Learn how pi is used by NASA and how many of its infinite digits have been calculated, then explore the science and engineering behind the 2024 Pi Day Challenge.

Update: March 15, 2024 – The answers to the 2024 NASA Pi Day Challenge are here! Take a peek at the illustrated answer key now available under each problem on the NASA Pi Day Challenge page.

This year marks the 11th installment of the NASA Pi Day Challenge. Celebrated on March 14, Pi Day is 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 on March 14, Pi Day gives us a reason to enjoy our favorite sweet and savory pies and celebrate the mathematical wonder that helps NASA explore the universe. Students can join in the fun once again by using pi to explore Earth and space themselves with the NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and get students solving real problems faced by NASA scientists and engineers exploring Earth, the Moon, asteroids, and beyond!

Visit the Pi in the Sky 11 lesson page to explore classroom resources and downloads for the 2024 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

### What is Pi

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 2022, mathematician Simon Plouffe discovered the formula to calculate any single digit of pi. In the same year, teams around the world used cloud computing technology to calculate pi to 100 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 map the Moon, measure Earth’s changing surface, receive laser-coded messages from deep space, and calculate asteroid orbits. 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. Transportation teams use pi when determining the size of new subway tunnels. Electricians can use pi when calculating the current or voltage passing through circuits. And you might even use pi to figure out how much fencing is needed around a circular school garden bed.

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 2024 NASA Pi Day Challenge

This 11th installment of the NASA Pi Day Challenge includes four illustrated math problems designed to get students thinking like scientists and engineers to calculate how to get a laser message to Earth, the change in an asteroid’s orbit, the amount of data that can be collected by an Earth satellite, and how a team of mini rovers will map portions of the Moon’s surface.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

In December 2023, NASA tested a new way to communicate with distant spacecraft using technology called Deep Space Optical Communications, or DSOC. From 19,000,000 miles (30,199,000 km) away, the Psyche spacecraft beamed a high-definition video encoded in a near-infrared laser to Earth. The video, showing a cat named Taters chasing a laser, traveled at the speed of light, where it was received at Caltech’s Palomar Observatory. Because of the great distance the laser had to travel, the team needed to aim the transmission at where Earth would be when the signal arrived. In Receiver Riddle, use pi to determine where along Earth's orbit the team needed to aim the laser so that it could be received at the Observatory at the correct moment.

This animation shows how DSOC's laser signals are sent between the Psyche spacecraft and ground stations on Earth - first as a pointing reference to ensure accurate aiming of the narrow laser signal and then as a data transmission to the receiving station. Credit: NASA/JPL-Caltech/ASU| Watch on YouTube

#### Daring Deflection

In 2022, NASA crashed a spacecraft into the asteroid Dimorphos in an attempt to alter its orbit. The mission, known as the Double Asteroid Redirection Test, or DART, took place at an asteroid that posed no threat to our planet. Rather, it was an ideal target for NASA to test an important element of its planetary defense plan. DART was designed as a kinetic impactor, meaning it transferred its momentum and kinetic energy to Dimorphos upon impact, altering the asteroid's orbit. In Daring Deflection, use pi to determine the shape of Dimorphos’ orbit after DART crashed into it.

This image shows the final minutes of images leading up to the DART spacecraft's intentional collision with asteroid Dimorphos. Credit: NASA/Johns Hopkins APL | › Enlarge image

#### Orbit Observation

The NISAR mission is an Earth orbiting satellite designed to study our planet's changing ecosystems. It will collect data about Earth's land- and ice-covered surfaces approximately every 6 days, allowing scientists to study changes at the centimeter scale – an unprecedented level of detail. To achieve this feat, NISAR will collect massive amounts of data. In Orbit Observation, students use pi to calculate how much data the NISAR spacecraft captures during each orbit of Earth.

