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

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Pi in the Sky 5

The 2018 NASA Pi Day Challenge

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

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

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

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

Why March 14?

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

NASA’s Pi Day Challenge

Pi in the Sky 5

Lessons: Pi in the Sky

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

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

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

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

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

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

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

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

  • Lyle Tavernier

UPDATE - May 9, 2016: NASA's Solar Dynamics Observatory, or SDO, spacecraft captured stunning images of the May 9, 2016 transit of Mercury. Visit the mission's Transit of Mercury page to see a collection of videos of the transit compiled using SDO images. And have students play "Can You Spot Mercury?" in our educational slideshow. 

In the News

It only happens about 13 times per century and hasn’t happened in nearly a decade, but on Monday, May 9, Mercury will transit the sun. A transit happens when a planet crosses in front of a star. From our perspective on Earth, we only ever see two planets transit the sun: Mercury and Venus. (Transits of Venus are even more rare. The next one won't happen until 2117!) On May 9, as Mercury passes in front of the sun, viewers around Earth (using the proper safety equipment) will be able to see a tiny dark spot moving slowly across the disk of the sun.

CAUTION: Looking directly at the sun can cause permanent vision damage – see below for tips on how to safely view the transit.

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 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 (the transit of Venus wasn’t visible from Europe). It was soon understood that transits could be used as an opportunity to measure the apparent diameter – how large a planet appears from Earth – with great accuracy.

In 1677, Edmond Halley observed the transit of Mercury and realized that the parallax shift of the planet – the variation in Mercury’s apparent position against the disk of the sun as seen by observers at distant points on Earth – could be used to accurately measure the distance between the sun and Earth, which wasn’t known at the time.

Today, radar is used to measure the distance between Earth and the sun with greater precision than can be found using transit observations, but the transit of Mercury still provides 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 in an ultra-thin atmosphere of gases called an exosphere. Scientists want to better understand the composition and density of the gases that make up 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.”

Mercury transits the sun in 2006
This image of Mercury passing in front of the sun was captured on Nov. 8, 2006 by the Solar Optical Telescope, one of three primary instruments on the Hinode spacecraft. Image credit: Hinode JAXA/NASA/PPARC

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, called exoplanets, that are otherwise obscured from view by the light of the 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 mission has found more than 1,000 exoplanets by looking for this telltale drop in brightness.

illustration of how transits are used to find exoplanets
This diagram shows how scientists use the light curves of distant stars to search for planets outside our solar system. A drop in the light curve, as illustrated here, is a good indication that there's a planet orbiting the observed star. Credit: NASA Ames

The Kepler mission measures the brightness of stars. The data will look like an EKG showing the heart beat. Whenever a planet passes in front of its parent star as viewed from the spacecraft, a tiny pulse or beat is produced. From the repeated beats, we can detect and verify the existence of Earth-size planets and learn about the orbit and size of the planet. Video credit: NASA Ames and Dana Berry

Additionally, scientists have begun exploring the exospheres of exoplanets. By observing the spectra of the light that passes through an exosphere – similar to how we study Mercury’s exosphere – scientists are beginning to understand the evolution of exoplanet atmospheres as well as the influence of stellar wind and magnetic fields.

Watch It

Mercury will appear as a tiny dot on the sun’s surface and will require a telescope or binoculars with a special solar filter to see. 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 solar filter.

The transit of Mercury will begin at 4:12 a.m. PDT, meaning by the time the sun rises on the West Coast, Mercury will have been transiting the sun for nearly two hours. Fortunately, it will take seven and a half hours for Mercury to completely cross the sun’s face, so there will be plenty of time for West Coast viewers to witness this event. See the transit map to learn when and where the transit will be visible.

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

NASA also will stream a live program on NASA TV and the agency’s Facebook page from 7:30 to 8:30 a.m. PDT (10:30 to 11:30 a.m. EDT) -- an informal roundtable during which experts representing planetary, heliophysics and astrophysics will discuss the science behind the Mercury transit. Viewers can ask questions via Facebook and Twitter using #AskNASA.

