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Teachable Moments | March 5, 2021

Take Math to Mars and Beyond With NASA's Pi Day Challenge

By Lyle Tavernier

Illustration of spacecraft on a light blue background that reads "NASA Pi Day Challenge"

Cartoonish illustration of spacecraft on a dark purple background with various pi formulas

Update: March 15, 2021 – The answers are here! Visit the NASA Pi Day Challenge slideshow to view the illustrated answer keys (also available as a text-only doc) with each problem.

Learn about pi and the history of Pi Day before exploring some of the ways the number is used at NASA. Then, try the math for yourself in our Pi Day Challenge.

Jump To
Infographic of all of the Pi in the Sky 7 graphics and problems

Visit the Pi in the Sky 8 lesson page to explore classroom resources and downloads for the 2021 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

In this black and white animated image, a circular device stretched out from a robotic arm descends quickly toward a rocky surface, touches it, and then ascends as debris flies all around.

Captured on Oct. 20, 2020, during the OSIRIS-REx mission’s Touch-And-Go (TAG) sample collection event, this series of images shows the SamCam imager’s field of view as the NASA spacecraft approached and touched asteroid Bennu’s surface. Image credit: NASA/Goddard/University of Arizona | › Full image and caption

The Ingenuity Mars helicopter has a small box-like body topped by two sets of oblong blades. Four stick-like legs extend from the body of the helicopter.

In this illustration, NASA's Ingenuity Mars Helicopter stands on the Red Planet's surface as NASA's Perseverance rover (partially visible on the left) rolls away. Image credit: NASA/JPL-Caltech | › Full image and caption

A giant dish with a honeycomb-patterned device at its center is shown in a desert landscape.

This artist's concept shows what Deep Space Station-23, a new antenna dish capable of supporting both radio wave and laser communications, will look like when completed at the Deep Space Network's Goldstone, California, complex. Image credit: NASA/JPL-Caltech | + Expand image

A swirling fabric of glowing neon green, orange, and pink extends above Earth's limb. A partial silhouette of the ISS frames the right corner of the image.

Expedition 52 Flight Engineer Jack Fischer of NASA shared photos and time-lapse video of a glowing green aurora seen from his vantage point 250 miles up, aboard the International Space Station. This aurora photo was taken on June 26, 2017. Image credit: NASA | › Full image and caption

In the News

As March 14 approaches, it’s time to get ready to celebrate Pi Day! 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.

Pi Day comes around only once a year, giving us a reason to chow down on our favorite sweet and savory pies while we appreciate the mathematical marvel that helps NASA explore Earth, the solar system, and beyond. There’s no better way to observe this day than by getting students exploring space right along with NASA by doing the math in our Pi Day Challenge. Keep reading to find out how students – and you – can put their math mettle to the test and solve real problems faced by NASA scientists and engineers as they explore the cosmos!

How It Works

Dividing any circle’s circumference by its diameter gives us pi, which is often rounded to 3.14. However, pi is an irrational number, meaning its decimal representation goes on forever and never repeats. Pi has been calculated to 50 trillion digits, but NASA uses far fewer for space exploration.

Some people may think that a circle has no points. In fact, a circle does have points, and knowing what pi is and how to use it is far from pointless. Pi is used for calculating the area and circumference of circular objects and the volume of shapes like spheres and cylinders. So it's useful for everyone from farmers storing crops in silos to manufacturers of water storage tanks to people who want to find the best value when ordering a pizza. At NASA, we use pi to find the best place to touch down on Mars, study the health of Earth's coral reefs, measure the size of a ring of planetary debris light years away, and lots more.

In the United States, one format to write March 14 is 3.14, which is why we celebrate on that date. 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 you're in luck, because that's precisely what the NASA Pi Day Challenge is all about.

The Science Behind the 2021 NASA Pi Day Challenge

This year, the NASA Pi Day Challenge offers up four brain-ticklers that will require students to use pi to collect samples from an asteroid, fly a helicopter on Mars for the first time, find efficient ways to talk with distant spacecraft, and study the forces behind Earth's beautiful auroras. Learn more about the science and engineering behind the problems below or click the link below to jump right into the challenge. Be sure to check back on March 15 for the answers to this year’s challenge.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Sample Science

NASA’s OSIRIS-REx mission has flown to an asteroid and collected a sample of surface material to bring back to Earth. (It will arrive back at Earth in 2023.) The mission is designed to help scientists understand how planets form and add to what we know about near-Earth asteroids, like the one visited by OSIRIS-REx, asteroid Bennu. Launched in 2016, OSIRIS-REx began orbiting Bennu in 2018 and successfully performed its maneuver to retrieve a sample on October 20, 2020. In the Sample Science problem, students use pi to determine how much of the spacecraft's sample-collection device needs to make contact with the surface of Bennu to meet mission requirements for success.

