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.

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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

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Animated illustration of Earth orbiting the Sun

You may have noticed that there's an extra day on your calendar this year. That's not a typo; it's leap day! Leap day is another name for Feb. 29, a date that typically comes around every four years, during a leap year. Why doesn't Feb. 29 appear on the calendar every year? Read on to find out how the imperfect match between the length of a calendar year and Earth's orbit results in the need to make small adjustments to our calendar on a regular basis. Explore leap day resources for students, too.

The length of a year is based on how long it takes a planet to revolve around the Sun. Earth takes about 365.2422 days to make one revolution around the Sun. That's about six hours longer than the 365 days that we typically include in a calendar year. As a result, every four years we have about 24 extra hours that we add to the calendar at the end of February in the form of leap day. Without leap day, the dates of annual events, such as equinoxes and solstices, would slowly shift to later in the year, changing the dates of each season. After only a century without leap day, summer wouldn’t start until mid-July!

But the peculiar adjustments don't end there. If Earth revolved around the Sun in exactly 365 days and six hours, this system of adding a leap day every four years would need no exceptions. However, Earth takes a little less time than that to orbit the Sun. Rounding up and inserting a 24-hour leap day every four years adds about 45 extra minutes to every four-year leap cycle. That adds up to about three days every 400 years. To correct for that, years that are divisible by 100 don't have leap days unless they’re also divisible by 400. If you do the math, you'll see that the year 2000 was a leap year, but 2100, 2200 and 2300 will not be.

After learning more about leap years with this article from NASA's Space Place, students can do the math for themselves with this leap day problem set. Follow that up with writing a letter or poem to be opened on the next leap day. And since we've got an extra 24 hours this year, don't forget to take a little time to relax!

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Illustration of spacecraft against a starry background

Update: March 15, 2019 – The answers to the 2019 NASA Pi Day Challenge are here! View the illustrated answer key


In the News

The excitement of Pi Day – and our annual excuse to chow down on pie – is upon us! The holiday celebrating the mathematical constant pi arrives on March 14, and with it comes the sixth installment of the NASA Pi Day Challenge from the Jet Propulsion Laboratory’s Education Office. This challenge gives students in grades 6-12 a chance to solve four real-world problems faced by NASA scientists and engineers. (Even if you’re done with school, they’re worth a try for the bragging rights.)

https://www.jpl.nasa.gov/edu/teach/activity/pi-in-the-sky-6/

Visit the "Pi in the Sky 6" lesson page to explore classroom resources and downloads for the 2019 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech/Kim Orr | + Expand image

Why March 14?

Pi, the ratio of a circle’s circumference to its diameter, is what is known as an irrational number. As an irrational number, its decimal representation never ends, and it never repeats. Though it has been calculated to trillions of digits, we use far fewer at NASA. In fact, 3.14 is a good approximation, which is why March 14 (or 3/14 in U.S. month/day format) came to be the date that we celebrate this mathematical marvel.

The first-known Pi Day celebration occurred in 1988. 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.

The 2019 Challenge

This year’s NASA Pi Day Challenge features four planetary puzzlers that show students how pi is used at the agency. The challenges involve weathering a Mars dust storm, sizing up a shrinking storm on Jupiter, estimating the water content of a rain cloud on Earth and blasting ice samples with lasers!

›Take on the 2019 NASA Pi Day Challenge!

The Science Behind the Challenge

In late spring of 2018, a dust storm began stretching across Mars and eventually nearly blanketed the entire planet in thick dust. Darkness fell across Mars’ surface, blocking the vital sunlight that the solar-powered Opportunity rover needed to survive. It was the beginning of the end for the rover’s 15-year mission on Mars. At its height, the storm covered all but the peak of Olympus Mons, the largest known volcano in the solar system. In the Deadly Dust challenge, students must use pi to calculate what percentage of the Red Planet was covered by the dust storm.

