θ would be the angle between the different positions of the star (p), the opposite leg of the triangle is the distance between us and the Sun (defined as 1 astronomical unit, AU), and the adjacent leg is the unknown distance to the star (d). This gives us the equation tan(p)=1AU/d, and solving for distance we have d = 1AU/tan(p).

Take Proxima Centauri as an example: it has an observed parallax of about 0.768 arcseconds, which is approximately 0.000213o (if you’re wondering where that came from, there are sixty arcminutes in a degree and sixty arcseconds in an arcminute; it’s just like converting seconds to hours). This just means the star has shifted approximately two ten-thousandths of one degree in the sky over six months. Taking the tangent of this degree, plugging it into the equation above and then converting from AU to light years, gives you 4.24 light years, verifying the statement back at the beginning.

Now for the composition.

We have figured out what elements make up a star based on the light that star gives off. If you’ve ever played with a prism, you probably noticed the rainbow of colors produced when you put it in the light. This comes from the light refracting through the prism, producing all the components that make up white light, aka a continuous spectrum. But what happens if the light goes through something first before going through the prism? It was discovered that if light travels through a cold gas before being split into its components, the spectrum, rather than being a continuous rainbow, has some dark lines throughout its spectrum called “absorption lines.” The spectra of hot gas was also studied, and it resulted in “emission lines,” meaning only a few bright strips of color appeared when the light was split. What was really interesting, however, was that for each element, the absorption lines would exactly match the emission lines, and now we know each element has its own unique spectra. This allows us to split the light coming from a distant star and match its spectra the corresponding element, telling us the star has that certain element in it.

Splitting light into its components will reveal which elements a star is made of. Picture:
Splitting light into its components will reveal which elements a star is made of. Picture:


There you have it.

The distance to the stars and their composition, just with a few simple observations such as position in the sky and the splitting of light. Astrophysics doesn’t end here, though. Many other techniques exist for finding out other things about distant objects, such as how fast they are moving, what their temperature is, how old they are, and so forth. It’s quite amazing what we’ve been able to discern by just sitting here on Earth; hopefully one day we will be able to venture out to the stars to prove once and for all that our calculations and deductions are correct. But until then, keep calm and study astrophysics!

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