Whirling Wonder

Joining the Perseverance rover on Mars is the first helicopter designed to fly on another planet. Named Ingenuity, the helicopter is a technology demonstration, meaning it's a test to see if a similar device could be used for a future Mars mission. To achieve the first powered flight on another planet, Ingenuity must spin its blades at a rapid rate to generate lift in Mars’ thin atmosphere. In Twirly Whirly, students use pi to compare the spin rate of Ingenuity’s blades to those of a typical helicopter on Earth.

Signal Solution

NASA uses radio signals to communicate with spacecraft across the solar system and in interstellar space. As more and more data flows between Earth and these distant spacecraft, NASA needs new technologies to improve how quickly data can be received. One such technology in development is Deep Space Optical Communications, which will use near-infrared light instead of radio waves to transmit data. Near-infrared light, with its higher frequency than radio waves, allows for more data to be transmitted per second. In Signal Solution, students can compare the efficiency of optical communication with radio communication, using pi to crunch the numbers.

Force Field

Earth’s magnetic field extends from within the planet to space, and it serves as a protective shield, blocking charged particles from the Sun. Known as the solar wind, these charged particles of helium and hydrogen race from the Sun at hundreds of miles per second. When they reach Earth, they would bombard our planet and orbiting satellites were it not for the magnetic field. Instead, they are deflected, though some particles become trapped by the field and are directed toward the poles, where they interact with the atmosphere, creating auroras. Knowing how Earth’s magnetic field shifts and how particles interact with the field can help keep satellites in safe orbits. In Force Field, students use pi to calculate how much force a hydrogen atom would experience at different points along Earth’s magnetic field.

Teach It

Pi Day is a fun and engaging way to get students thinking like NASA scientists and engineers. By solving the NASA Pi Day Challenge problems below, reading about other ways NASA uses pi, and doing the related activities, students can see first hand how math is an important part of STEM.

Pi Day Resources

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

Related Lessons for Educators

Related Activities for Students

TAGS: Pi, Pi Day, NASA Pi Day Challenge, Math, Mars, Perseverance, Ingenuity, Mars Helicopter, OSIRIS-REx, Bennu, Asteroid, Auroras, Earth, Magnetic Field, DSOC, Light Waves, DSN, Deep Space Network, Space Communications

  • Lyle Tavernier
    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.

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Earth to Intern | July 26, 2011

Incoming Critical Event: A Trip Inside NASA's Deep Space Network

By Andrew Crawford

Andrew Crawford looks out over the Goldstone Deep Space Communications Complex sign

Beep-beep ... incoming transmission:

Transmission Source: NASA's Dawn spacecraft on its final approach to the giant asteroid Vesta, situated between Mars and Jupiter.
Date of orbital insertion: Friday, July 15, 2011.
Mission status: Orbital insertion confirmed.

On July 15, history was made when NASA's Dawn spacecraft became the first probe to enter into a prolonged orbit around a celestial body in the asteroid belt. With telemetry and deep space communication provided by NASA's Deep Space Network, Dawn closed in on Vesta, a 330-mile wide asteroid, after four years and 1.7 billion miles of travel. This mission has huge significance for humankind, but also a particular significance to my job and internship with the Deep Space Network's Antenna Mechanical and Structural Analysis group because it is responsible for the vital design and engineering components that make communication with the Dawn spacecraft possible.

Recently, I had the chance to visit the Goldstone, Calif., Deep Space Network Tracking facility (check out my photo album on Facebook!), one of the three sites around the world that houses the network's massive antennas. And just when I thought my mind could not absorb and process any more surreal advanced technological wizardry and human determination, NASA, JPL and the Deep Space Network again exposed me to new horizons.

To provide you with a brief 101 of the Deep Space Network, or DSN: It is the largest and most sensitive scientific international telecommunications system in the world, charged with interplanetary spacecraft missions and radio and radar astronomy observations for the exploration of the solar system and the universe.  How's that for a job title!  In other words, it is responsible for communicating with and guiding spacecraft, probes and NASA missions sent into space, (including the rovers on Mars, whose driving team will be featured in a special guest interview for my next post). The DSN monitors asteroids and celestial objects and their proximity to Earth, searches for signals and anomalies from outer space, performs interferometry observations, measures variations in radio waves for science experiments and provides the vital two-way communication link that guides, controls, and brings back images and science data from planetary explorers.

There are three large deep-space communications facilities strategically placed approximately 120 degrees apart around the world: at Goldstone, in California's Mojave Desert; near Madrid, Spain; and near Canberra, Australia. This strategic placement permits constant observation of spacecraft as the Earth rotates and has been in constant operation monitoring the night skies with the first antenna being constructed in the '60s.