The Terra satellite, orbiting Earth since 1999, uses the nine cameras on its Multi-Angle Imaging SpectroRadiometer, or MISR, instrument to provide scientists with unique views of Earth, returning data about atmospheric particles, land-surface features and clouds. Estimating the amount of water in a cloud, and the potential for rainfall, is serious business. Knowing how much rain may fall in a given area can help residents and first responders prepare for emergencies like flooding and mudslides. In Cloud Computing, students can use their knowledge of pi and geometric shapes to estimate the amount of water contained in a cloud.

Jupiter’s Great Red Spot, a giant storm that has been fascinating observers since the early 19th century, is shrinking. The storm has been continuously observed since the 1830s, but measurements from spacecraft like Voyager, the Hubble Space Telescope and Juno indicate the storm is getting smaller. How much smaller? In Storm Spotter, students can determine the answer to that very question faced by scientists.

Scientists studying ices found in space, such as comets, want to understand what they’re made of and how they interact and react with the environment around them. To see what molecules may form in space when a comet comes into contact with solar wind or sunlight, scientists place an ice sample in a vacuum and then expose it to electrons or ultraviolet photons. Scientists have analyzed samples in the lab and detected molecules that were later observed in space on comet 67P/Churyumov-Gerasimenko. To analyze the lab samples, an infrared laser is aimed at the ice, causing it to explode. But the ice will explode only if the laser is powerful enough. Scientist use pi to figure out how strong the laser needs to be to explode the sample – and students can do the same when they solve the Icy Intel challenge.

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Pi in the Sky 5 promo graphic

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


In the News

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

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NASA Pi Day Challenge Pi in the Sky 4 from NASA/JPL Edu

NASA Pi Day Challenge – Pi in the Sky 4 from NASA/JPL Edu – Answer Key

UPDATE: March 16, 2017 – An illustrated answer key for the 2017 NASA Pi Day Challenge is now available here.

Pi in the Sky 4 Answers – NASA Pi Day Challenge

Check your answers!

Were you able to solve these stellar mysteries using pi? Check your answers on our illustrated answer key and download the free "Pi in the Sky4" poster set.


NASA is giving space fans a reason to celebrate Pi Day, the March 14 holiday created in honor of the mathematical constant pi. For the fourth year in a row, the agency’s Jet Propulsion Laboratory has created an illustrated Pi Day Challenge featuring four math problems NASA scientists and engineers must solve to explore space. The challenge is designed to get students excited about pi and its applications beyond the classroom. This year’s problem set, designed for students in grade six through high school – but fun for all – features Mars craters, a total solar eclipse, a close encounter with Saturn, and the search for habitable worlds.

› Take the NASA Pi Day Challenge!

› Educators, get the standards-aligned Pi Day Challenge lesson and download the free poster and handouts. The answers to all four problems will be released in a companion infographic on March 16.

Read on for more about Pi Day, the science behind the 2017 problem set and to learn how NASA scientists and engineers use pi.

NASA Pi Day Challenge - Student Slideshow

Take the NASA Pi Day Challenge

Solve a Martian crater mystery, measure the size of the moon’s shadow during a total solar eclipse, get into a daring orbit around Saturn, and discover potentially habitable worlds beyond our solar system. You don’t have to be a NASA rocket scientist to do stellar math with pi.

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 US month/day format). The first known celebration occurred in 1988, and in 2009, the US 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.

Why It’s Important

While many of us celebrate by eating pi-themed pie and trying to memorize as many digits of pi as possible (the record is 70,030 digits), scientists and engineers at NASA take pi even further, using it in their day-to-day work exploring space!

“Finding the volume of a sphere, area of a circle (and thus volume of a cylinder) are well known applications of pi,” said Charles Dandino, a JPL engineer who designs robots for extreme environments. “But those relationships also form the basis for how stiff a structure is, how it will vibrate, and understanding how a design might fail.”

Rachel Weinberg works on the Orbiting Carbon Observatory 3, or OCO-3, instrument, which will track the distribution of carbon dioxide across Earth. She says pi came in handy during her studies at MIT and still does today for her work at JPL. “Just the other day during a meeting, the team went to the whiteboard and used pi to discuss the angles and dimensions of optical components on OCO-3,” she said.

