Teachable Moments  March 8, 2019
NASA Rocket Science? It's Easy As Pi
Update: March 15, 2019 – The answers to the 2018 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 612 a chance to solve four realworld problems faced by NASA scientists and engineers. (Even if you’re done with school, they’re worth a try for the bragging rights.)
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 firstknown 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 solarpowered Opportunity rover needed to survive. It was the beginning of the end for the rover’s 15year 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 MultiAngle Imaging SpectroRadiometer, or MISR, instrument to provide scientists with unique views of Earth, returning data about atmospheric particles, landsurface 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/ChuryumovGerasimenko. 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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Participate

Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 412
Time Varies

Slideshow: NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 412
Time Varies

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

How Many Decimals of Pi Do We Really Need?
While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

Slideshow: 18 Ways NASA Uses Pi
Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
Related Activities

The Sky and Dichotomous Key
Students learn about cloud types to be able to predict inclement weather. They will then identify areas in the school affected by severe weather and develop a solution to ease the impacts of rain, wind, heat or sun.
Grades K3
Time 30 mins  1 hr

Precipitation Towers: Modeling Weather Data
This lesson uses stacking cubes as a way to graph precipitation data, comparing the precipitation averages and seasonal patterns for several locations.
Grades K5
Time 30 mins  1 hr

Create a Comet with Dry Ice
Build an icy model of a comet out of dry ice  complete with shooting jets!  as a demonstration for students.
Grades 25
Time < 30 mins

Comet on a Stick
Students build their own comet models using craft materials.
Grades 28
Time 30 mins  1 hr

Modeling the Water Budget
Students use a spreadsheet model to understand droughts and the movement of water in the water cycle.
Grades 58
Time 30 min  1 hr

Make a Cloud Mobile  NASA SpacePlace
This mobile of feathery clouds will twist and turn in a gentle breeze. It even includes rain clouds with sparkling showers!
Grades 36
Multimedia

