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

Update: March 16, 2020 – The answers to the 2020 NASA Pi Day Challenge are here! View the illustrated answer key (also available as a text-only doc).


In the News

Our annual opportunity to indulge in a shared love of space exploration, mathematics and sweet treats has come around again! Pi Day is the March 14 holiday that celebrates the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

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

Visit the Pi in the Sky 7 lesson page to explore classroom resources and downloads for the 2019 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

Overhead view of Mars with a comparison of the smaller landing ellipse made possible by Range Trigger technology

A new Mars landing technique called Range Trigger is reducing the size of the ellipse where spacecraft touch down. Image credit: NASA/JPL-Caltech | › Full image and caption

Composite image of the Kuiper Belt object Arrokoth from NASA's New Horizons spacecraft. Image credit: NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute/Roman Tkachenko | › Full image and caption

Diagram of an airplane flying over a section of ocean with an example of the spectral data that CORAL collects

The CORAL mission records the spectra of light reflected from the ocean to study the composition and health of Earth's coral reefs. Image credit: NASA | + Expand image

Rays of bright orange and red shoot out diagonally from a blue circle surrounding the star Beta Pictoris

The star Beta Pictoris and its surrounding debris disk in near-infrared light. Image credit: ESO/A.-M. Lagrange et al. | › Full image and caption

Besides providing an excuse to eat all varieties of pie, Pi Day gives us a chance to appreciate some of the ways NASA uses pi to explore the solar system and beyond. You can do the math for yourself – or get students doing it – by taking part in the NASA Pi Day Challenge. Find out below how to test your pi skills with real-world problems faced by NASA space explorers, plus get lessons and resources for educators.

How It Works

The ratio of any circle's circumference to its diameter is equal to pi, which is often rounded to 3.14. But pi is what is known as an irrational number, so its decimal representation never ends, and it never repeats. Though it has been calculated to trillions of digits, we use far fewer at NASA.

Pi is useful for all sorts of things, like calculating the circumference and area of circular objects and the volume of cylinders. That's helpful information for everyone from farmers irrigating crops to tire manufacturers to soup-makers filling their cans. At NASA, we use pi to calculate the densities of planets, point space telescopes at distant stars and galaxies, steer rovers on the Red Planet, put spacecraft into orbit and so much more! With so many practical applications, it's no wonder so many people love pi!

In the U.S., 3.14 is also how we refer to March 14, which is why we celebrate the mathematical marvel that is pi on that date each year. 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.

The NASA Pi Day Challenge

This year's NASA Pi Day Challenge poses four puzzlers that require pi to compare the sizes of Mars landing areas, calculate the length of a year for one of the most distant objects in the solar system, measure the depth of the ocean from an airplane, and determine the diameter of a distant debris disk. Learn more about the science and engineering behind the problems below or click the link to jump right into the challenge.

› Take the NASA Pi Day Challenge
› Educators, get the lesson here!

Mars Maneuver

Long before a Mars rover touches down on the Red Planet, scientists and engineers must determine where to land. Rather than choosing a specific landing spot, NASA selects an area known as a landing ellipse. A Mars rover could land anywhere within this ellipse. Choosing where the landing ellipse is located requires compromising between getting as close as possible to interesting science targets and avoiding hazards like steep slopes and large boulders, which could quickly bring a mission to its end. In the Mars Maneuver problem, students use pi to see how new technologies have reduced the size of landing ellipses from one Mars rover mission to the next.

Cold Case

In January 2019, NASA's New Horizons spacecraft sped past Arrokoth, a frigid, primitive object that orbits within the Kuiper Belt, a doughnut-shaped ring of icy bodies beyond the orbit of Neptune. Arrokoth is the most distant Kuiper Belt object to be visited by a spacecraft and only the second object in the region to have been explored up close. To get New Horizons to Arrokoth, mission navigators needed to know the orbital properties of the object, such as its speed, distance from the Sun, and the tilt and shape of its orbit. This information is also important for scientists studying the object. In the Cold Case problem, students can use pi to determine how long it takes the distant object to make one trip around the Sun.

