How To Use Mathematics and Measurements in Astronomy

Mathematics and astronomy go hand in hand. You really can’t have one without the other if you want to get a clearer picture of the universe. Great minds of the past have developed some extremely useful equations and laws that help us measure distances and sizes, understand the underlying rules of celestial bodies, and interpret observations in order to know as much as possible about worlds that are unimaginably far away. Here are some of the ways astronomers and astrophysicists use mathematics and measurements in the field of astronomy.


1. Measuring distances in light-years.
What sounds better to you: 10 trillion kilometers, or 1 light-year? When we’re talking about the scale of distances in the universe, light-years make much more sense and save astronomers from having to write a lot of zeros. A light-year is how far light can travel in approximately one year. It’s not an exact figure, but it’s a good approximation that can help us understand and compare distances in space. For example, Alpha Centauri, which is the closest star system to us, is 4.37 light-years away (4.13x1013 km). Compare that to the farthest individual star we’ve been able to detect, Icarus, which is 5 billion light-years away (4.73x1022 km). In kilometers, the difference isn’t all that obvious. In light-years, it’s staggering.


2. Kepler’s Third Law
Kepler make significant contributions to the field of astronomy, most notably his laws of motion which helped others understand how and why the Sun, and not the Earth, is at the center of the solar system. His third law of motion is a neat and tidy way of explaining the relationship between orbital distances and orbital speeds. His equation, p2 = a3, represents a planet’s orbital period in years (p) and its average distance from the Sun in astronomical units (a). The result? The farther away a planet is from the Sun, the slower the speed of its orbit.

3. Wavelength, frequency, and emission lines.
How do we know the composition of distant stars, or our own star for that matter, without dropping down onto the surface and taking a sample? Light. Light conveys a great deal of information, and experiments conducted here on Earth with light allow us to apply our knowledge to more distant objects.

Individual atoms emit and absorb light at very specific wavelengths. Using emission and absorption line spectra, we can determine what atoms are present in a star based on the lines that show up on a line spectrum. If we see lines that we know based on past experiments belong to hydrogen or carbon in the emission line spectrum of a distant star, we know that the star contains those elements (based on the wavelength emitted). Similarly, using an absorption line spectrum, if certain wavelengths of light are missing, we can determine the composition of a cloud of gas that the photons passed through (based on the wavelengths absorbed).

4. Doppler shift to determine direction of movement.
Light can also tell us about the speed and direction of distant objects. We know the universe is expanding because of observations that took into account the Doppler effect. The Doppler effect, when applied to light, allows us to determine if an object is moving towards or away from us and at what speed based on the light’s wavelength. Shorter wavelengths are moving towards us and are shifted to the blue end of the light spectrum. Objects moving away have longer wavelengths and are shifted towards the red. Using this knowledge, astronomers were able to determine that nearly every galaxy we see is moving away from us, indicating that the universe itself is expanding.