3 min read

Cosmic Piece of Pi

What is pi? We’re not talking about your favorite pastry with yummy fillings and a side of ice cream. Pi can be written as the Greek letter 𝞹 or the number 3.14159..., which goes on and on because pi is an irrational number. That doesn't mean it can't be reasoned with! It means this number can't be written as a simple fraction like ½.

Pi is perhaps most familiar as the ratio of a circle’s circumference (the distance around its edge) to its diameter (the distance across it). Pi will always be the same number, regardless of the size of the circle.

But did you know that pi is involved nearly anywhere you look? Here are some places you can find it in the universe around us!

Two circular views of the night sky captured by NASA’s TESS mission are side by side. Each is made up of segments that look like a film strip studded with stars. On the left is the southern hemisphere, which is a complete circle of segments. A band of white light runs through the upper half of the circle in a gentle arc. This bright band is the plane of the Milky Way. On the right is the northern hemisphere. The bright white band continues through this hemisphere as a gentle downward arc in the bottom part of the circle.
Two year-long panoramas from NASA’s TESS appear side by side in twin polar views centered on the southern (left) and northern (right) ecliptic poles. The prominent glowing band of the Milky Way – our galaxy seen edgewise – sweeps across both vistas.
NASA/MIT/TESS and Ethan Kruse (USRA)

Our Transiting Exoplanet Survey Satellite, TESS, watches slices of the sky in its hunt for worlds outside our solar system. How many exoplanets are in its night-sky pie? Using this data, TESS scientists created mosaics of the southern and northern skies. Since each awe-inspiring image is of one hemisphere (or half of a 3D circle), there will always be pi! And every slice contains something delicious for scientists to study.

This animation shows two balls glowing in blue-white light orbiting each other. One is about twice the size of the other. The larger ball starts on the left side of the screen and passes in front of the other to the left, then around the back. When the two cross in the middle, they don’t completely cover each other. Trailing behind them as they move are light blue lines indicating the path of their orbits. The animation is watermarked with the text: “Illustration.”
This animation illustrates a preliminary model of the Alpha Draconis system, an eclipsing binary system. We view the system at an angle such that the two stars undergo mutual eclipses, but neither is ever completely covered up by its partner.
NASA's Goddard Space Flight Center/Chris Smith (USRA)

Pi played a crucial role in discoveries about Alpha Draconis, a well-studied pair of stars. After these stars were seen to regularly eclipse each other, pi helped scientists learn more about them. Scientists detected the eclipses while monitoring TESS data of Alpha Draconis for periodic dips in its brightness that could’ve been caused by planets passing between the star and us. Instead of a planet, though, researchers found that its smaller partner in crime was passing in between us and the larger star for about six hours at a time!

This animation opens with a band of a starry sky running along the left side of the image, angled up and to the right. The right part of the image is black. The black represents areas of the sky that have not been imaged by TESS. In the center is a star with a blue circle drawn around it. As the animation plays, another band of starry sky appears, covering most of the right half of the image. This is another swath of TESS data that overlaps the other piece but adds in more of the sky.
The long orbital period of the Alpha Draconis system (circled) required multiple sectors of TESS data to reveal the eclipses. This discovery, together with future observations and modeling, will help astronomers better understand the stars and their orbits.

Pi comes in handy as we learn more about these two stars. Knowing the percentage of the decrease in Alpha Draconis’ light and the formula for the area of a circle (A=𝞹r2 – or area equals pi times the square of the circle's radius), scientists can predict the sizes of both stars. Because stars typically orbit in an elliptical (or oval) shape, pi also helps scientists use the detection of these eclipses to figure out the orbits of the two stars!

This animation shows a fuzzy bright circle that drifts from the top left toward the bottom right of the frame, representing a comet moving through the solar system. A triangular tail extends to the left and is composed of bluish, cloudy light. All of this is on a black background dotted with stars. The graphic is watermarked, “Animation.”
A comet flies by, leaving a tail of gas as it passes through the solar system in this animation.
NASA's Goddard Space Flight Center

So far, we’ve seen pi in many places, but it's also interesting to look at where pi can't be found! We mentioned earlier that many orbit calculations involve pi … but not all of them do. Pi does not factor into calculations of hyperbolic orbits – orbits that aren't complete, or don't return to where they started – the same way that it does with elliptical orbits. This is most commonly seen with comets. While many comets orbit normally in our solar system, some oddballs just pass through, like the interstellar visitor ‘Oumuamua that zipped through the solar system in 2017.

This image shows a pie decorated to celebrate the Fermi Gamma-ray Space Telescope sitting on a wood-grained brown background. The pie is in a silver pie plate with a tan crimped outer crust and is filled with shiny purplish blueberries. A simple two-dimensional model of Fermi made of pie crust spans the center of the pie. It is shaped like a box with long solar panels extending from it, with scored lines to add details. The image is watermarked with the text “Pie: J. Racusin” and “Image: J. Friedlander.”
Some members of our Fermi satellite team bake in their free time – including this blueberry pie with a Fermi-shaped top crust.
J. Friedlander

Perhaps the most popular place you may find pi is in the shape of a typical pie! While NASA’s Fermi Gamma-ray Space Telescope studies gamma-rays, and not blueberries, we think this cool Fermi pie is worth sharing for Pi Day!

Find more ways scientists look up at the night sky and use pi here. And now, don’t be irrational, and go have some pi(e)!