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!

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

• 
  Pi in the Sky Lessons

  Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

  Grades 4-12

  Time Varies

• 
  NASA Pi Day Challenge

  The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

  Grades 4-12

  Time Varies

• 
  How Many Decimals of Pi Do We Really Need?

  While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

• 
  18 Ways NASA Uses Pi

  Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

• 
  10 Ways to Celebrate Pi Day With NASA on March 14

  Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.

• 
  Infographic: Planet Pi

  This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

• 

  Downloads

  Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

  • Pi in the Sky 9 Poster (PDF, 11.2 MB)
  • Lunar Flashlight Background: Phone | Desktop
  • Mars InSight Lander Background: Phone | Desktop
  • SWOT Mission Background: Phone | Desktop
  • TESS Mission - Downlink Background: Phone | Desktop
  • TESS Mission - Science Background (not pictured): Phone | Desktop
  • Medley Background (not pictured): Phone | Desktop
• 
  Pi Day: What's Going 'Round

  Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.

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

Recursos en español

• 
  18 Maneras en Que la NASA Usa Pi

  Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.

Related Lessons for Educators

• 
  Planetary Egg Wobble and Newton's First Law

  Students try to determine the interior makeup of an egg (hard-boiled or raw) based on their understanding of center of mass and Newton’s first law of motion.

  Grades 3-8

  Time 30 min to 1 hour

• 
  Whip Up a Moon-Like Crater

  Whip up a moon-like crater with baking ingredients as a demonstration for students.

  Grades 1-6

  Time 30 min to 1 hour

• 
  Exploring Exoplanets with Kepler

  Students use math concepts related to transits to discover real-world data about Mercury, Venus and planets outside our solar system.

  Grades 6-12

  Time 30 min to 1 hour

• 
  Tracking Water Using NASA Satellite Data

  Using real data from NASA’s GRACE satellites, students will track water mass changes in the U.S.

  Grades 4-8

  Time 30 min to 1 hour

• 
  Modeling the Water Budget

  Students use a spreadsheet model to understand droughts and the movement of water in the water cycle.

  Grades 5-8

  Time 30 min to 1 hour

Related Activities for Students

• 
  NASA's Earth Minute: Mission to Earth?

  NASA doesn't just explore outer space! It studies Earth, too, with a fleet of spacecraft and scientists far and wide.

  Type Video

  Subject Science

• 
  Look at the Moon! Journaling Project

  Draw what you see in a Moon Journal and see if you can predict the moon phase that comes next.

  Type Project

  Subject Science

• 
  Mars in a Minute: Are There Quakes on Mars?

  Are there earthquakes on Mars – or rather, "marsquakes"? What could they teach us about the Red Planet?

  Type Video

  Subject Science

Explore More

Infographic

• Mars Quick Facts

Facts and Figures

• Earth's Moon
• Mars
• Earth
• Exoplanet Discoveries Dashboard

Missions and Instruments

• Mars InSight Lander
• TESS Mission
• SWOT Mission
• Lunar Flashlight

Websites

• Exoplanets Exploration
• Mars Exploration
• NASA Climate
• NASA Science: Earth's Moon
• Artemis

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

• 

  ABOUT THE AUTHOR

  Lyle Tavernier, Educational Technology Specialist, NASA-JPL Education Office

  Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.

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.

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.

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.

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.

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!

Teach It

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

• 
  Exploring Exoplanets with Kepler

  Students use math concepts related to transits to discover real-world data about Mercury, Venus and planets outside our solar system.

  Grades 6-12

  Time 30 mins - 1 hr

• 
  Sun Screen: A 'Pi in the Sky' Math Challenge

  When Mercury passes in front of the Sun, how much sunlight is lost on Earth? Students use the mathematical constant pi to find the solution in this illustrated math challenge.

  Grades 6-9

  Time < 30 mins

• 
  Solar Sleuth: A 'Pi in the Sky' Math Challenge

  In this illustrated math problem, students use pi and data from the Kepler space telescope to find the size of a planet outside our solar system.

  Grades 6-9

  Time < 30 mins

• 
  Can You Spot Mercury?

  Play science sleuth and see if you can spot Mercury passing in front of – or transiting – the sun in these images from NASA.

  Type Slideshow

  Subject Science

• 
  Oh, the Places We Go: 18 Ways NASA Uses Pi

  Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

  Type List

  Subject Math

Explore More

Transit Resources:

• NASA near-real-time transit images
• Video: What’s Up – November 2019
• 2019 Mercury Transit Map
• Night Sky Network Events
• NASA Museum Alliance Resources

Exoplanet Resources:

• Exoplanet Exploration Website
• Interactive: 5 Ways to Find a Planet
• Interactive: Eyes on Exoplanets
• Posters: Exoplanet Travel Bureau
• Video: What’s in an Exoplanet Name?
• Video: The Search for Another Earth
• Kepler Mission Website
• Kepler Education Activities

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

• All About Mercury
• Article: What is a transit?
• Article: What is an exoplanet?

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

• 

  ABOUT THE AUTHOR

  Lyle Tavernier, Educational Technology Specialist, NASA-JPL Education Office

  Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.

Explore More

Join the Conversation

• Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
• Pi Day: What’s Going ‘Round – Tell us what you’re up to this Pi Day and share your stories and photos with NASA.

Standards-Aligned Lessons

• Pi in the Sky 5
• Pi in the Sky 4
• Pi in the Sky 3
• Pi in the Sky 2
• Pi in the Sky
• Pi in the Sky Challenge (slideshow for students)
  

Multimedia

• 18 Ways NASA Uses Pi – Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
• Kepler-186f Travel Poster
  
• Video: First Interstellar Asteroid Wows Scientists
• Planet Pi
  

Facts and Figures

• Mars
• Jupiter
• exoplanet Kepler-186f
• asteroid 'Oumuamua

Missions

• InSight
• Juno
• Kepler
• Transiting Exoplanet Survey Satellite (TESS)

Websites

• Mars Exploration
• Solar System Exploration
• Exoplanets

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

• 

  ABOUT THE AUTHOR

  Lyle Tavernier, Educational Technology Specialist, NASA-JPL Education Office

  Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.