Collage of spacecraft featured in the 2022 NASA Pi Day Challenge

Graphic showing the various spacecraft featured in the 2022 NASA Pi Day Challenge overlaid with text that reads NASA Pi Day Challenge Answers

Learn about pi and some of the ways the number is used at NASA. Then, dig into the science behind the Pi Day Challenge.

Update: March 15, 2022 – The answers are here! Visit the NASA Pi Day Challenge slideshow to view the illustrated answer keys for each of the problems in the 2022 challenge.

In the News

No matter what Punxsutawney Phil saw on Groundhog Day, a sure sign that spring approaches is Pi Day. Celebrated on March 14, it’s the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

Every year, Pi Day gives us a reason to not only celebrate the mathematical wonder that helps NASA explore the universe, but also to enjoy our favorite sweet and savory pies. Students can join in the fun by using pi to explore Earth and space themselves in our ninth annual NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and find out how students can put their math mettle to the test to solve real problems faced by NASA scientists and engineers as we explore Earth, the Moon, Mars, and beyond!
Infographic of all of the Pi in the Sky 9 graphics and problems

Visit the Pi in the Sky 9 lesson page to explore classroom resources and downloads for the 2022 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

An spacecraft orbiting the Moon shines a laser into a dark crater.

This artist's concept shows the Lunar Flashlight spacecraft, a six-unit CubeSat designed to search for ice on the Moon's surface using special lasers. Image credit: NASA/JPL-Caltech | › Full image details

Dome-covered seismometer sits on the surface of Mars while clouds pass overhead.

Clouds drift over the dome-covered seismometer, known as SEIS, belonging to NASA's InSight lander, on Mars. Credit: NASA/JPL-Caltech. | › Full image and caption

The SWOT spacecraft passes over Florida, sending signals and collecting data.

This animation shows the collection of data over the state of Florida, which is rich with rivers, lakes and wetlands. Credits: NASA/JPL-Caltech | + Expand image

A spacecraft points to a star that has three planets orbiting it.

Illustration of NASA’s Transiting Exoplanet Survey Satellite (TESS). Credits: NASA | + Expand image

How It Works

Dividing any circle’s circumference by its diameter gives you an answer of pi, which is usually rounded to 3.14. Because pi is an irrational number, its decimal representation goes on forever and never repeats. In 2021, a supercomputer calculated pi to more than 62 trillion digits. But you might be surprised to learn that for space exploration, NASA uses far fewer digits of pi.

Here at NASA, we use pi to understand how much signal we can receive from a distant spacecraft, to calculate the rotation speed of a Mars helicopter blade, and to collect asteroid samples. But pi isn’t just used for exploring the cosmos. Since pi can be used to find the area or circumference of round objects and the volume or surface area of shapes like cylinders, cones, and spheres, it is useful in all sorts of ways. Architects use pi when designing bridges or buildings with arches; electricians use pi when calculating the conductance of wire; and you might even want to use pi to figure out how much frozen goodness you are getting in your ice cream cone.

In the United States, March 14 can be written as 3.14, which is why that date was chosen for celebrating all things pi. In 2009, the U.S. House of Representatives passed a resolution officially designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi. And that's precisely what the NASA Pi Day Challenge is all about!

The Science Behind the 2022 NASA Pi Day Challenge

This ninth installment of the NASA Pi Day Challenge includes four brain-busters that get students using pi to measure frost deep within craters on the Moon, estimate the density of Mars’ core, calculate the water output from a dam to assess its potential environmental impact, and find how far a planet-hunting satellite needs to travel to send data back to Earth.

Read on to learn more about the science and engineering behind the problems or click the link below to jump right into the challenge.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Lunar Logic

NASA’s Lunar Flashlight mission is a small satellite that will seek out signs of frost in deep, permanently shadowed craters around the Moon’s south pole. By sending infrared laser pulses to the surface and measuring how much light is reflected back, scientists can determine which areas of the lunar surface contain frost and which are dry. Knowing the locations of water-ice on the Moon could be key for future crewed missions to the Moon, when water will be a precious resource. In Lunar Logic, students use pi to find out how much surface area Lunar Flashlight will measure with a single pulse from its laser.

Core Conundrum

Since 2018, the InSight lander has studied the interior of Mars by measuring vibrations from marsquakes and the “wobble” of the planet as it rotates on its axis. Through careful analysis of the data returned from InSight, scientists were able to measure the size of Mars’ liquid core for the first time and estimate its density. In Core Conundrum, students use pi to do some of the same calculations, determining the volume and density of the Red Planet’s core and comparing it to that of Earth’s core.