Pi allows us to calculate the size and area of two- and three-dimensional shapes, says Anita Sengupta, a JPL engineer, who has worked on a variety of planetary missions. “In my career, pi has allowed me to calculate the size of a shield needed to enter the atmosphere of Venus and the size of a parachute that could safely land the Curiosity rover on the surface of Mars. Most recently we used pi in our calculations of the expanding atom cloud we will create for an experiment called the Cold Atom Laboratory, which will fly aboard the International Space Station.”

The Science Behind the Challenge

The Pi Day Challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers.

“Students always want to know how math is used in the real world,” said Ota Lutz, a senior education specialist at JPL who helped create the Pi Day Challenge. “This problem set demonstrates the interconnectedness of science, math and engineering, providing teachers with excellent examples of cross-cutting concepts in action and students with the opportunity to solve real-world problems.”

Pi in the Sky 4 standards-aligned lesson - NASA Pi Day Challenge

NASA's Pi Day Challenge in the Classroom!

The NASA Pi Day Challenge is available as a standards-aligned lesson for grades 6-12. In the illustrated math problem set, students use pi to solve real-world science and engineering problems related to craters on Mars, a total solar eclipse, a daring orbit about Saturn, and the search for habitable worlds.

Here’s some of the science behind this year’s problem set.

The craters that cover Mars can tell us a lot about the Red Planet. Studying ejecta – the material blasted out during an impact – can tell us even more. Information about ejecta patterns even came up during a recent workshop to discuss and select the final candidates for the Mars 2020 rover landing site. For the first problem in our Pi Day Challenge, students use pi and the area and perimeter of two craters to identify which was made by an impactor that struck Mars at a low angle. Researchers found that low-angle impactors create an unusual ejecta pattern around craters on Mars. As part of the research, scientists are currently working to identify and catalog these craters.

The year 2017 brings a unique astronomical event to the United States for the first time in nearly 40 years! On August 21, 2017, a total solar eclipse will cross the continental United States. Starting in Oregon, the shadow of the moon will cross the country at more than 1,000 miles per hour, making its way to the Atlantic Ocean off the coast of South Carolina. Everyone inside the moon’s shadow will witness one of the most impressive sights nature has to offer. So how big is the shadow? In the second part of NASA’s Pi Day Challenge, students will use pi to calculate the area of the moon’s shadow on Earth during the total solar eclipse.

This year also marks the final chapter in the exciting story of NASA’s Cassini mission at Saturn. Since 2004, Cassini has been orbiting the ringed giant, vastly improving our understanding of the second largest planet in the solar system. After more than 12 years around Saturn, Cassini’s fuel is running low, so mission operators have devised a grand finale that will take the spacecraft closer to Saturn than ever before – inside the gap between the planet and its rings – and finally into Saturn’s cloud tops, where it will burn up. The finale is designed to prevent the spacecraft from crashing into and possibly contaminating any of Saturn’s scientifically intriguing moons. In the Pi Day Challenge, students will use pi to safely navigate the spacecraft on its final orbits and dive into Saturn.

Finally, students will investigate a relatively new and very exciting realm in astronomy, the search for habitable worlds. The discovery of exoplanets – worlds orbiting stars outside of our solar system – has changed our understanding of the universe. Until 1995, exoplanets hadn’t even been detected. Now, using the transit method – where planets are detected by measuring the light they block as they pass in front of a star – more than 2,300 exoplanets have been discovered. Recently, astronomers discovered a record seven Earth-size planets orbiting a single star called Trappist-1. Students will use pi to identify which of Trappist-1’s planets orbit in the star’s habitable zone – the area where liquid water could exist.

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

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Cartoon animation of NASA-JPL spacecraft

UPDATE: March 16, 2016 – The answers the the NASA Pi Day Challenge are now available as an illustrated answer key. Download a poster version of the answer key on the "Pi in the Sky 3" activity page.

NASA Pi Day Challenge Answer Key

› Check your answers!