The NISAR satellite, shown in this artist’s concept, will use advanced radar imaging to provide an unprecedented view of changes to Earth’s land- and ice-covered surfaces. Credit: NASA/JPL-Caltech. | › Full image and caption

#### Moon Mappers

The CADRE project aims to land a team of mini rovers on the Moon in 2025 as a test of new exploration technology. Three suitcase-size rovers, each working mostly autonomously, will communicate with each other and a base station on their lunar lander to simultaneously measure data from different locations. If successful, the project could open the door for future multi-robot exploration missions. In Moon Mappers, students explore the Moon with pi by determining how far a CADRE rover drives on the Moon’s surface.

Engineers test the system that will lower three small rovers onto the lunar surface as part of the CADRE project. Credit: NASA/JPL-Caltech | › Full image and caption

### Bring the Challenge Into the Classroom

Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in the NASA Pi Day Challenge. In addition to solving the 2024 challenge, you can also dig into the 40 puzzlers from previous challenges available in our Pi Day collection. 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.

#### Interactives

TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, moon, earth, asteroid, psyche, DART, CADRE, NISAR DSOC

Find out more about the historic first test, which could be used to defend our planet if a hazardous asteroid were discovered. Plus, explore lessons to bring the science and engineering of the mission into the classroom.

Update: Oct. 20, 2022 – The DART spacecraft successfully impacted the asteroid Dimorphos on September 26, reducing the period of the asteroid's orbit by 32 minutes. Scientists considered a change of 73 seconds to be the minimum amount for success. This article has been updated to reflect the latest data and images from the impact.

In a successful attempt to alter the orbit of an asteroid for the first time in history, NASA crashed a spacecraft into the asteroid Dimorphos on Sept. 26, 2022. The mission, known as the Double Asteroid Redirection Test, or DART, took place at an asteroid that posed no threat to our planet. Rather, it was an ideal target for NASA to test an important element of its planetary defense plan.

Read further to learn about DART, how it worked, and how the science and engineering behind the mission can be used to teach a variety of STEM topics.

### Why It's Important

The vast majority of asteroids and comets are not dangerous, and never will be. Asteroids and comets are considered potentially hazardous objects, or PHOs, if they are 100-165 feet (30-50 meters) in diameter or larger and their orbit around the Sun comes within five million miles (eight million kilometers) of Earth’s orbit. NASA's planetary defense strategy involves detecting and tracking these objects using telescopes on the ground and in space. In fact, NASA’s Center for Near Earth Object Studies, or CNEOS, monitors all known near-Earth objects to assess any impact risk they may pose. Any relatively close approach is reported on the Asteroid Watch dashboard.

NASA's Planetary Defense Coordination Office runs a variety of programs and initiatives aimed at detecting and responding to threats from potentially hazardous objects, should one be discovered. The DART mission is one component and the first mission being flown by the team. Image credit: NASA | + Expand image

While there are no known objects currently posing a threat to Earth, scientists continue scanning the skies for unknown asteroids. NASA is actively researching and planning for ways to prevent or reduce the effects of a potential impact, should one be discovered. The DART mission was the first test of such a plan – in this case, whether it was possible to divert an asteroid from its predicted course by slamming into it with a spacecraft.

Eyes on Asteroids is a real-time visualization of every known asteroid or comet that is classified as a near-Earth object, or NEO. Asteroids are represented as blue dots and comets as shown as white dots. Use your mouse to explore the interactive further and learn more about the objects and how we track them. Credit: NASA/JPL-Caltech | Explore the full interactive

With the knowledge gained from the demonstration, similar techniques could be used in the future to deflect an asteroid or comet away from Earth if it were deemed hazardous to the planet.

### How It Worked

With a diameter of about 525 feet (160 meters) – the length of 1.5 football fields – Dimorphos is the smaller of two asteroids in a double-asteroid system. Before DART's impact, Dimorphos orbited the larger asteroid called Didymos (Greek for "twin"), every 11 hours and 55 minutes.