Dam Deduction

The Surface Water and Ocean Topography, or SWOT mission will conduct NASA's first global survey of Earth's surface water. SWOT’s state-of-the-art radar will measure the elevation of water in major lakes, rivers, wetlands, and reservoirs while revealing unprecedented detail on the ocean surface. This data will help scientists track how these bodies of water are changing over time and improve weather and climate models. In Dam Deduction, students learn how data from SWOT can be used to assess the environmental impact of dams. Students then use pi to do their own analysis, finding the powered output of a dam based on the water height of its reservoir and inferring potential impacts of this quick-flowing water.

Telescope Tango

The Transiting Exoplanet Survey Satellite, or TESS, is designed to survey the sky in search of planets orbiting bright, nearby stars. TESS does this while circling Earth in a unique, never-before-used orbit that brings the spacecraft close to Earth about once every two weeks to transmit its data. This special orbit keeps TESS stable while giving it an unobstructed view of space. In its first two years, TESS identified more than 2,600 possible exoplanets in our galaxy with thousands more discovered during its extended mission. In Telescope Tango, students will use pi to calculate the distance traveled by TESS each time it sends data back to Earth.

Teach It

Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in NASA Pi Day Challenge. Completing the problem set and reading about other ways NASA uses pi is a great way for students to see the importance of the M in STEM.

Pi Day Resources

Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.

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TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, Moon, Lunar Flashlight, Mars, InSight, Earth, Climate, SWOT, Exoplanets, Universe, TESS, Teachers, Educators, Parents, Students, Lessons, Activities, Resources, K-12

  • Lyle Tavernier

Animated image of Mercury passing in front of the Sun during the 2019 transit of Mercury

In the News

It only happens about 13 times a century and won’t happen again until 2032, so don’t miss the transit of Mercury on Monday, Nov. 11! A transit happens when a planet crosses in front of a star. From our perspective on Earth, we only ever see two planets transit the Sun: Mercury and Venus. This is because these are the only planets between us and the Sun. (Transits of Venus are especially rare. The next one won’t happen until 2117.) During the upcoming transit of Mercury, viewers around Earth (using the proper safety equipment) will be able to see a tiny dark spot moving slowly across the disk of the Sun.

Read on to learn how transits contributed to past scientific discoveries and for a look at how scientists use them today. Plus, find resources for engaging students in this rare celestial event!

Why It's Important

Then and Now

In the early 1600s, Johannes Kepler discovered that both Mercury and Venus would transit the Sun in 1631. It was fortunate timing: The telescope had been invented just 23 years earlier, and the transits of both planets wouldn’t happen in the same year again until 13425. Kepler didn’t survive to see the transits, but French astronomer Pierre Gassendi became the first person to see the transit of Mercury. Poor weather kept other astronomers in Europe from seeing it. (Gassendi attempted to view the transit of Venus the following month, but inaccurate astronomical data led him to mistakenly believe it would be visible from his location.) It was soon understood that transits could be used as an opportunity to measure apparent diameter – how large a planet appears from Earth – with great accuracy.

After observing the transit of Mercury in 1677, Edmond Halley predicted that transits could be used to accurately measure the distance between the Sun and Earth, which wasn’t known at the time. This could be done by having observers at distant points on Earth look at the variation in a planet’s apparent position against the disk of the Sun – a phenomenon known as parallax shift. This phenomenon is what makes nearby objects appear to shift more than distant objects when you look out the window of a car, for example.

Today, radar is used to measure the distance between Earth and the Sun with greater precision than transit observations. But the transits of Mercury and Venus still provide scientists with opportunities for scientific investigation in two important areas: exospheres and exoplanets.

Exosphere Science

Some objects, like the Moon and Mercury, were originally thought to have no atmosphere. But scientists have discovered that these bodies are actually surrounded by an ultrathin atmosphere of gases called an exosphere. Scientists want to better understand the composition and density of the gases in Mercury’s exosphere, and transits make that possible.

“When Mercury is in front of the Sun, we can study the exosphere close to the planet,” said NASA scientist Rosemary Killen. “Sodium in the exosphere absorbs and re-emits a yellow-orange color from sunlight, and by measuring that absorption, we can learn about the density of gas there.”

Exoplanet Discoveries

When Mercury transits the Sun, it causes a slight dip in the Sun’s brightness as it blocks a tiny portion of the Sun’s light. Scientists discovered they could use that phenomenon to search for planets orbiting distant stars. These planets, called exoplanets, are otherwise obscured from view by the light of their star. When measuring the brightness of far-off stars, a slight recurring dip in the light curve (a graph of light intensity) could indicate an exoplanet orbiting and transiting its star. NASA’s Kepler space telescope found more than 2,700 exoplanets by looking for this telltale drop in brightness. NASA’s TESS mission is surveying 200,000 of the brightest stars near our solar system and is expected to potentially discover more than 10,000 transiting exoplanets.