Teach It

Here are two ways to turn the transit of Mercury into a lesson for students.

  • 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.
  • Pi in the Sky 3 - Try the "Sun Screen" problem on this illustrated math problem set that has students calculate the percentage drop in sunlight reaching Earth when Mercury transits.

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Transit Resources:

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TAGS: Transit, Transit of Mercury, Mercury, Venus, Sun, Exoplanets, Teach, Classroom Activities, Lessons,

  • Lyle Tavernier

Illustration of Kepler 452b

In the News

Twenty years after the first discovery of a planet orbiting another sun-like star, scientists have discovered the most Earth-like exoplanet ever: Kepler-452b. Located in the habitable zone of a star very much like our sun, Kepler-452b is only about 60 percent wider than Earth.

What makes it the most Earth-like exoplanet ever discovered?

First a couple definitions: An exoplanet is simply a planet that orbits another star. And the habitable zone? That’s the area around a star in which water has the potential to be liquid -- not so close to the star that all water would evaporate, and not so far that all water would freeze. Think about Goldilocks eating porridge. The habitable zone is not too hot, and not too cold. It’s just right.

Okay, back to Kepler-452b. Out of more than a thousand exoplanets that NASA’s Kepler spacecraft has detected, only 12 have been found in the habitable zone of their stars and are smaller than twice the size of Earth, making Earth-like planets a rarity. Until this discovery, all of them have orbited stars that are smaller and cooler than our sun.

Graphic showing habitable zone planets

Twelve Exoplanet discoveries from Kepler that are less than twice the size of Earth and reside in the habitable zone of their host star. The sizes of the exoplanets are represented by the size of each sphere. These are arranged by size from left to right, and by the type of star they orbit, from the M stars that are significantly cooler and smaller than the sun, to the K stars that are somewhat cooler and smaller than the sun, to the G stars that include the sun. The sizes of the planets are enlarged by 25X compared to the stars. The Earth is shown for reference. Image credit: NASA/JPL-Caltech/R. Hurt

Graphic showing habitable zone planets

The sweep of NASA Kepler mission’s search for small, habitable planets in the last six years. The first planet smaller than Earth, Kepler-20e, was discovered in December 2011 orbiting a Sun-like star slightly cooler and smaller than our sun every six days. But it is scorching hot and unable to maintain an atmosphere or a liquid water ocean. Kepler-22b was announced in the same month, as the first planet in the habitable zone of a sun-like star, but is more than twice the size of Earth and therefore unlikely to have a solid surface. Kepler-186f was discovered in April 2014 and is the first Earth-size planet found in the habitable zone of a small, cool M dwarf about half the size and mass of our sun. Kepler-452b is the first near-Earth-Size planet in the habitable zone of a star very similar to the sun. Image credits: NASA Ames/W. Stenzel

Kepler-452b is the first to be discovered orbiting a star that is about the same size and temperature as our sun. Not only that, but it orbits at nearly the same distance from its star as Earth does from our sun! Conditions on Kepler-452b could be similar to conditions here on Earth and the light you would feel there would be much like the sunlight you feel here on Earth. Scientists believe that Kepler-452b has been in the habitable zone for around six billion years -- longer than Earth has even existed!

Graphic comparing our solar system and Kepler-452b's system

This size and scale of the Kepler-452 system compared alongside the Kepler-186 system and the solar system. Kepler-186 is a miniature solar system that would fit entirely inside the orbit of Mercury. The habitable zone of Kepler-186 is very small compared to that of Kepler-452 or the sun because it is a much smaller, cooler star. The size and extent of the habitable zone of Kepler-452 is nearly the same as that of the sun, but is slightly bigger because Kepler-452 is somewhat older, bigger and brighter. The size of the orbit of Kepler-452b is nearly the same as that of the Earth at 1.05 AU. Kepler-452b orbits its star once every 385 days.Image credit: NASA/JPL-Caltech/R. Hurt

How They Did It

The Kepler spacecraft, named for mathematician and astronomer Johannes Kepler, has been working since 2009 to find distant worlds like Kepler-452b. It does so by looking at more than 100,000 stars near the constellation Cygnus. If one of those stars dims temporarily, it could be that an object passed between the spacecraft and the star. If it dims with a repeatable pattern, there’s a good chance an exoplanet is passing by again and again as it orbits the star. The repeated dimming around one of those stars is what led to the discovery of Kepler-452b.