The sizes of the two asteroids in the Didymos system relative to objects on Earth. Image credit: NASA/Johns Hopkins APL | + Expand image

Neither asteroid poses a threat to our planet, which is one reason why this asteroid system was the ideal place to test asteroid redirection techniques. At the time of DART's impact, the asteroid pair was 6.8 million miles (11 million kilometers) away from Earth as they traveled on their orbit around the Sun.

The DART spacecraft was designed to collide head-on with Dimorphos to alter its orbit, shortening the time it takes the small asteroid to travel around Didymos. Compared with Dimorphos, which has a mass of about 11 billion pounds (five billion kilograms), the DART spacecraft was light. It weighed just 1,210 pounds (550 kilograms) at the time of impact. So how did such a light spacecraft affect the orbit of a relatively massive asteroid?

You can use your mouse to explore this interactive view of DART's impact with Dimorphos from NASA's Eyes on the Solar System. Credit: NASA/JPL-Caltech | Explore the full interactive

DART was designed as a kinetic impactor, meaning it transferred its momentum and kinetic energy to Dimorphos upon impact, altering the asteroid's orbit in return. Scientists were able to make predictions about some of these effects thanks to principles described in Newton's laws of motion.

Newton’s first law told us that the asteroid’s orbit would remain unchanged until something acted upon it. Using the formula for linear momentum (p = m * v), we could calculate that the spacecraft, which at the time of impact would be traveling at 3.8 miles (6.1 kilometers) per second, would have about 0.5% of the asteroid’s momentum. The momentum of the spacecraft may seem small in comparison, but calculations suggested it would be enough to make a detectable change in the speed of Dimorphos' orbit. However, mission planners felt that changing Dimorphos’ orbit by at least 73 seconds would be enough to consider the test a success.

But there was more to consider in testing whether the technique could be used in the future for planetary defense. For example, the formula for kinetic energy (KE = 0.5 * m * v2) tells us that a fast moving spacecraft possesses a lot of energy.

When DART hit the surface of the asteroid, its kinetic energy was 10 billion joules! A crater was formed and material known as ejecta was blasted out as a result of the impact. Scientists are still studying the data returned from the mission to determine the amount of material ejected out of the crater, but estimates prior to impact put the number at 10-100 times the mass of the spacecraft itself. The force needed to push this material out was then matched by an equal reaction force pushing on the asteroid in the opposite direction, as described by Newton’s third law.

This animation shows conceptually how DART's impact is predicted to change Dimorphos' orbit from a larger orbit to a slightly smaller one that's several minutes shorter than the original. Credit: NASA/Johns Hopkins APL/Jon Emmerich | Watch on YouTube

How much material was ejected and its recoil momentum is still unknown. A lot depends on the surface composition of the asteroid, which scientists are still investigating. Laboratory tests on Earth suggested that if the surface material was poorly conglomerated, or loosely formed, more material would be blasted out. A surface that was well conglomerated, or densely compacted, would eject less material.

After the DART impact, scientists used a technique called the transit method to see how much the impact changed Dimorphos' orbit. As observed from Earth, the Didymos pair is what’s known as an eclipsing binary, meaning Dimorphos passes in front of and behind Didymos from our view, creating what appears from Earth to be a subtle dip in the combined brightness of the pair. Scientists used ground-based telescopes to measure this change in brightness and calculate how quickly Dimorphos orbits Didymos. By comparing measurements from before and after impact, scientists determined that the orbit of Dimorphos had slowed by 32 minutes to 11 hours and 23 minutes.