Animated cartoon image of a planet crossing in front of a star and an inset that shows a graph dipping as the planet does so

This animation shows one method scientists use to hunt for planets outside our solar system. When exoplanets transit their parent star, we can detect the dip in the star’s brightness using space telescopes. Credit: NASA/JPL-Caltech | + Expand image

Additionally, scientists have been exploring the atmospheres of exoplanets. Similarly to how we study Mercury’s exosphere, scientists can observe the spectra – a measure of light intensity and wavelength – that passes through an exoplanet’s atmosphere. As a result, they’re beginning to understand the evolution and composition of exoplanet atmospheres, as well as the influence of stellar wind and magnetic fields.

Collage of exoplanet posters from NASA

Using the transit method and other techniques, scientists are learning more and more about planets beyond our solar system. These discoveries have even inspired a series of posters created by artists at NASA, who imagine what future explorers might encounter on these faraway worlds. Credit: NASA | › Download posters

Watch It

During the transit of Mercury, the planet will appear as a tiny dot on the Sun’s surface. To see it, you’ll need a telescope or binoculars outfitted with a special solar filter.

WARNING! Looking at the Sun directly or through a telescope without proper protection can lead to serious and permanent vision damage. Do not look directly at the Sun without a certified solar filter.

The transit of Mercury will be partly or fully visible across much of the globe. However, it won’t be visible from Australia or most of Asia and Alaska.

Graphic showing Mercury's path across the Sun on Nov. 11, 2019 and the times that it will be at each location

The transit of Mercury on Nov. 11, 2019, begins at 4:35 a.m. PST (7:35 a.m. EST), but it won’t be visible to West Coast viewers until after sunrise. Luckily, viewers will have several more hours to take in the stellar show, which lasts until 10:04 a.m. PST (1:04 p.m. EST). Credit: NASA/JPL-Caltech | + Expand image

Mercury’s trek across the Sun begins at 4:35 a.m. PST (7:35 a.m. EST), meaning viewers on the East Coast of the U.S. can experience the entire event, as the Sun will have already risen before the transit begins. By the time the Sun rises on the West Coast, Mercury will have been transiting the Sun for nearly two hours. Fortunately, the planet will take almost 5.5 hours to completely cross the face of the Sun, so there will be plenty of time for West Coast viewers to witness this event. See the transit map below to learn when and where the transit will be visible.

Graphic showing a flat map of the world with areas where the transit of Mercury on Nov. 11, 2019 will be partially to fully visible indicated along with transit start and end times

This map shows where and when the transit will be visible on November 11. Image credit: NASA/JPL-Caltech | + Expand image

Don’t have access to a telescope or binoculars with a solar filter? Visit the Night Sky Network website to find events near you where amateur astronomers will have viewing opportunities available.

During the transit, NASA will share near-real-time images of the Sun directly from the Solar Dynamics Observatory. Beginning at 4:41 a.m. PST (7:41 a.m. EST) you can see images of Mercury passing in front of the Sun at NASA’s 2019 Mercury Transit page, with updates through the end of the transit at 10:04 a.m. PST (1:04 p.m. EST).

If you’re in the U.S., don’t miss the show, as this is the last time a transit will be visible from the continental United States until 2049!

Watch this month's installment of "What's Up" to learn more about how to watch the Nov. 11 transit of Mercury. Credit: NASA/JPL-Caltech | Watch on YouTube

Teach It

Use these lessons and activities to engage students in the transit of Mercury and the hunt for planets beyond our solar system:

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Transit Resources:

Exoplanet Resources:

Check out these related resources for kids from NASA’s Space Place:

TAGS: K-12 Education, Teachers, Students, Educators, Mercury, Transit, Transit of Mercury, What's Up, Astronomy, Resources for Educators, Exoplanets, Kepler, TESS

  • Lyle Tavernier

Pi in the Sky 5 promo graphic

Update: March 15, 2018 – The answers to the 2018 NASA Pi Day Challenge are here! View the illustrated answer key

In the News

Pi in the Sky 5

The 2018 NASA Pi Day Challenge

Can you solve these stellar mysteries with pi? Click to get started.

Pi Day, the annual celebration of one of mathematics’ most popular numbers, is back! Representing the ratio of a circle’s circumference to its diameter, pi has many practical applications, including the development and operation of space missions at NASA’s Jet Propulsion Laboratory.