This post was originally published on March 9, 2016

In the News

Pi Day, the informal holiday beloved by math enthusiasts – and even by the math averse – is almost here! March 14 marks the yearly celebration of the mathematical constant (pi), which represents the ratio of a circle’s circumference to its diameter. More than just a number for mathematicians, pi has all sorts of applications in the real world, including on missions developed by NASA’s Jet Propulsion Laboratory. And as a holiday that encourages more than a little creativity – whether it’s making pi-themed pies or reciting from memory as many of the never-ending decimals of pi as possible (the record is 70,030 digits) – it’s a great way to have fun and celebrate the M in STEM.

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 3.14 is often a precise enough approximation, hence the celebration occurring on March 14, or 3/14 (when written in US month/day format). The first known celebration occurred in 1988, and in 2009, the US 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.

Why It’s Important

Pi Day is lots of fun, but its importance lies in the role that pi plays in the everyday work of scientists and engineers at JPL.

Fred Calef, a geospatial information scientist at JPL, uses pi to make measurements – like perimeter, area and volume – of features on Mars. “I use pi to measure the circularity of features, or how round or compact they are," said Calef. "Craters become more elliptical if the projectile hits the surface at a lower angle, so I use pi to measure how round a crater is to see if it impacted at a low angle.”

"We use pi every day commanding rovers on Mars," said Hallie Gengl, a rover planner for the Mars Exploration Rover Opportunity, "Everything from taking images, turning the wheels, driving around, operating the robotic arm, and even talking to Earth.”

Bryana Henderson, who specializes in planetary ices, uses lasers to explode ice samples and study their composition. "I use pi to calculate the width of my laser beam, which in turn can be used to calculate the amount of energy, or fluence, that hits my ice sample," said Henderson. "A larger fluence equals a bigger explosion in the ice, so this is a very important parameter for us."

The Pi Day Challenge

JPL has released the third installment of its popular Pi Day challenge, which gives students and the public a chance to put their pi skills to the test to solve some of the same problems NASA scientists and engineers do. The set of four illustrated math problems are compiled into a graphic (as well as classroom handouts) designed for students in grade 4 through high school – but fun for all!

Pi in the Sky 3 activity

› Check out this year's Pi Day challenge!

This year’s problem set shows how pi can be used to map the surface of Saturn’s hazy moon Titan, track the Mars Reconnaissance Orbiter as it explores the Red Planet, keep Earth’s satellites powered as Mercury transits the sun, and put the Juno spacecraft into orbit around Jupiter.

“For Pi Day, we like to give students and the public a glimpse into how math is used at JPL through questions that feature current events involving our space missions,” said Ota Lutz, an education specialist at JPL who helped create the problem set. “For instance, to put the Juno spacecraft into orbit around Jupiter on July 4, engineers will have to slow the spacecraft just the right amount. In the Pi Day challenge, students use pi to calculate that change in velocity.”

In the challenge, students will also use pi to calculate how much sunlight is blocked by our solar system’s innermost planet as it passes between Earth and the sun. This year, Pi Day comes just a few months before the May 9 transit of Mercury, making this a timely problem.

On March 16, the answers to all four problems and the steps needed to find those answers will be released in a companion infographic on the Pi Day challenge activity page.

In addition to the Pi Day challenge, JPL is inviting the public to share their Pi Day pictures and stories online. On March 14, JPL will join in on the fun with Pi Day photos and stories from the lab.

› Share Your Pi Day photos and stories

To see a compilation of all 12 Pi Day challenge questions optimized for mobile devices and screen readers, visit: http://www.jpl.nasa.gov/edu/nasapidaychallenge

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Artist concept of NASA's Juno spacecraft

In the News

NASA’s Juno mission, the first solar-powered mission to Jupiter, has become the farthest solar-powered spacecraft ever! Juno, and its eight science instruments designed to study the interior of Jupiter, has passed the mark previously held by the European Space Agency’s Rosetta mission and reached a distance of 5.3 astronomical units from the sun (an astronomical unit is equal to the average distance between Earth and the sun – about 149.6 million kilometers). Using only power from the sun, Juno will complete the five-year trip to Jupiter in July 2016 and begin studying the solar system’s most massive world in an attempt to better understand the origins of the planet, and in turn, our solar system.

