Lesson .

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

Last Updated: Oct. 11, 2024

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

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

Overview

Materials

Background

Procedures

Assessment