Coral Calculus

Coral reefs provide food and shelter to many ocean species and protect coastal communities against extreme weather events. Ocean warming, invasive species, pollutants, and acidification caused by climate change can harm the tiny living coral organisms responsible for building coral reefs. To better understand the health of Earth's coral reefs, NASA's COral Reef Airborne Laboratory, or CORAL, mission maps them from the air using spectroscopy, studying how light interacts with the reefs. To make accurate maps, CORAL must be able to differentiate among coral, algae and sand on the ocean floor from an airplane. And to do that, it needs to calculate the depth of the ocean at every point it maps by measuring how much sunlight passes through the ocean and is reflected upward from the ocean floor. In Coral Calculus, students use pi to measure the water depth of an area mapped by the CORAL mission and help scientists better understand the status of Earth's coral reefs.

Planet Pinpointer

Our galaxy contains billions of stars, many of which are likely home to exoplanets – planets outside our solar system. So how do scientists decide where to look for these worlds? Using data gathered by NASA's Spitzer Space Telescope, researchers found that they're more likely to find giant exoplanets around young stars surrounded by debris disks, which are made up of material similar to what's found in the asteroid belt and Kuiper Belt in our solar system. Sure enough, after discovering a debris disk around the star Beta Pictoris, researchers later confirmed that it is home to at least two giant exoplanets. Learning more about Beta Pictoris' debris disk could give scientists insight into the formation of these giant worlds. In Planet Pinpointer, put yourself in the role of a NASA scientist to learn more about Beta Pictoris' debris disk, using pi to calculate the distance across it.

Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

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TAGS: K-12 Education, Math, Pi Day, Pi, NASA Pi Day Challenge, Events, Space, Educators, Teachers, Parents, Students, STEM, Lessons, Problem Set, Mars 2020, Perseverance, Curiosity, Mars rovers, Mars landing, MU69, Arrokoth, New Horizons, Earth science, Climate change, CORAL, NASA Expeditions, coral reefs, oceans, Spitzer, exoplanets, Beta Pictoris, stars, universe, space telescope

  • Lyle Tavernier
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In the News

On Jan. 30, 2020, the venerable Spitzer Space Telescope mission will officially come to an end as NASA makes way for a next-generation observatory. For more than 16 years, Spitzer has served as one of NASA’s four Great Observatories, surveying the sky in infrared. During its lifetime, Spitzer detected planets and signs of habitability beyond our solar system, returned stunning images of regions where stars are born, spied light from distant galaxies formed when the universe was young, and discovered a huge, previously-unseen ring around Saturn. Read on to learn more about this amazing mission and gather tools to teach your students that there truly is more than meets the eye in the infrared universe!

How It Worked

Human eyes can see only the portion of the electromagnetic spectrum known as visible light. This is because the human retina can detect only certain wavelengths of light through special photoreceptors called rods and cones. Everything we see with our eyes either emits or reflects visible light. But visible light is just a small portion of the electromagnetic spectrum. To "see" things that emit or reflect other wavelengths of light, we must rely on technology designed to sense those portions of the electromagnetic spectrum. Using this specialized technology allows us to peer into space and observe objects and processes we wouldn’t otherwise be able to see.

Infographic showing the electromagnetic spectrum and applications for various wavelengths.

This diagram shows wavelengths of light on the electromagnetic spectrum and how they're used for various applications. Image credit: NASA | + Expand image

Infrared is one of the wavelengths of light that cannot be seen by human eyes. (It can sometimes be felt by our skin as heat if we are close enough to a strong source.) All objects that have temperature emit many wavelengths of light. The warmer they are, the more light they emit. Most things in the universe are warm enough to emit infrared radiation, and that light can be seen by an infrared-detecting telescope. Because Earth’s atmosphere absorbs most infrared radiation, infrared observations of space are best conducted from outside the planet's atmosphere.