What Made It Possible

Just as a bright source of light dims as you move away from it, sunlight becomes less intense the farther a spacecraft travels from the sun, limiting the amount of power that can be generated using solar cells. Previous missions that visited Jupiter, like Galileo, Voyager 1 and Voyager 2, couldn’t use solar power and instead used radioisotope thermoelectric generators (RTGs) to supply power.

Advances in solar panel efficiency along with improvements in the way spacecraft and their instruments use power have recently made solar power a viable option for spacecraft heading as far as Jupiter – though going beyond will require further technological advances.

Engineers designed Juno with three massive solar panels, each nearly 30 feet long. Combined, they provide Juno with 49.7 m2 of active solar cells. Once it reaches Jupiter, Juno will generate more than 400 watts of power, which may not sound like a lot, but it’s an impressive feat at so great a distance. For comparison, Juno’s solar panels can generate about 14 kilowatts near Earth.

NASA's Juno spacecraft being prepped for launch
Technicians stow for launch a solar array on NASA's Juno spacecraft. Each of Juno's three solar arrays is 9 feet (2.7 meters wide), by 29 feet (8.9 meters long). Image credit: NASA/JPL-Caltech/KSC

Teach It

Juno's record-setting achievement translates into a powerful lesson in exponents.

> Get the problem set!

Middle school students and other students working with exponents will find challenging, real-world applications related to the work being done here at NASA while addressing four Common Core Math standards:

  • Grade 6: Expressions and Equations A.1 - "Write and evaluate numerical expressions involving whole-number exponents."
  • Grade 6: Expressions and Equations A.2 - "Write, read, and evaluate expressions in which letters stand for numbers."
  • Grade 6: Expressions and Equations A.2.C - "Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)."
  • Grade 8: Expressions and Equations A.1 - "Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27."

Explore More!

  • Juno mission website - News, resources and updates on NASA's mission to Jupiter.

  • Eyes on the Solar System - Take a virtual journey to Jupiter with Juno (scroll to "Solar System Tours" and click on Juno).

  • To Jupiter with JunoCam! - Find out how classrooms can participate in the Juno mission to Jupiter using the spacecraft's on-board educational camera.

  • Infographic: Solar Power Explorers - This graphic shows how NASA’s Juno mission to Jupiter became the most distant solar-powered explorer and influenced the future of space exploration powered by the sun.

TAGS: Juno, Jupiter, Exponents, Math, Lesson, Activity, Teachable Moment

  • Lyle Tavernier
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Saturn's moon Enceladus

In the News

Saturn’s icy moon Enceladus has been making news lately, and it could make even bigger news soon! In September, scientists confirmed that there was a global ocean underneath Enceladus’ thick icy shell. That was just the latest in a long history of exciting finds dating back to the beginning of NASA’s Cassini-Huygens Mission to Saturn in 2004 that have helped scientists to better understand this fascinating world!

Even while Cassini was still on its way to Saturn, its Cosmic Dust Analyzer detected microscopic grains of silica (tiny grains of sand). On Earth, grains of silica similar in size to those detected near Saturn form when hydrothermal activity -- the processes involving heated water beneath Earth’s surface or ocean -- causes salty water to chemically interact with rocky material to form silica. But where were these grains coming from in the space around Saturn?

In 2005, scientists were surprised to find out that Enceladus’ south pole is both warmer than expected and warmer than the surrounding areas, suggesting there is a heat source inside Enceladus. Not only that, but they also discovered long parallel cracks in the ice on Enceladus’ south pole. The young age of these cracks, nicknamed Tiger Stripes, meant that Saturn’s icy moon is a geologically active place.