The roots for what would eventually become the DSN began in 1958 with the establishment of an antenna and tracking system to receive telemetry and plot the orbit of NASA's Explorer 1, the first successful U.S. satellite. Shortly after, NASA established the concept of the DSN as a separately managed and operated communications facility that would accommodate all deep space missions, thereby avoiding the need for each flight project to acquire and operate its own specialized space communications network.

The component of the DSN that I'm working with, Antenna Mechanical and Structural Analysis, is a phenomenal team that provides ground support and engineering, and builds, designs, and fabricates the antennas and components that make up these massive spacecraft-tracking facilities. In particular, my task this summer is to design, model, and fabricate the future addition of a platform to hold the cryogenic equipment and processing hardware on a brand new, 34-meter beam-waveguide antenna being built in Australia! 

Even cooler - literally -- is the fact that the incoming signals from the Mars rovers and interplanetary spacecraft are funneled down these giant antennas through a network of mirrors, then cooled to cryogenic states where molecules can actually be separated and extracted from the "noise" of other space signals, processed in a maze of computers and analyzed for whomever or whatever that signal is for or from.  I must admit that gathering the seismic, vibration dampening tolerances and heat exchange data for the build requirements was a little nerve-racking, yet also so exciting!  Basically, I was charged with gathering data such as Australia seismic codes, dampening and vibration tolerances for the feed cone, material strength and human "live-load" factors of safety, all of which are used in international engineering projects. Luckily, my group members are an amazing and highly encouraging team who help me out tremendously and guide me with precision and experienced accuracy.

To help gain a better perspective on and appreciation for the magnitude and caliber of the Deep Space Network's responsibilities, we took a trip to one of the three DSN tracking facilities: Goldstone, Calif. And boy did it give me goose-bumps -- in a good way!  After several military checkpoints, security screenings and identity checks, we soon arrived at what can only be described as something straight out of "Star Wars" or some other sci-fi movie, a site fittingly called "Mars," with antennas that seem as big as my hometown pointed at the sky. My jaw dropped, my mentor Jason laughed, and we stepped out of the car to look straight up at what looked like part of the Death Star aimed into outer space. 


A view of the 70 meter DSN antenna and Andrew Crawford below the antenna
If you can spot me just below NASA's Deep Space Network antenna (left), you'll get an idea of just how big these things really are. One highlight of my visit was a trip below the antenna (right) to view the inner-workings of how the DSN tracks and communicates with spacecraft throughout the solar system. Image credit: NASA/JPL-Caltech

This particular antenna at the Goldstone site is among the biggest and most sensitive of all of the DSN antennas, spanning 70 meters (230 feet) across and capable of tracking a spacecraft traveling more than 10 billion miles from Earth. The precision across the antenna surface is maintained within one centimeter (0.4 inch) of the signal wavelength, an amazing feat that reminds me what an incredible opportunity it is to be working with this team.

The day consisted of exploring and analyzing all the systems and subsystems that comprise the massive array of tracking antennas.  All the while, I couldn't help but think how cool it was that as Earth rotated, these can be programed to switch control to an antenna on the other side of the world in order to maintain constant contact with all the spacecraft and signals out there.

One highlight was walking down one of the antenna tunnels that led underground to the inside of the massive concrete pedestal that houses the huge 34-meter antenna above as well as the space-age cryogenic processing equipment and platforms that hold them. The signals are essentially funneled down the antenna structure and dish by a matrix of precisely aligned mirrors. They are then captured and funneled into a network called "wave guides." Radio waves coming from deep space and other sources, like spacecraft, are guided along this tubing, which gets smaller and smaller passing though filters that eventually lead to a certain bandwidth ready for a trip to cryogenic-ville. All of this takes place in preparation for a result that to me seems like black magic but is definitely the coolest thing I've heard about: molecular separation for extracting the desired signals from the rest of the "space noise."

As I contemplated the complexity and wonderment of how many people and years it must have taken to design and build all of this, an alarm and voice came on over the loudspeaker announcing that the antenna would be moving and tracking in two minutes, which was our cue to exit the premises. And it could only mean one thing: The antenna was adjusting to track some distant spacecraft or asteroid in the stars above, and once again, I couldn't help but smile and pinch myself at how amazing the universe and humankind can be.

Stay tuned for my next post on how the Deep Space Network and the Antenna Mechanical group contribute to navigating spacecraft and rovers 15 million miles away, when I interview the Mars rover driving team!


TAGS: Deep Space Network, Engineering, Space Communications

  • Andrew Crawford
    ABOUT THE AUTHOR

    Andrew Crawford, Student, Montana State University

    Andrew's career has spanned a vast universe from classical violinist to professional snowboarder to mechanical/aerospace engineering student. He spent the summers of 2011 and 2012 interning at NASA's Jet Propulsion Laboratory with the Deep Space Network's Antenna Mechanical Group.

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