Learn more about the infrared portion of the electromagnetic spectrum and how NASA uses it to explore space. Credit: NASA/JPL-Caltech | Watch on YouTube

So, to get a look at space objects that were otherwise hidden from view, NASA launched the Spitzer Space Telescope in 2003. Cooled by liquid helium and capable of viewing the sky in infrared, Spitzer launched into an Earth-trailing orbit around the Sun, where it became part of the agency's Great Observatory program along with the visible-light and near-infrared-detecting Hubble Space Telescope, Compton Gamma-Ray Observatory and Chandra X-ray Observatory. (Keeping the telescope cold reduces the chances of heat, or infrared light, from the spacecraft interfering with its astronomical observations.)

Over its lifetime, Spitzer has been used to detect light from objects and regions in space where the human eye and optical, or visible-light-sensing, telescopes may see nothing.

Why It's Important

NASA's Spitzer Space Telescope has returned volumes of data, yielding numerous scientific discoveries.

Vast, dense clouds of dust and gas block our view of many regions of the universe. Infrared light can penetrate these clouds, enabling Spitzer to peer into otherwise hidden regions of star formation, newly forming planetary systems and the centers of galaxies.

A whisp of orange and green dust bows out beside a large blue star among a field of smaller blue stars.

The bow shock, or shock wave, in front of the giant star Zeta Ophiuchi shown in this image from Spitzer is visible only in infrared light. The bow shock is created by winds that flow from the star, making ripples in the surrounding dust. Image credit: NASA/JPL-Caltech | › Full image and caption

Infrared astronomy also reveals information about cooler objects in space, such as smaller stars too dim to be detected by their visible light, planets beyond our solar system (called exoplanets) and giant molecular clouds where new stars are born. Additionally, many molecules in space, including organic molecules thought to be key to life's formation, have unique spectral signatures in the infrared. Spitzer has been able to detect those molecules when other instruments have not.

Bursts of reds, oranges, greens, blues and violets spread out in all directions from a bright center source. Reds and oranges dominate the left side of the image.

Both NASA's Spitzer and Hubble space telescopes contributed to this vibrant image of the Orion nebula. Spitzer's infrared view exposed carbon-rich molecules, shown in this image as wisps of red and orange. Image credit: NASA/JPL-Caltech/T. Megeath (University of Toledo) & M. Robberto (STScI) | › Full image and caption

Stars are born from condensing clouds of dust and gas. These newly formed stars are optically visible only once they have blown away the cocoon of dust and gas in which they were born. But Spitzer has been able to see infant stars as they form within their gas and dust clouds, helping us learn more about the life cycles of stars and the formation of solar systems.

A blanket of green- and orange-colored stellar dust surrounds a grouping of purple, blue and red stars.

Newborn stars peek out from beneath their natal blanket of dust in this dynamic image of the Rho Ophiuchi dark cloud from Spitzer. The colors in this image reflect the relative temperatures and evolutionary states of the various stars. The youngest stars are shown as red while more evolved stars are shown as blue. Image credit: NASA/JPL-Caltech/Harvard-Smithsonian CfA | › Full image and caption

Infrared emissions from most galaxies come primarily from stars as well as interstellar gas and dust. With Spitzer, astronomers have been able to see which galaxies are furiously forming stars, locate the regions within them where stars are born and pinpoint the cause of the stellar baby boom. Spitzer has given astronomers valuable insights into the structure of our own Milky Way galaxy by revealing where all the new stars are forming.

A bright band of crimson-colored dust stretches across the center of this image covered in tiny specs of light from hundreds of thousands of stars.

This Spitzer image, which covers a horizontal span of 890 light-years, shows hundreds of thousands of stars crowded into the swirling core of our spiral Milky Way galaxy. In visible-light pictures, this region cannot be seen at all because dust lying between Earth and the galactic center blocks our view. Image credit: NASA/JPL-Caltech | › Full image and caption

Spitzer marked a new age in the study of planets outside our solar system by being the first telescope to directly detect light emitted by these so-called exoplanets. This has made it possible for us to directly study and compare these exoplanets. Using Spitzer, astronomers have been able to measure temperatures, winds and the atmospheric composition of exoplanets – and to better understand their potential habitability. The discoveries have even inspired artists at NASA to envision what it might be like to visit these planets.