Color image of the cracks, or Tiger Stripes, on the South Pole of Saturn's moon Enceladus
This enhanced color view of Saturn's moon Enceladus shows the south polar terrain, where jets of material spray out form long cracks called Tiger Stripes. Image credit: NASA/JPL-Caltech/Space Science Institute | Full image and caption


Heat map of Saturn's moon Enceladus
This image shows the infrared (heat) radiation at the south pole of Saturn's moon Enceladus, including the dramatic warm spot centered on the pole near the moon's Tiger Stripes feature. The data were taken during the spacecraft's third flyby of Enceladus on July 14, 2005. Image credit: NASA/JPL-Caltech/Space Science Institute | Full image and caption

Another piece of this puzzle was put in place with the discovery of jets of material spraying out of the Tiger Stripes. Studies have shown these jets are composed of mostly of water vapor, tiny ice particles and small amounts of other material (for example, microscopic silica grains). Together, over 100 jets make up a feature called a plume. Investigating further, scientists have hypothesized that these silica grains are the result of hydrothermal activity on the ocean floor below Enceladus’ icy crust.


Movie of the Plume on Saturn's moon Enceladus
Jets of icy particles burst from Saturn’s moon Enceladus in this brief movie sequence of four images taken on Nov. 27, 2005. Credit: NASA/JPL-Caltech/Space Science Institute | Full image and caption

On October 28, Cassini will fly right through the plume jetting out of Enceladus’ south pole at an altitude of only 49 kilometers (30 miles) – closer than any previous passes directly through the plume! This is an exciting moment in the mission -- one that allows science teams to use a combination of tools on board the spacecraft to strengthen previous findings and potentially make new discoveries.

Why It's Important

Cassini will use its Cosmic Dust Analyzer to study the solid plume particles and an instrument called the Ion and Neutral Mass Spectrometer to “sniff” the gas vapor in order to determine the composition of the jets. Specifically, the latter instrument is looking for H2, or molecular hydrogen. Finding H2 in the plume will strengthen the evidence that hydrothermal activity is occurring on Enceladus’ ocean floor. And the amount of H2 in the plume, will tell scientists just how much activity is happening.

In addition to indicating that hydrothermal activity is taking place, figuring out the amount of hydrothermal activity will give scientists a good indication of how much internal energy there is deep inside Enceladus.

That Cassini is making a pass through the plume at such a low, 49-kilometer-high altitude is also important. Organic compounds -- substances formed when carbon bonds with hydrogen, nitrogen, oxygen, phosphorus or sulfur -- tend to be heavy and would fall out of the plume before reaching the heights of Cassini’s previous, higher altitude flybys and be undetected. Organic compounds are the building blocks of life on Earth. Without them, life as we know it wouldn’t exist. If they are present in Enceladus’ oceans, they could be detected when Cassini passes through the plume on this encounter.

Perhaps more important, though, are the implications of finding hydrothermal activity somewhere other than Earth. It was once believed that all forms of life needed sunlight as a source of energy, but in 1977, the first hydrothermal vent -- essentially an underwater geyser of hot, mineral-rich water -- was discovered and it was teeming with life. The organisms were using the heat and minerals as a source of energy! Some scientists have hypothesized that hydrothermal vents could be where life on our planet first took hold and could represent environments in the solar system with the necessary ingredients to support life.

Teach It

Here are a handful of lessons and resources you can use to teach key concepts related to the October 28 Enceladus flyby and help your students feel connected to this exciting moment in science at Saturn.

Modeling

Standard(s):

  • NGSS 5-ESS2-1 - Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact.

Activity:

Because scientists can’t dig beneath the ice and see what’s below, they rely on creating models that show what is happening beneath the surface. A model helps us imagine what can’t be seen and explains the things that we can see and measure. A model could be a drawing, a diagram or a computer simulation. For this model, students will draw a cut away model of Enceladus and iterate, or improve, their model as you provide more description, just as scientists improved their models as they learned more about Enceladus.

  1. Tell students there is a moon around Saturn. They should draw a moon (likely a circle, half-circle, or arc, depending on how big you want the drawing to be).

  2. Explain to students that the moon is covered in a shell of ice (students will need to modify their model by drawing a layer of ice). Thus far, everything students are modeling is observable by looking at the moon.

