## Classroom Activity

# Pi in the Sky 4

*This activity is related to a Teachable Moment from March 14, 2017. See "Celebrate Pi Day Like a NASA Rocket Scientist."*

### Overview

In the fourth installment of this illustrated problem set, students use the mathematical constant pi to solve real-world science and engineering problems. Students will use pi to calculate the angle of crater impacts on Mars, measure the size of the shadow that will fall on North America during the 2017 total solar eclipse, determine the orbital period of the Cassini spacecraft during its final weeks around Saturn, and find the habitable zone around TRAPPIST-1, a star that is home to seven Earth-size planets!### Materials

### Background

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 integrates mechanical engineering and electronics,“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 investigate the distribution of carbon dioxide on 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.”

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 across Mars.

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. To prevent the spacecraft from crashing into and possibly contaminating Saturn’s moons Enceladus and Titan, two locations with potentially habitable environments, students will use pi to safely navigate the spacecraft on its grand finale orbits and final 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 – over 2300 exoplanets have been discovered. This has great implications in the search for life outside our solar system. Recently, astronomers discovered a record seven Earth-size planets orbiting a single star called TRAPPIST-1! Students will use pi to identify which of these planets orbit in the star’s habitable zone – the area where liquid water could exist.

### Procedures

### Assessment

Download the free NASA "Pi in the Sky 4" poster and companion answer key:

› Digital poster (PNG, 2.4 MB)

› Digital answer key (PNG, 2.3 MB)

› Print poster (PDF, 24.1 MB)

› Print answer key (PDF, 24 MB)

### Extensions

Join the Conversation

- Join the conversation and share your Pi Day Challenge answers with @NASA/JPL_Edu on social media using the hashtag #NASAPiDayChallenge
- Share how you're celebrating Pi Day 2017!

Pi Day Challenges

- Pi in the Sky
- Pi in the Sky 2
- Pi in the Sky 3
- Pi in the Sky Challenge (slideshow for students)

Multimedia

Facts and Figures

Missions

Websites