Collage of exoplanet posters from NASA

Thanks to Spitzer, 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 imagined what future explorers might encounter on these faraway worlds. Image credit: NASA/JPL-Caltech | › Download posters

Data collected by Spitzer will continue to be analyzed for decades to come and is sure to yield even more scientific findings. It's certainly not the end of NASA's quest to get an infrared window into our stellar surroundings. In the coming years, the agency plans to launch its James Webb Space Telescope, with a mirror more than seven times the diameter of Spitzer's, to see the universe in even more detail. And NASA's Wide Field Infrared Survey Telescope, or WFIRST, will continue infrared observations in space with improved technology. Stay tuned for even more exciting infrared imagery, discoveries and learning!

Teach It

Use these lessons, videos and online interactive features to teach students how we use various wavelengths of light, including infrared, to learn about our universe:


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Also, check out these related resources for kids from NASA’s Space Place:

TAGS: Teachable Moments, science, astronomy, K-12 education, teachers, educators, parents, STEM, lessons, activities, Spitzer, Space Telescope, Missions, Spacecraft, Stars, Galaxies, Universe, Infrared, Wavelengths, Spectrum, Light

  • Ota Lutz
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In the News

This year marks the 40th anniversary of the launch of the world’s farthest and longest-lived spacecraft, NASA’s Voyager 1 and 2. Four decades ago, they embarked on an ambitious mission to explore the giant outer planets, the two outermost of which had never been visited. And since completing their flybys of Jupiter, Saturn, Uranus and Neptune in 1989, they have been journeying toward the farthest reaches of our solar system – where no spacecraft has been before. These two intrepid spacecraft continue to return data to NASA daily, offering a window into the mysterious outer realms of our solar system and beyond.

Illustration of Voyager in space
Teach It!

Try these standards-aligned lessons and activities with students to bring the wonder of the Voyager mission to your classroom or education group.

How They Did It

The Voyager spacecraft were launched during a very short window that took advantage of a unique alignment of the four giant outer planets – one that would not occur again for another 176 years. (Try this lesson in calculating launch windows to get an idea of how it was done.) Launching at this point in time enabled the spacecraft to fly by all four planets in a single journey, returning never-before-seen, close-up images and scientific data from Jupiter, Saturn, Uranus and Neptune that greatly contributed to our current understanding of these planets and the solar system.

Voyager Golden Record
Mission planners knew Voyager would be a historic mission to parts of the solar system never visited by a human-made object. To commemorate the journey, NASA endowed each spacecraft with a time capsule of sorts called the Golden Record intended to communicate the story of our world to extraterrestrials. Both Voyagers carry the 12-inch, gold-plated copper phonograph record containing sounds and images selected to portray the diversity of life and culture on Earth. Find out more about the Golden Record on the Voyager website. Credit: NASA/JPL-Caltech

Why It’s Important

diagram of solar system components

These images of Jupiter, Saturn, Uranus and Neptune (clockwise from top) were taken by Voyager 1 and 2 as the spacecraft journeyed through the solar system. See a gallery of images that Voyager took on the Voyager website. Credit: NASA/JPL-Caltech

In addition to shaping our understanding of the outer planets, the Voyager spacecraft are helping us learn more about the space beyond the planets – the outer region of our solar system. After completing their “grand tour” of the outer planets, the Voyagers continued on an extended mission to the outer solar system. They are now more than 10 billion miles from Earth, exploring the boundary region between our planetary system and what’s called interstellar space.