  3. Share with students that temperature measurements of the south pole revealed spots that are warmer than the rest of the moon’s surface. Ask students to brainstorm possible sources of heat at the south pole and explain what might happen to ice near a heat source. Based on this new information, and what they think might be causing the heat, allow them to modify their drawing. (Depending on what students brainstorm, their drawing might now include volcanoes, hot spots, magma, hydrothermal vents and a pool of liquid water beneath the ice).

  4. The next piece of information the students will need to incorporate into their drawing is that there are large cracks in the ice over the warmer south-pole region.

  5. Explain that students have now received images that show jets expelling material from the cracks. They will need to incorporate this new data and add it to their drawing.

  6. Tell students that by studying the gravity of the moon, scientists now believe there is an ocean covering the whole surface of the moon beneath the ice. Ask students to share how they would represent that in the model. Allow them to modify their drawing.

  7. Show students the following image depicting a model of Enceladus:

    Saturn's moon Enceladus global ocean model

    This model shows what scientists believe the interior of Enceladus may look like. Have students compare it to what they drew and note similarities and differences.

Particle Travel Rate

Standard(s):

  • CCSS.MATH 6.RP.A.3.B - - Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Problem:

Based on the size of the silica grains (6 to 9 nanometers), scientists think they spend anywhere from several months to a few years (a longer time than that means the grains would be larger) traveling from hydrothermal vents to space, a distance of 40 to 50 km.

  1. What rate (in km/day) are the particles traveling if it takes them 6 months to travel 50 km (assume 182 days)?

    50 km ÷ 182 days = 0.27 km/day

  2. What rate are they traveling if it takes two years to travel 40 km?

    40 km ÷ 730 days = 0.05 km/day

  3. Do you think the particles in each example traveled at the same speed the entire time they moved?

  4. Why might the particle rate vary?

  5. At what point in their journey might particles have been traveling at the highest rate?

Plume Data

Standard(s):

  • CCSS.MATH 6.RP.A.3.B - Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
  • CCSS.MATH 8.G.B.7 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Problem:

Cassini will be flying past Enceladus at a staggering 8.5 km per second (19,014 mph). At an altitude of 49 km, the plume is estimated to be approximately 130 km across.

  • How long will Cassini have to capture particles and record data while within the plume?

    130 km ÷ 8.5 km/sec ≈ 15 seconds

  • If Cassini is 49 km above the surface of Enceladus at the center of the plume, what is its altitude as it enters and exits the plume (the radius of Enceladus is 252.1 km)?

    252.1 km + 49 km = 301.1 km
    (301.1 km)2 + (65 km)2 ≈ 95,000 km2
    √(95,000 km2) ≈ 308 km
    ≈ 308 km – 252.1 km ≈ 56 km

  • This information can help scientists determine where in the plume heavy particles may fall out if they are not detected on the edge of the plume but are detected closer to the middle of the plume. It is also important because the Cosmic Dust Analyzer uses a high-rate detector that can count impacting particles at over 10,000 parts per second to tell us how much material is being sprayed out.

Volume of Enceladus’ Ocean

Standard(s):

  • CCSS.MATH 8.G.C.9 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
  • CCSS.MATH HSG.GMD.A.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Problem:

Gravity field measurements of Enceladus and the wobble in its orbital motion show a 10 km deep ocean beneath a layer of ice estimated to be between 30 km and 40 km thick. If the mean radius of Enceladus is 252.1 km, what is the minimum and maximum volume of water contained within its ocean?

Volume of a sphere = 43πr3

Minimum volume with a 40 km thick crust
43 π212.1 km3 - 43π202.1 km3 ≈ 40,000,000 km3 – 35,000,000 km3 ≈ 5,000,000 km3

Maximum volume with a 30 km thick crust
43 π222.1 km343 π212.1 km3 ≈ 46,000,000 km3 – 40,000,000 km3 ≈ 6,000,000 km3

This is important because if scientists know how much water is in the ocean and how much vapor is escaping through the plume, they can make estimates about how long the plume has existed -- or could continue to exist.

Download the Full Problem Set

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TAGS: Enceladus, moon, Saturn, Cassini, flyby, spacecraft, plume, jets, geysers, science, math, Ocean Worlds

  • Lyle Tavernier
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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
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