Metal Math: A ‘Pi in the Sky’ Math Challenge
The "Pi in the Sky" math 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. In this problem from the 10th set, students use pi to calculate the approximate density of the asteroid (16) Psyche and compare that to the density of known terrestrial materials.
Orbiting the Sun between Mars and Jupiter, the asteroid (16) Psyche is of particular interest to scientists because its surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. By sending a spacecraft to study Psyche up close, scientists hope to learn more about terrestrial planet cores and our solar system’s history. That's where NASA's Psyche comes in. The mission will use specialized tools to study Psyche's composition from orbit. Determining how much metal exists on the asteroid is one of the key objectives of the mission. In Metal Math, students will do their own investigation of the asteroid's makeup, using pi to calculate the approximate density of Psyche and compare that to the density of known terrestrial materials.
Asteroid (16) Psyche is of particular interest to scientists because ground-based observations indicate that the surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. If Psyche consists of a large amount of metal, it might resemble a planetary core from which we could learn about terrestrial planet core formation. Determining how much metal exists on the asteroid is one of the goals of NASA’s Psyche mission, which will use specialized tools to study the asteroid's composition from orbit.
Psyche has a roughly triaxial ellipsoid shape with axes of about 290 km, 245 km, and 170 km. Its mass, as estimated from its gravitational effects on nearby bodies such as Mars, is about 2.7 x 1019 kg. Use the formula for volume, V = 4/3 πabc, where a, b, and c are the lengths of the semi-axes, to compute Psyche's approximate density.
Based on the average density of terrestrial materials (listed below), does Psyche's density support the observations indicating the presence of metal?
Average density of terrestrial materials
- ice: 917 kg/m3
- water: 997 kg/m3
- rock: 1,600 - 3,500 kg/m3
- metal: 534 - 22,590 kg/m3
Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
NASA Pi Day Challenge
In this challenge, students can use pi to solve some of the same problems faced by NASA scientists and engineers.
Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos with NASA.
National Council of Teachers of Mathematics: Notice and Wonder
Creative brainstorming through noticing and wondering encourages student participation, engagement, and students' understanding of the NASA Pi Day Challenge.
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 Lessons for Educators
Modeling an Asteroid
Lead a discussion about asteroids and their physical properties, then have students mold their own asteroids out of clay.
Time 30 min to 1 hour
Math Rocks: A Lesson in Asteroid Dynamics
Students use math to investigate a real-life asteroid impact.
Time 30 min to 1 hour
Related Activities for Students
What's That Space Rock?
Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.
Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:
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.
Recursos en español
18 Maneras en Que la NASA Usa Pi
Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.