Problem Set
Orbit Observation: 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 11th set, students use pi to figure out how much data the NISAR spacecraft collects every day.
Materials
Background
Orbit Observation
The NISAR mission is an Earth orbiting satellite designed to study our planet's changing ecosystems. It will collect data about Earth's land and icecovered surfaces approximately every 6 days, allowing scientists to study changes at the centimeter scale – an unprecedented level of detail. To achieve this feat, NISAR will collect massive amounts of data. In Orbit Observation, students use pi to calculate how much data the NISAR spacecraft captures during each orbit of Earth.
Procedures
Orbit Observation
NISAR is an Earthorbiting satellite mission designed to measure centimeterscale movements and other changes of Earth's land and icecovered surfaces twice every 12 days – a scale of coverage and sampling never before achieved.
Using a technique called Synthetic Aperture Radar, NISAR will produce more than 85 terabytes of data products every day (1 TB = 1,000 gigabytes) that will allow scientists to better monitor and mitigate natural disasters and understand the effects of climate change.
NISAR has an imaging swath of 240 kilometers, but the ground track spacing is 231 km to allow overlap between swaths. Given that the Earth’s radius is 6,371 km, how many orbits are executed in one day? How much data is produced per orbit on average?
Assessment
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 412
Time Varies

NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy collection for students.
Grades 412
Time Varies

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.

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.

10 Ways to Celebrate Pi Day With NASA on March 14
Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.

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.

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