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
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 10^{23} 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/cm^{3}?
What does that tell us about the makeup of Mars’ core?
Assessment
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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Slideshow: NASA Pi Day Challenge
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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 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

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.