The March 14 holiday is celebrated around the world by math enthusiasts and casual fans alike – from memorizing digits of pi (the current Pi World Ranking record is 70,030 digits) to baking and eating pies.

JPL is inviting people to participate in its 2018 NASA Pi Day Challenge – four illustrated math puzzlers involving pi and real problems scientists and engineers solve to explore space, also available as a free poster! Answers will be released on March 15. 

Why March 14?

Pi is what’s known as an irrational number, meaning its decimal representation never ends and it never repeats. It has been calculated to more than one trillion digits, but NASA scientists and engineers actually use far fewer digits in their calculations (see “How Many Decimals of Pi Do We Really Need?”). The approximation 3.14 is often precise enough, hence the celebration occurring on March 14, or 3/14 (when written in U.S. month/day format). The first known celebration occurred in 1988, and in 2009, the U.S. House of Representatives passed a resolution designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi.

NASA’s Pi Day Challenge

Pi in the Sky 5

Lessons: Pi in the Sky

Explore the entire NASA Pi Day Challenge lesson collection, including free posters and handouts!

To show students how pi is used at NASA and give them a chance to do the very same math, the JPL Education Office has once again put together a Pi Day challenge featuring real-world math problems used for space exploration. This year’s challenge includes exploring the interior of Mars, finding missing helium in the clouds of Jupiter, searching for Earth-size exoplanets and uncovering the mysteries of an asteroid from outside our solar system.

Here’s some of the science behind this year’s challenge:

Scheduled to launch May 5, 2018, the InSight Mars lander will be equipped with several scientific instruments, including a heat flow probe and a seismometer. Together, these instruments will help scientists understand the interior structure of the Red Planet. It’s the first time we’ll get an in-depth look at what’s happening inside Mars. On Earth, seismometers are used to measure the strength and location of earthquakes. Similarly, the seismometer on Insight will allow us to measure marsquakes! The way seismic waves travel through the interior of Mars can tell us a lot about what lies beneath the surface. This year’s Quake Quandary problem challenges students to determine the distance from InSight to a hypothetical marsquake using pi!

Also launching in spring is NASA’s Transiting Exoplanet Survey Satellite, or TESS, mission. TESS is designed to build upon the discoveries made by NASA’s Kepler Space Telescope by searching for exoplanets – planets that orbit stars other than our Sun. Like Kepler, TESS will monitor hundreds of thousands of stars across the sky, looking for the temporary dips in brightness that occur when an exoplanet passes in front of its star from the perspective of TESS. The amount that the star dims helps scientists determine the radius of the exoplanet. Like those exoplanet-hunting scientists, students will have to use pi along with data from Kepler to find the size of an exoplanet in the Solar Sleuth challenge.

Jupiter is our solar system’s largest planet. Shrouded in clouds, the planet’s interior holds clues to the formation of our solar system. In 1995, NASA’s Galileo spacecraft dropped a probe into Jupiter’s atmosphere. The probe detected unusually low levels of helium in the upper atmosphere. It has been hypothesized that the helium was depleted out of the upper atmosphere and transported deeper inside the planet. The extreme pressure inside Jupiter condenses helium into droplets that form inside a liquid metallic hydrogen layer below. Because the helium is denser than the surrounding hydrogen, the helium droplets fall like rain through the liquid metallic hydrogen. In 2016, the Juno spacecraft, which is designed to study Jupiter’s interior, entered orbit around the planet. Juno’s initial gravity measurements have helped scientists better understand the inner layers of Jupiter and how they interact, giving them a clearer window into what goes on inside the planet. In the Helium Heist problem, students can use pi to find out just how much helium has been depleted from Jupiter’s upper atmosphere over the planet’s lifetime.

In October 2017, astronomers spotted a uniquely-shaped object traveling in our solar system. Its path and high velocity led scientists to believe ‘Oumuamua, as it has been dubbed, is actually an object from outside of our solar system – the first ever interstellar visitor to be detected – that made its way to our neighborhood thanks to the Sun’s gravity. In addition to its high speed, ‘Oumuamua is reflecting the Sun’s light with great variation as the asteroid rotates on its axis, causing scientists to conclude it has an elongated shape. In the Asteroid Ace problem, students can use pi to find the rate of rotation for ‘Oumuamua and compare it with Earth’s rotation rate.

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TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K-12, Lesson, Activity, Slideshow, Mars, Jupiter, Exoplanets, Kepler, Kepler-186f, Juno, InSight, TESS, ‘Oumuamua, asteroid, asteroids, NEO, Nearth Earth Object

  • Lyle Tavernier