Lesson .

Mars Maneuver: A 'Pi in the Sky' Math Challenge

Subject

Math

Grade Levels

6-12

Time Required

Under 30 mins

Illustration (split-screen) of Perseverance landing on Mars in a smaller landing ellipse compared with Curiosity's.

Overview

The "Pi in the Sky" math challenge gives students a chance to find solutions to real-world problems all while using math and pi just like NASA scientists and engineers. In this problem from the seventh installment of the set, students use the mathematical constant pi to compare the size of the landing zones for the Mars rovers Curiosity and Perseverance.

Materials

Pi in the Sky 7: Mars Maneuver worksheet – Download PDF
Pi in the Sky 7: Mars Maneuver answer key – Download PDF (also available as a text-only doc)

Background

Overhead view of Mars with a comparison of the smaller landing ellipse made possible by Range Trigger technology

A new Mars landing technique called Range Trigger is making it possible to reduce the size of the ellipse where spacecraft touch down. › Full image and caption.

Credit: NASA/JPL-Caltech

Long before a Mars rover touches down on the Red Planet, scientists and engineers must determine where to land. Rather than choosing a specific landing spot, NASA selects an area known as a landing ellipse. A Mars rover could land anywhere within this ellipse. Choosing where the landing ellipse is located requires compromising between getting as close as possible to interesting science targets and avoiding hazards like steep slopes and large boulders, which could quickly bring a mission to its end. In the Mars Maneuver problem, students use pi to see how new technologies have reduced the size of landing ellipses from one Mars rover mission to the next.

Procedures

When we plan where to land a spacecraft on Mars, we don’t choose a specific spot, but a larger area called a landing ellipse. It's like choosing a parking lot rather than a parking spot. To choose a landing ellipse, we have to compromise between getting as close as possible to interesting science targets and avoiding hazards. As we've created new technology to help direct spacecraft, landing ellipses have gotten smaller and smaller. That means that we're able to land in places we couldn't before and get closer to the stuff we want to study.

In 2012, the Curiosity rover used its sky crane landing system to touch down in a 20 km by 7 km ellipse. When the Perseverance rover lands on Feb. 18, 2021, it will use the same system along with a new technique called Range Trigger that will allow the spacecraft to land in the smallest ellipse yet, measuring just 13 km by 7 km. What percentage of Curiosity's landing ellipse is Perseverance's landing ellipse?

› Learn more about the Mars rover Perseverance

› Download PDF.

Credit: NASA/JPL-Caltech

Assessment

Illustrated answer key for the Mars Maneuver problem

› Download text-only answer key (doc)

Extensions

Participate

educators.

Pi Day Challenge Lessons

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

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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.

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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.

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

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

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Touchdown

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Related Activities for Students

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Make a Moon or Mars Rover Game

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Build a rubber-band-powered rover that can scramble across a room.

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Mars in a Minute: How Do You Choose a Landing Site?

So, you want to study Mars with a lander or rover – but where exactly do you send it? Learn how scientists and engineers tackle the question of where to land on Mars in this 60-second video.

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Mars in a Minute: How Do You Land on Mars?

Getting a spacecraft to Mars is one thing. Getting it safely to the ground is a whole other challenge! This 60-second video from NASA's Jet Propulsion Laboratory explains three ways to land on the surface of the Red Planet.

Multimedia

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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.

Mars Maneuver: A 'Pi in the Sky' Math Challenge

Overview

Materials

Background

Procedures

Assessment