Problem Set
Core Conundrum: A 'Pi in the Sky' Math Challenge
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 ninth set, students use the mathematical constant pi to calculate the volume and density of Mars' liquid core.
Materials
Background
Clouds drift over the dome-covered seismometer, known as SEIS, belonging to NASA's InSight lander, on Mars. Credit: NASA/JPL-Caltech. | › Full image and caption
Core Conundrum
Since 2018, the InSight lander has studied the interior of Mars by measuring vibrations from marsquakes and the “wobble” of the planet as it rotates on its axis. Through careful analysis of the data returned from InSight, scientists were able to measure the size of Mars’ liquid core for the first time and estimate its density. In Core Conundrum, students use pi to do some of the same calculations, determining the volume and density of the Red Planet’s core and comparing it to that of Earth’s core.
Procedures
Core Conundrum
The InSight Mars lander is equipped with several tools to help scientists learn more about the interior of the Red Planet, including a seismometer that detects marsquakes. By measuring the vibrations that travel across the surface of Mars and through its interior layers, scientists were able to accurately measure the size of Mars’ liquid core and estimate its density. Knowing the size and density of Mars' core will help us learn more about how the planet formed, how its magnetic field developed, and what materials make up the core, which will ultimately lead to a better understanding of how Earth and other planets form.
If Mars' core has a mass of 1.54 x 1023 kg and a radius of 1,830 km, as measured by InSight, what is the density of the core?
How does that compare to the density of Earth’s core, which ranges from 10 to 13 g/cm3?
What does that tell us about the makeup of Mars’ core?
› Learn more about the InSight lander
Image credit: NASA/JPL-Caltech | + Expand image
Assessment
Image credit: NASA/JPL-Caltech | + Expand image
Extensions
Participate
Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
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Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 4-12
Time Varies
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Slideshow: NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 4-12
Time Varies
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Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos with NASA.
Blogs and Features
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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.
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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
Related Activities for Students
Multimedia
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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 9 Poster (PDF, 11.2 MB)
- Lunar Flashlight Background: Phone | Desktop
- Mars InSight Lander Background: Phone | Desktop
- SWOT Mission Background: Phone | Desktop
- TESS Mission - Downlink Background: Phone | Desktop
- TESS Mission - Science Background (not pictured): Phone | Desktop
- Medley Background (not pictured): Phone | Desktop
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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.