The green circle shows the location of the Dimorphos asteroid, which orbits the larger asteroid, Didymos, seen here as the bright line across the middle of the images. The blue circle shows where Dimorphos would have been had its orbit not changed due to NASA’s DART mission purposefully impacting the smaller asteroid on Sept. 26, 2022. The images were obtained from the NASA Jet Propulsion Laboratory’s Goldstone planetary radar in California and the National Science Foundation’s Green Bank Observatory in West Virginia. Image credit: NASA/Johns Hopkins APL/JPL/NASA JPL Goldstone Planetary Radar/National Science Foundation’s Green Bank Observatory | + Expand image | › DART image gallery

One of the biggest challenges of the DART mission was navigating a small spacecraft to a head-on collision with a small asteroid millions of miles away. To solve that problem, the spacecraft was equipped with a single instrument, the DRACO camera, which worked together with an autonomous navigation system called SMART Nav to guide the spacecraft without direct control from engineers on Earth. About four hours before impact, images captured by the camera were sent to the spacecraft's navigation system, allowing it to identify which of the two asteroids was Dimorphos and independently navigate to the target.

A composite of 243 images of Didymos and Dimorphos taken by the DART spacecraft's DRACO camera on July 27, 2022, as the spacecraft was navigating to its target. Image credit: JPL DART Navigation Team | + Expand image | › DART image gallery

DART was not just an experimental asteroid impactor. The mission also used cutting-edge technology never before flown on a planetary spacecraft and tested new technologies designed to improve how we power and communicate with spacecraft.

Learn more about the engineering behind the DART mission, including the innovative Roll Out Solar Array and NEXT-C ion propulsion system, in this video featuring experts from the mission. Credit: APL | Watch on YouTube

One such technology that was first tested on the International Space Station and was later used on the solar-powered DART spacecraft, is the Roll Out Solar Array, or ROSA, power system. As its name suggests, the power system consisted of flexible solar panel material that was rolled up for launch and unrolled in space.

The Roll Out Solar Array, shown in this animated image captured during a test on the International Space Station, is making its first planetary journey on DART. Image credit: NASA | + Expand image

Some of the power generated by the solar array was used for another innovative technology, the spacecraft's NEXT-C ion propulsion system. Rather than using traditional chemical propulsion, DART was propelled by charged particles of xenon pushed from its engine. Ion propulsion has been used on other missions to asteroids and comets including Dawn and Deep Space 1, but DART's ion thrusters had higher performance and efficiency.

In the days following the event, NASA received images of the impact from a cubesat, LICIACube, that was deployed by DART before impact. The cubesat, which was provided by the Italian Space Agency, captured images of the impact and the ejecta cloud.

This image from LICIACube shows plumes of ejecta streaming from Dimorphos after DART's impact. Each rectangle represents a different level of contrast to better see fine structure in the plumes. By studying these streams of material, scientists will be able to learn more about the asteroid and the impact process. | + Expand image | › DART image gallery

Meanwhile, the James Webb Space Telescope, the Hubble Space Telescope, and the Lucy spacecraft observed Didymos to monitor how soon reflected sunlight from the ejecta plume could be seen. Going forward, DART team members will continue observing the asteroid system to measure the change in Dimorphos’ orbit and determine what happened on its surface. And in 2024, the European Space Agency plans to launch the Hera spacecraft to conduct an in-depth post-impact study of the Didymos system.

This animation, a timelapse of images from NASA’s James Webb Space Telescope, covers the time spanning just before DART's impact at 4:14 p.m. PDT (7:14 p.m. EDT) on Septtember 26 through 5 hours post-impact. Plumes of material from a compact core appear as wisps streaming away from where the impact took place. An area of rapid, extreme brightening is also visible in the animation. Image credit: Science: NASA, ESA, CSA, Cristina Thomas (Northern Arizona University), Ian Wong (NASA-GSFC); Joseph DePasquale (STScI) | + Expand image | › DART image gallery

Continue following along with all the science from DART, including the latest images and updates on the mission website. Plus, explore even more resources on this handy page.

### Teach It

The mission is a great opportunity to engage students in the real world applications of STEM topics. Start exploring these lessons and resources to get students engaging in STEM along with the mission.

#### Resources for Kids

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

### Explore More

TAGS: Asteroids and Comets, DART, near-Earth objects, planetary defense, Science, K-12 Education, Teachers, Educators, Parents, Teachable Moments, Asteroid TM

With 180 lessons in our online catalog, you can explore Earth and space with us all year long. We show you how with this handy NASA-JPL school year calendar.