Kepler measures the brightness of stars. The data will look like an EKG showing the heart beat. Whenever a planet passes in front of its parent star as viewed from the spacecraft, a tiny pulse or beat is produced. From the repeated beats we can detect and verify the existence of Earth-size planets and learn about the orbit and size of the planet.Video credit: NASA Ames and Dana Berry

Teach It

This exciting discovery provides opportunities for students to practice math skills in upper elementary and middle school, and gives high school students a practical application of Kepler’s third law of planetary motion. Take a look below to see where these might fit into your curriculum.

Upper Elementary and Middle School

After learning about Earth’s cousin, students might wonder about a trip to this world. Scientists have calculated the distance between Earth and Kepler-452b at 1,400 light years. A light year is a measure of distance that shows how far light travels in one year. It’s equal to about 10 trillion kilometers (six trillion miles) or, to be more precise, 9,461,000,000,000 kilometers (5,878,000,000,000 miles). Ask students to calculate the distance between Earth and Kepler-452b at various levels of precision, depending on what they are prepared for or learning. For an added challenge, have them determine how long it would take a fast moving spacecraft like Voyager 1 traveling at 61,000 kph (38,000 mph) to reach this new world.

Note: Due to the approximations of spacecraft speed and light year distance used for these problems in both standard and metric units, there is a variation among the answers.

    Distance: 10 trillion km x 1,400 = 14,000 trillion km (that’s 14,000,000,000,000,000 kilometers!)

    Travel time: 14,000 trillion km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 26,000,000 years

    Distance: 6 trillion miles x 1,400 = 8,400 trillion miles (that’s 8,400,000,000,000,000 miles!)

    Travel time: 8,400 trillion miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years

or more precisely…

    Distance: 9,461,000,000,000 km x 1,400 = 13,245,400,000,000,000 km

    Travel time: 13,245,400,000,000,000 km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 25,000,000 years

    Distance: 5,878,000,000,000 miles x 1,400 = 8,229,200,000,000,000 miles

    Travel time: 8,229,200,000,000,000 miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years

or using exponents and powers of 10…

    Distance: 9.461 x 1012 x km x 1.4 x 103 = 1.32454 x 1016 km

    Travel time: 1.32454 x 1016 km ÷ 6.1 x 104 kph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years

    Distance: 5.878 x 1012 miles x 1.4 x 103 = 8.2292 x 1015 miles

    Travel time: 8.2292 x 1015 miles ÷ 3.8 x 104 mph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years

Middle and High School

The time between detected periods of dimming, the duration of the dimming, and the amount of dimming, combined with a little math, can be used to calculate a great deal of information about an exoplanet, such as the length of its orbital period (year), the distance from its star, and its size.

Kepler-452b has an orbital period of 384.84 days -- very similar to Earth’s 365.25 days. Students can use the orbital period to find the distance from its star in astronomical units. An astronomical unit is the average distance between Earth and our Sun, about 150 million kilometers (93 million miles).

Kepler’s 3rd law states that the square of the orbital period is proportional to the cube of the semi-major axis of an ellipse about the sun. For planets orbiting other stars, we can use R = ∛(T2 ∙ Ms)  where R = semi-major axis, T = orbital period in Earth years, and Ms = the mass of the star relative to our sun (the star that Kepler-452b orbits has been measured to be 1.037 times the mass of our sun).

    T = 384.84 ÷ 365.25 = 1.05

    R = ∛(1.052 ∙ 1.037)

    R = ∛1.143 = 1.05 AU

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TAGS: Exoplanets, Kepler, Kepler-452b, Habitable Zone, Math, Activities, Classroom Activities, Resources

  • Lyle Tavernier