In the 10th installment of the Pi in the Sky illustrated problem set, students use pi to calculate the size of a rock sample collected by the Perseverance Mars rover, compare the sensitivity of two space telescopes, determine the composition of an asteroid, and find out how much of the Sun will be covered during a solar eclipse.
NASA’s Mars rover, Perseverance, was designed to collect rock samples that will eventually be brought to Earth by a future mission. Sending objects from Mars to Earth is very difficult and something we've never done before. To keep the rock cores pristine on the journey to Earth, the rover hermetically seals them inside a specially designed sample tube. Once the samples are brought to Earth, scientists will be able to study them more closely with equipment that is too large to make the trip to Mars. In Tubular Tally, students use pi to determine the volume of a rock sample collected in a single tube.
When NASA launched the Hubble Space Telescope in 1990, scientists hoped that the telescope, with its large mirror and sensitivity to ultraviolet, visible, and near-infrared light, would unlock secrets of the universe from an orbit high above the atmosphere. Indeed, their hope became reality. Hubble’s discoveries, which are made possible in part by its mirror, rewrote astronomy textbooks. In 2022, the next great observatory, the James Webb Space Telescope, began exploring the infrared universe with an even larger mirror from a location beyond the orbit of the Moon. In Rad Reflection, students use pi to gain a new understanding of our ability to peer deep into the cosmos by comparing the area of Hubble’s primary mirror with the one on Webb.
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.
On Oct. 14, 2023, a solar eclipse will be visible across North and South America, as the Moon passes between Earth and the Sun, blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. Depending on those distances, the Sun's disk area might be fully or only partially blocked during a solar eclipse. In Eclipsing Enigma, students get a sneak peek at what to expect in October by using pi to determine how much of the Sun’s disk will be eclipsed by the Moon and whether to expect a total or annular eclipse.
The Perseverance Mars rover is designed to collect rock samples that will eventually be brought to Earth for further study. This would be the first time we've ever brought back samples from Mars! After scientists identify an interesting rock they would like the rover to collect, Perseverance uses a special coring bit to drill out a rock cylinder 13 mm in diameter. As the rover drills, the rock core moves into one of 38 available tubes that will store the rock sample – sealed until it is opened one day in a lab on Earth.
If the coring bit collects a rock cylinder 60 mm in length, what is the volume of the rock in the sample tube?
The James Webb Space Telescope was designed to look back at some of the earliest galaxies in the universe. To capture light from these distant and faint objects, the telescope must be very sensitive. Webb uses 18 hexagonal mirrors that combine to form a massive primary mirror with a surface area of 26.4 m2. This large mirror allows the telescope to collect incredibly faint infrared light and reflect it onto four onboard science instruments, like the Mid-Infrared Instrument, or MIRI. This science instrument can reveal stars hidden within gas and dust clouds and tell scientists about the materials that make up distant galaxies.
Launched in 1990, the Hubble Space Telescope changed our understanding of the universe when it began operations using a primary mirror that had a diameter of just 2.4 meters.
How much bigger is the area of Webb’s primary mirror than Hubble’s?
NASA's Universe of Learning materials are based upon work supported by NASA under award number NNX16AC65A to the Space Telescope Science Institute, working in partnership with Caltech/IPAC, Center for Astrophysics | Harvard & Smithsonian, and the Jet Propulsion Laboratory.
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
A solar eclipse occurs when the Moon passes between Earth and the Sun, fully or partially blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. During a total eclipse, the distances are such that the Moon covers all of the Sun's disk area. When the Moon is farther from Earth during an eclipse, it leaves a glowing ring of sunlight shining around the Moon, resulting in an annular eclipse.
On Oct. 14, 2023, a solar eclipse will be visible across North and South America. The Sun, with a radius of 695,700 km, will be 148,523,036 km from Earth. The Moon, with a radius of 1,737 km, will be 388,901 km from Earth.
What percentage of the Sun’s disk area will be obscured by the Moon? Will the eclipse be an annular eclipse or total eclipse?
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
Robotic Arm Challenge
In this challenge, students will create a model robotic arm to move items from one location to another. They will engage in the engineering design process to design, build and operate the arm.
Time 30 min to 1 hour
NASA's Mission to Mars Student Challenge
Take part in the exploration of Mars and bring students along for the ride with NASA's Perseverance rover.
Students learn about the phases of the moon by acting them out.
Time 30 min to 1 hour
Modeling the Earth-Moon System
Students learn about scale models and distance by creating a classroom-size Earth-Moon system.
Time 30 min to 1 hour
Math of the Expanding Universe
Students will learn about the expanding universe and the redshift of lightwaves, then perform their own calculations with a distant supernova.
Time 30 min to 1 hour
The Expanded Universe: Playing with Time Activity Guide
In this activity, participants use balloons to model the expansion of the universe and observe how expansion affects wavelengths of light and distance between galaxies
James Webb Space Telescope STEM Toolkit
Find a collection of resources, activities, videos, and more for your students to learn about NASA’s newest space observatory.
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
How to Make a Pinhole Camera
Learn how to make your very own pinhole camera to safely see a solar eclipse in action!
Collection: Exploring Mars
Make a cardboard rover, design a Mars exploration video game and explore more STEM projects, slideshows and videos 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.
10 Things We Can Learn from Webb's First Images
Take a closer look at how images from NASA's most powerful space telescope yet are helping to answer some of astronomers' most burning questions.
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.
Facts and Figures
- Webb Space Telescope
- Mars Exploration
- Perseverance Mars Rover
- Mars Sample Return
- Psyche Mission
- MIRI Instrument
- 2023 Eclipse