Overview

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 compare the area of the Hubble Space Telescope and Webb Telescope’s primary mirror.

Materials

Pi in the Sky 10: Rad Reflection worksheet – download PDF (for best results, download and print from Adobe Reader)

Pi in the Sky 10: Rad Reflection answer key – download PDF (also available as a text-only doc)

Background

Image from animation comparing the relative sizes of James Webb's primary mirror to Hubble's primary mirror. Credit: NASA/Goddard Space Flight Center . | › Full animation

Rad Reflection

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.

• 
  Teachable Moments: 10 Years of NASA's Pi Day Challenge

  Learn more about pi, the history of Pi Day, and the science behind the 2023 NASA Pi Day Challenge.

Procedures

Rad Reflection

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?

› Learn more about the James Webb Space Telescope

Image credit: NASA/JPL-Caltech | + Expand image

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.

Assessment

Image credit: NASA/JPL-Caltech | + Expand image

› Download text-only answer key (Google Docs)

Extensions

Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

• 
  Pi in the Sky Lessons

  Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

  Grades 4-12

  Time Varies

• 
  NASA Pi Day Challenge

  In this challenge, students can use pi to solve some of the same problems faced by NASA scientists and engineers.

  Grades 4-12

  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.

• 
  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.

  Subject Mathematics

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

• 
  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.

  Grades 9-12

  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.

Related Activities for Students

• 
  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.

  Type Slideshow

  Subject Science

Multimedia

• 

  Downloads

  Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

  • Pi in the Sky 10 Poster (PDF, 11.3 MB)
  • Perseverance Mars Rover Background: Phone | Desktop
  • James Webb Space Telescope Background: Phone | Desktop
  • Psyche Mission Background: Phone | Desktop
  • 2023 Eclipse Background: Phone | Desktop
• 
  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 Telescope Key Facts
• MIRI Instrument

Websites

• Webb Space Telescope

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.