The beginning of interstellar space is where the constant flow of material from the Sun and its magnetic field stop influencing the surroundings. Most of the Sun’s influence is contained within the heliosphere, a bubble created by the Sun and limited by forces in interstellar space. (Note that the heliosphere doesn’t actually look like a sphere when it travels through space; it’s more of a blunt sphere with a tail.) The outer edge of the heliosphere, before interstellar space, is a boundary region called the heliopause. The heliopause is the outermost boundary of the solar wind, a stream of electrically charged atoms, composed primarily of ionized hydrogen, that stream outward from the Sun. Our planetary system lies inside the bubble of the heliosphere, bordered by the heliopause and surrounded by interstellar space.

solar system components visualized in a kitchen sink
Any flat-bottom sink can provide a visual analogy of these solar system components. In this video, the water traveling radially away from where the faucet stream impacts the sink represents the solar wind. The termination shock is the point at which the speed of the solar wind (water) drops abruptly as it begins to be influenced by interstellar wind. The outer edge of the thick ring of water at the bottom of the sink represents the heliopause. Just like the water in the sink, the solar wind at the heliopause changes direction and flows back into the heliosphere. Credit: NASA/JPL-Caltech.

Though we’ve learned a lot about the heliopause thanks to the Voyager spacecraft, its thickness and variation are still key unanswered questions in space physics. As the Voyagers continue their journey, scientists hope to learn more about the location and properties of the heliopause.

From their unique vantage points – Voyager 1 in the northern hemisphere and Voyager 2 in the southern hemisphere – the spacecraft have already detected differences and asymmetries in the solar wind termination shock, where the wind abruptly slows as it approaches the heliopause. For example, Voyager 2 crossed the termination shock at a distance of about 83.7 AU in the southern hemisphere. (One AU, or astronomical unit, is equal to 150 kilometers (93 million miles), the distance between Earth and the Sun.) That’s about 10 AU closer to the Sun than where Voyager 1 crossed the shock in the north. As shown in this diagram, Voyager 1 traveled through the compressed “nose” of the termination shock and Voyager 2 is expected to travel through the flank of the termination shock.

With four remaining powered instruments on Voyager 1 and five remaining powered instruments on Voyager 2, the two spacecraft continue to collect science data comparing their two distinct locations at the far reaches of the solar system.

diagram of solar system components

In August 2012, Voyager 1 detected a dramatic increase in galactic cosmic rays (as shown in this animated chart). The increase, which has continued to the current peak, was associated with the spacecraft's crossing into interstellar space. Credit: NASA/JPL-Caltech

Since it launched from Earth in 1977, Voyager 1 has been using an instrument to measure high-energy, dangerous particles traveling through space called galactic cosmic rays. While studying the interaction between the bubble of the heliosphere and interstellar space, Voyager 1 revealed that the heliosphere is functioning as a radiation shield, protecting our planetary system from most of these galactic cosmic rays. So in August 2012, when Voyager 1 detected a dramatic increase in the rays, which has continued to the current peak, it was associated with the spacecraft’s crossing into interstellar space.

Meanwhile, Voyager 2 ­­– which is still in the heliosheath, the outermost layer of the heliosphere between the shock and the heliopause ­– is using its solar wind instrument to measure the directional change of solar wind particles there. Within the next few years, Voyager 2 is also expected to cross into interstellar space, providing us with even more detailed data about this mysterious region.

In another 10 years, we expect one or both Voyagers to cruise outward into a more pristine region of interstellar space, returning data to inform our hypotheses about the concentration of galactic particles and the characteristics of interstellar wind.

Even with 40 years of space flight behind them, the Voyagers are expected to continue returning valuable data until about 2025. Communications will be maintained until the spacecraft’s nuclear power sources can no longer supply enough electrical energy to power critical functions. Until then, there’s still much to learn about the boundary of our heliosphere and what lies beyond in the space between the stars.

Teach It

Use these standards-aligned lessons and related activities to get students doing math and science with a real-world (and space!) connection.

  • Hear Here - Students use the mathematical constant pi and information about the current location of Voyager 1 to learn about the faint data-filled signal being returned to Earth.
  • Solar System Bead Activity – Students calculate and construct a scale model of solar system distances using beads and string.
  • Catching a Whisper from Space – Students kinesthetically model the mathematics of how NASA communicates with spacecraft.

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TAGS: Voyager, Farthest, Golden Record, STEM, Teachable Moments, Science, Engineering, Solar System, Interstellar Space, Heliopause, Heliosphere, Heliosheath, Termination Shock, Stars, Heliophysics

  • Ota Lutz
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