We just added the 180th lesson to our online catalog of standards-aligned STEM lessons, which means JPL Education now has a lesson for every day of the school year. To celebrate and help you make the year ahead stellar, we've put together this monthly calendar of upcoming NASA events along with links to our related lessons, Teachable Moments articles, and student projects you can use to engage students in STEM while they explore Earth and space with us all year long.

### August

#### The Voyagers Turn 45

The twin Voyager spacecraft launched in 1977 on a journey to explore the outer planets and beyond – and they're still going. Now more than 12 billion miles (19 billion kilometers) from Earth in a region known as interstellar space, they're the most distant human-made objects in space.

Get a primer on these fascinating spacecraft from Teachable Moments, then use it as a jumping off point for lessons on the scale, size, and structure of our solar system and how we communicate with distant spacecraft.

Lessons & Resources:

### September

#### Rendezvous with an Asteroid

A distant asteroid system 6.8 million miles (11 million kilometers) from Earth was the site of NASA's first attempt at redirecting an asteroid. On September 26, the Double Asteroid Redirection Test, or DART, mission impacted the asteroid Dimorphos in an attempt to alter its speed and path around a larger asteroid known as Didymos. Dimorphos and Didymos do not pose a threat to Earth, which makes them a good proving ground for testing whether a similar technique could be used to defend Earth against potential impacts by hazardous asteroids in the future.

Get a primer on the DART mission and find related resources for the classroom in this article from our Teachable Moments series. Plus, explore our collection of standards-aligned lessons and activities all about asteroids to get students learning about different kinds of space rocks, geology, and meteoroid math.

Lessons & Resources:

#### A Closer Look at Europa

Just a few days later, on September 29, the Juno spacecraft that had been orbiting Jupiter since 2016 captured the closest views of Jupiter’s moon Europa in more than 20 years. The ice-covered moon is thought to contain a subsurface liquid-water ocean, making it an exciting new frontier in our search for life beyond Earth. NASA's Europa Clipper mission, which is scheduled to launch in 2024 is designed to study the moon in more detail. But until Europa Clipper arrives at the Jovian system in 2030, these observations from Juno are our best chance to get a closer look at this fascinating moon.

Learn more about Europa and why it is interesting to scientists in this talk from our Teaching Space With NASA series featuring a Europa Clipper mission scientist. Then, explore our Ocean Worlds Lesson Collection for ideas on making classroom connections.

Lessons & Resources:

### October

#### Celebrate Halloween Like a Space Explorer

The month of October is the perfect time to get students exploring our STEM activities with a Halloween twist. Students can learn how to carve a pumpkin like a JPL engineer, take a tour of mysterious locations throughout the solar system, and dig into the geology inside their Halloween candy.

October 31 is also JPL's 86th birthday, which makes October a great time to learn more about JPL history, including the team of female mathematicians known as "human computers" who performed some of the earliest spacecraft-tracking calculations and the Laboratory's role in launching the first U.S. space satellite.

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### November

#### Watch a Total Lunar Eclipse

Look up in the early morning hours of November 8 to watch one of the most stunning spectacles visible from Earth: a total lunar eclipse. This one will be viewable in North and South America, as well as Asia and Australia.

Learn more about lunar eclipses and how to watch them from our Teachable Moments series. Then, get students of all ages outside and observing the Moon with lessons on moon phases and the hows and whys of eclipses. Students can even build a Moon calendar so they always know when and where to look for the next eclipse.

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#### Artemis Takes a Giant Leap

NASA is making plans to send astronauts back to the Moon for the first time since 1972 – this time to establish a sustainable presence and prepare for future human missions to Mars. The first major step is Artemis I, which is testing three key components required to send astronauts beyond the Moon: the Orion spacecraft, the Space Launch System, or SLS, rocket and the ground systems at Kennedy Space Center in Florida. The uncrewed Artemis I mission marks the first test of all three components at once.