Infographic: Planet Pi
This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

Game: Comet Quest  NASA SpacePlace
Control a spacecraft and use it to explore an icy comet!
Facts and Figures
 Mars
 Jupiter
 Earth
 Comets
 Comet 67P/ ChuryumovGerasimenko
 What is a Laser? – NASA SpacePlace
 What Is the Water Cycle? – Climate Kids
Missions and Instruments
 Hubble Space Telescope
 Voyager
 Juno
 Opportunity Rover
 Rosetta
 MISR instrument
 Ice Spectroscopy Laboratory
Websites
TAGS: Pi Day, K12, STEM, Science, Engineering, Technology, Math, Pi, Educators, Teachers, Informal Education, Museums
Teachable Moments  March 9, 2018
Pi Goes the Distance at NASA
Update: March 15, 2018 – The answers to the 2018 NASA Pi Day Challenge are here! View the illustrated answer key
In the News
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
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 realworld 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 Earthsize 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 indepth 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 exoplanethunting 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 uniquelyshaped 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.
Explore More
Join the Conversation
 Join the conversation and share your Pi Day Challenge answers with @NASAJPL_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.
StandardsAligned Lessons
 Pi in the Sky 5
 Pi in the Sky 4
 Pi in the Sky 3
 Pi in the Sky 2
 Pi in the Sky
 Pi in the Sky Challenge (slideshow for students)
Multimedia
 18 Ways NASA Uses Pi – Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
 Kepler186f Travel Poster
 Video: First Interstellar Asteroid Wows Scientists
 Planet Pi
Facts and Figures
Missions
Websites
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K12, Lesson, Activity, Slideshow, Mars, Jupiter, Exoplanets, Kepler, Kepler186f, Juno, InSight, TESS, ‘Oumuamua, asteroid, asteroids, NEO, Nearth Earth Object
Teachable Moments  March 10, 2017
Celebrate Pi Day Like a NASA Rocket Scientist
UPDATE: March 16, 2017 – An illustrated answer key for the 2017 NASA Pi Day Challenge is now available here.
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 Sky^{4}" 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 standardsaligned 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.
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 pithemed 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 daytoday 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 OCO3, 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 OCO3,” she said.
Pi allows us to calculate the size and area of two and threedimensional 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 crosscutting concepts in action and students with the opportunity to solve realworld problems.”
NASA's Pi Day Challenge in the Classroom!
The NASA Pi Day Challenge is available as a standardsaligned lesson for grades 612. In the illustrated math problem set, students use pi to solve realworld 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 lowangle 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 Earthsize planets orbiting a single star called Trappist1. Students will use pi to identify which of Trappist1’s planets orbit in the star’s habitable zone – the area where liquid water could exist.
Explore More
Join the Conversation
 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.
StandardsAligned Lessons
Multimedia
Facts and Figures
Missions
Websites
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K12, Lesson, Activity, Slideshow
Teachable Moments  March 16, 2016
Pi Day the NASA Way
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.
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 pithemed pies or reciting from memory as many of the neverending 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!
› 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 storiesTo 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
Explore More
Pi Day Challenges
Multimedia
Facts and Figures
Missions
Websites
TAGS: pi, pi day, math, mathematics
Teachable Moments  January 13, 2016
Cruising to Jupiter: A Powerful Math Lesson
In the News
NASA’s Juno mission, the first solarpowered mission to Jupiter, has become the farthest solarpowered 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 fiveyear 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 m^{2} 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.
Teach It
Juno's recordsetting achievement translates into a powerful lesson in exponents.
Middle school students and other students working with exponents will find challenging, realworld 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 wholenumber 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 realworld problems. Perform arithmetic operations, including those involving wholenumber 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, 3^{2} × 3^{5} = 3^{3} = 1/3^{3} = 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 onboard educational camera.
 Infographic: Solar Power Explorers  This graphic shows how NASA’s Juno mission to Jupiter became the most distant solarpowered explorer and influenced the future of space exploration powered by the sun.
TAGS: Juno, Jupiter, Exponents, Math, Lesson, Activity, Teachable Moment
Teachable Moments  October 23, 2015
Flying Through the Plume on 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 CassiniHuygens 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.
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.
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 H_{2}, or molecular hydrogen. Finding H_{2} in the plume will strengthen the evidence that hydrothermal activity is occurring on Enceladus’ ocean floor. And the amount of H_{2} 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, 49kilometerhigh 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, mineralrich 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 5ESS21  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.
 Tell students there is a moon around Saturn. They should draw a moon (likely a circle, halfcircle, or arc, depending on how big you want the drawing to be).
 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.
 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).
 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 southpole region.
 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.
 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.
 Show students the following image depicting a model of Enceladus:
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.
 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  What rate are they traveling if it takes two years to travel 40 km?
40 km ÷ 730 days = 0.05 km/day  Do you think the particles in each example traveled at the same speed the entire time they moved?
 Why might the particle rate vary?
 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 realworld 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 km^{2}
√(95,000 km^{2}) ≈ 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 highrate 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 realworld 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 = ^{4}⁄_{3}πr^{3}
Minimum volume with a 40 km thick crust
^{4}⁄_{3} π212.1 km^{3}  ^{4}⁄_{3}π202.1 km^{3} ≈ 40,000,000 km^{3} – 35,000,000 km^{3} ≈ 5,000,000 km^{3}
Maximum volume with a 30 km thick crust
^{4}⁄_{3} π222.1 km^{3}  ^{4}⁄_{3} π212.1 km^{3} ≈ 46,000,000 km^{3} – 40,000,000 km^{3} ≈ 6,000,000 km^{3}
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
Explore More!
 Enceladus flyby information page
 Slideshow and poster: 8 Real World Science Facts About Saturn's Moon Enceladus
 Enceladus facts and figures
 Enceladus images
 Eyes on the Solar System: Enceladus flyby simulation
 Cassini mission overview
TAGS: Enceladus, moon, Saturn, Cassini, flyby, spacecraft, plume, jets, geysers, science, math
Teachable Moments  August 17, 2015
'Exoplanets' and the Search for Habitable Worlds
In the News
Twenty years after the first discovery of a planet orbiting another sunlike star, scientists have discovered the most Earthlike exoplanet ever: Kepler452b. Located in the habitable zone of a star very much like our sun, Kepler452b is only about 60 percent wider than Earth.
What makes it the most Earthlike 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 Kepler452b. 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 Earthlike planets a rarity. Until this discovery, all of them have orbited stars that are smaller and cooler than our sun.
Kepler452b 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 Kepler452b 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 Kepler452b has been in the habitable zone for around six billion years  longer than Earth has even existed!
How They Did It
The Kepler spacecraft, named for mathematician and astronomer Johannes Kepler, has been working since 2009 to find distant worlds like Kepler452b. 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 Kepler452b.
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 Kepler452b 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 Kepler452b 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 10^{12} x km x 1.4 x 10^{3} = 1.32454 x 10^{16} km
Travel time: 1.32454 x 10^{16} km ÷ 6.1 x 10^{4} kph ÷ 2.4 x 10^{1} ÷ 3.65 x 10^{2} ≈ 2.5 x 10^{7} years
Distance: 5.878 x 10^{12} miles x 1.4 x 10^{3} = 8.2292 x 10^{15} miles
Travel time: 8.2292 x 10^{15} miles ÷ 3.8 x 10^{4} mph ÷ 2.4 x 10^{1} ÷ 3.65 x 10^{2} ≈ 2.5 x 10^{7} 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.
Kepler452b 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 semimajor axis of an ellipse about the sun. For planets orbiting other stars, we can use R = ∛(T^{2} ∙ M_{s}) where R = semimajor axis, T = orbital period in Earth years, and M_{s} = the mass of the star relative to our sun (the star that Kepler452b orbits has been measured to be 1.037 times the mass of our sun).
T = 384.84 ÷ 365.25 = 1.05
R = ∛(1.05^{2} ∙ 1.037)
R = ∛1.143 = 1.05 AU
Explore More
Activities
Multimedia
 Exoplanet Travel Bureau Posters
 Video: What’s a “habitable zone?”
 Video: What’s in an Exoplanet Name?
Interactives
Facts and Figures
Websites
Events
TAGS: Exoplanets, Kepler, Kepler452b, Habitable Zone, Math, Activities, Classroom Activities, Resources
Teachable Moments  July 16, 2015
NASA's New Horizons Mission Flies by Pluto
In the News
We visited Pluto!
On July 14, 2015 at 4:49 a.m. PDT, NASA's New Horizons spacecraft sped past Pluto  a destination that took nearly nine and a half years to reach  and collected scientific data along with images of the dwarf planet.
Pluto, famous for once being the ninth planet, was reclassified as a dwarf planet in 2006 after new information emerged about the outer reaches of our solar system. Worlds similar to Pluto were discovered in the region of our solar system known as the Kuiper Belt. The Kuiper Belt named for astronomer Gerard Kuiper is a doughnutshaped area beyond the orbit of Neptune that is home to Pluto, other dwarf planets such as Eris, Makemake, and Haumaea, as well as hundreds of thousands of other large icy bodies, and perhaps trillions of comets orbiting our sun. Over the next several years, the New Horizons spacecraft is expected to visit one to two more Kuiper Belt objects.
Even though it will take 16 months for New Horizons to return all the Pluto science data to Earth, we have already made some interesting and important discoveries about Pluto.
Why It's Important
Through careful measurements of new images, scientists have determined that Pluto is actually larger than previously thought: 2,370 kilometers in diameter. This is important information for scientists because it helps them understand the composition of Pluto. Because of the orbital interactions between Pluto and its moon Charon, Pluto’s mass is well known and understood. Having a more precise diameter gives scientists the ability to more accurately calculate the average density. A greater diameter means Pluto’s density is less than we thought. If you do the math, you’ll see that Pluto’s calculated density dropped from 2,051 kg/m^{3} to 1,879 kg/m^{3} with this new finding. Most rock has a density between 20003000 kg/m^{3} and ice at very cold temperatures has a density of 927 kg/m^{3}, so we can conclude that Pluto is a bit more icy than previously believed. In addition to helping scientists calculate the density of Pluto, this measurement confirms Pluto as the largest known object in the Kuiper Belt!
Teach It
We’ve provided some math problems (and answers) for you to use in the classroom. They’re a great way to provide students with realworld examples of how the math they’re learning in class is used by scientists. There are also some additional resources below that you can use to integrate the Pluto flyby into your lessons, or use the flyby as a lesson opener!
Pluto Math Problems
 Find the radius(r) of Pluto.
2,370 kilometers ÷ 2 = 1,185 km  Find the circumference of Pluto.
C = 2 π r = 7,446 km  Find the surface area of Pluto.
SA = 4 π r^{2} = 17,646,012 km^{2}  Find the volume of Pluto.
4/3 π r^{3} = 6,970,174,651 km^{3}  Find the density of Pluto in kg/m^{3}.
mass/volume
Pluto mass = 1.31 × 10^{22}kg
Convert volume in km^{3} to m^{3}: 6,970,174,651 × 1,000,000,000 = 6.970174651 × 10^{18}m^{3}
1.31 × 10^{22}kg / 6.970174651 × 10^{18}m^{3} = 1,879 kg/m^{3}  How does this new density calculation compare to the previous calculation (2051 kg/m^{3}) when Pluto’s diameter was thought to be 2,302 km?
Explore More
Take a look at some of the lessons, videos, activities and interactives related to Pluto. They’re a great way to engage students in STEM and learning more about their solar system!
 Video: What is a Dwarf Planet? (K12)
Dwarf planets are a lot like regular planets. What’s the big difference? Find out in 60 seconds.  Activity: Solar System Bead Activity (48)
The solar system is big, and Pluto is way out there! Students calculate scale distances to create a model of objects in our solar system.
Next Generation Science Standards: MSESS13
Common Core Math: 4.MD.A.2, 5.NBT.B.7  Activity: How Far? How Faint? (912)
Calculate how much light Pluto receives from the sun, compared to Earth.
Common Core Math: HSF.IF.C.7.E  Resource: Pluto Facts and Figures
Get lots of facts and figures about this dwarf planet in the Kuiper belt!  Interactive: Eyes on Pluto
Ride along with New Horizons in this simulation of its closest approach to Pluto!  Participate: Pluto Time
Though Pluto is a distant world with very different characteristics from Earth, for just a moment near dawn and dusk each day, you can experience “Pluto Time.” This is when the amount of light reaching Earth matches that of noon on Pluto. Find out exactly when Pluto Time happens in your area and share your photos online!  News and Images: NASA New Horizons Website
Get the latest news and images from NASA's New Horizons mission.
TAGS: Pluto, New Horizons, Math, Teachable Moment
Edu News  March 14, 2013
How Pi Makes NASA/JPL Go 'Round
In honor of Pi Day, March 14 (or 3.14), 2013, the JPL Education Office has released an infographic highlighting some of the ways scientists and engineers at the laboratory use pi in their daily work. For example, scientists can use pi (along with mass and radius) to calculate the density of an asteroid and its material makeup.
The infographic is available on the JPL Infographics website and as a fullresolution download below.
"Planet Pi" Downloads:
 Poster  Download PDF (27 MB)