Get your K-12 students following along with lessons in rocketry and what it takes to live in space. Plus, register to follow along with the mission with resources and updates from NASA's Office of STEM Engagement.

Lessons & Resources:

### December

#### Satellite Launches on a Mission to Follow the Water

As crucial as water is to human life, did you know that no one has ever completed a global survey of Earth’s surface water? That is about to change with the launch of the SWOT mission. SWOT, which stands for Surface Water Ocean Topography, will use a state-of-the-art radar to measure the elevation of water in major lakes, rivers, wetlands, and reservoirs. It will also provide an unprecedented level of 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.

Engage your students in learning about Earth’s water budget and how we monitor Earth from space with these lessons. And be sure to check out our Teachable Moments article for more about the SWOT mission and the science of our changing climate.

#### Prepare for the Science Fair

Before you know it, it'll be science fair time. Avoid the stress of science fair prep by getting students organized and thinking about their projects before the winter recess. Start by watching our video series How to Do a Science Fair Project. A scientist and an engineer from JPL walk your students through all the steps they will need to create an original science fair project by observing the world around them and asking questions. You can also explore our science fair starter pack of lessons and projects to get students generating ideas and thinking like scientists and engineers.

Lessons & Resources:

### January

#### Explore STEM Careers

January is the time when many of us set goals for the year ahead, so it's the perfect month to get students exploring their career goals and opportunities in STEM. Students can learn more about careers in STEM and hear directly from scientists and engineers working on NASA missions in our Teaching Space video series. Meanwhile, our news page has more on what it takes to be a NASA astronaut and what it's like to be a JPL intern.

For students already in college and pursuing STEM degrees, now is the time to start exploring internship opportunities for the summer. The deadline for JPL summer internships is in March, so it's a good idea to refresh your resume and get your application started now. Learn how to stand out with this article on how to get an internship at JPL – which also includes advice for pre-college students.

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### February

#### Mars Rover Celebrates 2-Year 'Landiversary'

NASA's Perseverance Mars rover celebrates its "landiversary" on February 18, which marks two years since the rover made its nail-biting descent on the Red Planet. The rover continues to explore Jezero Crater using science tools to analyze rocks and soil in search of signs of ancient microbial life. As of this writing, the rover has collected twelve rock core samples that will be sent to Earth by a future mission. Perseverance even witnessed a solar eclipse! Meanwhile, the Ingenuity Mars helicopter, which the rover deployed shortly after landing, has gone on to achieve feats of its own.

The Mission to Mars Student Challenge is a great way to get students of all ages exploring STEM and the Red Planet right along with the Perseverance rover. The challenge includes seven weeks of education content that can be customized for your classroom as well as education plans, expert talks, and resources from NASA.

Lessons & Resources:

### March

#### Take On the Pi Day Challenge

Math teachers, pie-lovers, and pun-aficionados rejoice! March 14 is Pi Day, the annual celebration of the mathematical constant used throughout the STEM world – and especially for space exploration. This year's celebration brings the 10th installment of the NASA Pi Day Challenge, featuring four new illustrated math problems involving pi along with NASA missions and science.

Explore the full collection of pi math lessons, get students learning about how we use pi at NASA, and hear from a JPL engineer on how many decimals of pi we use for space exploration at the links below.

Lessons & Resources:

### April

#### Celebrate Earth Day With NASA

You may not immediately think of Earth science when you think of NASA, but it's a big part of what we do. Earth Day on April 22 is a great time to explore Earth science with NASA, especially as new missions are taking to the skies to study the movements of dust, measure surface water across the planet, and track tiny land movements to better predict natural disasters.

Whether you want to focus on Earth’s surface and geology, climate change, extreme weather, or the water budget, we have an abundance of lessons, student projects and Teachable Moments to guide your way.

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